1 00:00:05,886 --> 00:00:07,260 PROFESSOR: So for today's lecture 2 00:00:07,260 --> 00:00:09,310 we have Jason Ku guest lecturing. 3 00:00:09,310 --> 00:00:11,790 And he's the president of OrigaMIT, which you should all 4 00:00:11,790 --> 00:00:16,360 check out Sunday afternoons, origami club at MIT. 5 00:00:16,360 --> 00:00:18,472 He's an origami designer and a grad student 6 00:00:18,472 --> 00:00:19,930 in mechanical engineering, and he's 7 00:00:19,930 --> 00:00:23,170 going to talk about the more artistic perspective on how 8 00:00:23,170 --> 00:00:24,910 origami design works, in particular 9 00:00:24,910 --> 00:00:28,940 in the representational and tree method of origami design world. 10 00:00:28,940 --> 00:00:31,688 So take it away, Jason. 11 00:00:31,688 --> 00:00:32,229 JASON KU: Hi. 12 00:00:32,229 --> 00:00:35,090 I'm Jason. 13 00:00:35,090 --> 00:00:37,590 Eric gave a bit of an introduction. 14 00:00:37,590 --> 00:00:40,390 I've been folding origami instance maybe 15 00:00:40,390 --> 00:00:42,580 I was five years old, and I've been designing 16 00:00:42,580 --> 00:00:47,180 origami for maybe the past 10 years. 17 00:00:47,180 --> 00:00:50,600 I'm a PhD student in mechanical engineering, 18 00:00:50,600 --> 00:00:53,740 working in folding things on the micro and nano scale. 19 00:00:53,740 --> 00:00:58,340 So that's how this is applying to my research. 20 00:00:58,340 --> 00:01:02,460 I'm here to talk a little bit about origami art 21 00:01:02,460 --> 00:01:07,970 and how the concepts we've been talking about in class 22 00:01:07,970 --> 00:01:15,140 apply to origami in actually designing and folding 23 00:01:15,140 --> 00:01:17,620 artwork out of paper. 24 00:01:17,620 --> 00:01:19,170 These are all the websites that I'm 25 00:01:19,170 --> 00:01:22,170 going to be pulling pictures from. 26 00:01:22,170 --> 00:01:25,440 So if we can't use these pictures 27 00:01:25,440 --> 00:01:30,460 in future versions of this lecture, 28 00:01:30,460 --> 00:01:34,830 then you can still see some of the media. 29 00:01:34,830 --> 00:01:40,350 I want first make the analogy of origami art to music. 30 00:01:40,350 --> 00:01:43,230 Many, many people make this analogy, 31 00:01:43,230 --> 00:01:46,570 and it's actually very apt analogy. 32 00:01:46,570 --> 00:01:51,790 In music you have composers, you have 33 00:01:51,790 --> 00:02:01,450 people who produce a work of music, design the structure, 34 00:02:01,450 --> 00:02:05,850 design what the main aspects of the piece 35 00:02:05,850 --> 00:02:08,139 are, in terms of a structural sense, 36 00:02:08,139 --> 00:02:10,720 but aren't necessarily performers themselves. 37 00:02:10,720 --> 00:02:14,380 Now in origami, the performer and the composer 38 00:02:14,380 --> 00:02:15,630 are usually one and the same. 39 00:02:15,630 --> 00:02:21,110 But hopefully in the future, that won't always be the case. 40 00:02:21,110 --> 00:02:25,975 In music the composer usually makes 41 00:02:25,975 --> 00:02:29,780 a piece for multiple instruments or multiple voices or things 42 00:02:29,780 --> 00:02:34,027 like that, so most the time can't do all that performance. 43 00:02:34,027 --> 00:02:36,360 And some people are more gifted in the performance side. 44 00:02:36,360 --> 00:02:39,980 Some people are more gifted in the composition side. 45 00:02:39,980 --> 00:02:44,370 And I think it's a fairly apt analogy. 46 00:02:44,370 --> 00:02:46,560 There's tons of mathematics in music. 47 00:02:46,560 --> 00:02:49,350 There's tons of mathematics in origami. 48 00:02:49,350 --> 00:02:53,890 But there's also this level of artistic complexity, which 49 00:02:53,890 --> 00:02:56,640 we'll see later in this lecture. 50 00:02:56,640 --> 00:02:59,710 I'm going to concentrate mostly on representational origami. 51 00:02:59,710 --> 00:03:03,060 Representational origami is traditionally 52 00:03:03,060 --> 00:03:06,520 representing living things in our world, 53 00:03:06,520 --> 00:03:11,390 but it's pretty much, you see something not necessarily 54 00:03:11,390 --> 00:03:13,210 living, but you see something and you 55 00:03:13,210 --> 00:03:16,580 want to make that form for the form's sake, 56 00:03:16,580 --> 00:03:18,290 to represent that form. 57 00:03:18,290 --> 00:03:21,750 And this is different than, say, patterning 58 00:03:21,750 --> 00:03:27,160 to create artistic patterns on a sheet of paper, 59 00:03:27,160 --> 00:03:30,910 tessellating, making geometric polyhedra, 60 00:03:30,910 --> 00:03:38,060 or making more abstract art that doesn't necessarily 61 00:03:38,060 --> 00:03:41,580 have a relation to a real world object. 62 00:03:41,580 --> 00:03:44,400 So I'm going to start with a little bit about origami art. 63 00:03:44,400 --> 00:03:46,380 We've heard this. 64 00:03:46,380 --> 00:03:52,106 Eric mentioned this particular individual, Akira Yoshizawa. 65 00:03:52,106 --> 00:03:57,810 He is widely understood to be the father of modern origami. 66 00:03:57,810 --> 00:03:59,340 He was born in 1911. 67 00:03:59,340 --> 00:04:02,020 He was around for a very long time. 68 00:04:02,020 --> 00:04:04,580 Unfortunately, passed away in 2005. 69 00:04:04,580 --> 00:04:08,600 I was lucky enough to get to meet Akira Yoshizawa when 70 00:04:08,600 --> 00:04:11,140 he attended a convention in North Carolina 71 00:04:11,140 --> 00:04:15,250 when I was maybe around 10. 72 00:04:15,250 --> 00:04:22,320 He was very powerful and influential 73 00:04:22,320 --> 00:04:26,470 in the world of origami, because he was one of the first people 74 00:04:26,470 --> 00:04:33,130 to start creating new models, be able to look at an object 75 00:04:33,130 --> 00:04:37,890 and create that object just from folding. 76 00:04:37,890 --> 00:04:40,300 He was one of the first people to actually try 77 00:04:40,300 --> 00:04:43,450 to make a large number of new models, 78 00:04:43,450 --> 00:04:47,080 as opposed to the past many centuries 79 00:04:47,080 --> 00:04:53,440 when only a few traditional models were known or pursued. 80 00:04:53,440 --> 00:04:58,110 This is a picture of Yoshizawa right here. 81 00:04:58,110 --> 00:05:01,260 He's fairly happy in this picture. 82 00:05:01,260 --> 00:05:05,800 But he's holding the logo of the US organization 83 00:05:05,800 --> 00:05:09,770 in origami, OrigamiUSA, which is this sailboat. 84 00:05:09,770 --> 00:05:14,470 But as you can see, different than the traditional origami 85 00:05:14,470 --> 00:05:18,790 crane or the frog or things like that, you 86 00:05:18,790 --> 00:05:23,320 see a lot of curves in his work, a lot of shaping. 87 00:05:23,320 --> 00:05:27,410 He uses a technique called wet-folding, in which he 88 00:05:27,410 --> 00:05:29,770 weakens the paper to some degree, 89 00:05:29,770 --> 00:05:33,710 weakens the paper fibers by applying water, shaping 90 00:05:33,710 --> 00:05:38,170 the paper, and letting it dry so that it holds that form. 91 00:05:38,170 --> 00:05:44,130 And you can see in this sparrow-- this is particularly 92 00:05:44,130 --> 00:05:47,280 one of my favorite works by Yoshizawa-- 93 00:05:47,280 --> 00:05:51,870 it really has the essence of this little bird, 94 00:05:51,870 --> 00:05:55,190 but is actually very simple and elegant. 95 00:05:55,190 --> 00:05:57,680 Origami design isn't all about making 96 00:05:57,680 --> 00:05:59,630 the most complex thing in the world. 97 00:05:59,630 --> 00:06:04,750 It's really trying to represent a subject elegantly. 98 00:06:04,750 --> 00:06:08,930 And I think this model does a very good job with that. 99 00:06:08,930 --> 00:06:14,660 But you can see here, very clean surfaces, not a lot 100 00:06:14,660 --> 00:06:17,160 of extra creases that you can see. 101 00:06:17,160 --> 00:06:22,450 Traditionally, wet-folding uses thicker paper 102 00:06:22,450 --> 00:06:23,825 and is slightly more substantial. 103 00:06:27,980 --> 00:06:31,100 So here are some of his other works. 104 00:06:31,100 --> 00:06:34,020 And I want to start out with Yoshizawa 105 00:06:34,020 --> 00:06:39,770 because he was represented as the father and the master, 106 00:06:39,770 --> 00:06:44,470 and many, many of the origami designers, 107 00:06:44,470 --> 00:06:47,080 if not all of the origami designers that I'm 108 00:06:47,080 --> 00:06:49,580 going to continue to talk about were heavily 109 00:06:49,580 --> 00:06:52,630 influenced by Yoshizawa. 110 00:06:52,630 --> 00:06:55,920 So I'm going to first talk about the traditional style. 111 00:06:55,920 --> 00:07:00,690 And I'm going to compare it to, say, the crane or the frog. 112 00:07:00,690 --> 00:07:04,470 These types of models are characterized by straight, 113 00:07:04,470 --> 00:07:09,610 well-defined, polygons in the final form, 114 00:07:09,610 --> 00:07:12,540 typically folded flat. 115 00:07:12,540 --> 00:07:16,500 Little shaping is traditionally needed 116 00:07:16,500 --> 00:07:22,110 to go from the base of the model to the final form. 117 00:07:25,230 --> 00:07:29,040 It's very geometric, these models, 118 00:07:29,040 --> 00:07:33,600 characterized by very straight, precise creases. 119 00:07:33,600 --> 00:07:38,220 So here is, I think, a very good example 120 00:07:38,220 --> 00:07:41,220 of this traditional style. 121 00:07:41,220 --> 00:07:43,200 While there are some curves here, 122 00:07:43,200 --> 00:07:47,440 everything is very well-defined, maybe 123 00:07:47,440 --> 00:07:49,260 just a slight shaping here. 124 00:07:49,260 --> 00:07:52,070 But even that is fairly well-defined. 125 00:07:52,070 --> 00:07:59,820 But you can see Komatsu, Hideo Komatsu, a Japanese folder, 126 00:07:59,820 --> 00:08:06,450 uses really clean, large polygons of open paper 127 00:08:06,450 --> 00:08:09,650 without creases on them to represent polygons 128 00:08:09,650 --> 00:08:11,690 on the model. 129 00:08:11,690 --> 00:08:13,060 The folded form. 130 00:08:13,060 --> 00:08:17,780 His design process isn't really using tree theory. 131 00:08:17,780 --> 00:08:21,460 I mean, all origami design is subjected to the condition 132 00:08:21,460 --> 00:08:27,470 that no two points on the unfolded square 133 00:08:27,470 --> 00:08:31,400 can increase in distance in the folded form. 134 00:08:31,400 --> 00:08:37,039 That's a property called developability of the paper. 135 00:08:37,039 --> 00:08:40,960 The paper's not going to stretch, basically. 136 00:08:40,960 --> 00:08:44,710 So all origami design is subject to that condition, 137 00:08:44,710 --> 00:08:47,800 but you don't have to deal with necessarily these things called 138 00:08:47,800 --> 00:08:49,050 uniaxial bases. 139 00:08:49,050 --> 00:08:53,550 Pretty much all of these models are non-uniaxial. 140 00:08:53,550 --> 00:08:56,510 His design process is kind of a trial and error 141 00:08:56,510 --> 00:09:03,760 process of folding along different 22.5 degree grids. 142 00:09:03,760 --> 00:09:12,800 22.5 degrees is, I guess, 1/8 of pi. 143 00:09:12,800 --> 00:09:16,580 1/16 of 360 degrees. 144 00:09:16,580 --> 00:09:22,160 And it's a particularly nice and useful discretization 145 00:09:22,160 --> 00:09:25,900 of angles in origami design. 146 00:09:25,900 --> 00:09:30,280 All the traditional bases are based on this 22.5 degree grid 147 00:09:30,280 --> 00:09:31,770 system. 148 00:09:31,770 --> 00:09:33,550 And there's a certain elegance of that. 149 00:09:33,550 --> 00:09:37,030 Actually I think, the mouse is based on a 30 degree grid 150 00:09:37,030 --> 00:09:42,400 system, but is kind of an exception, 151 00:09:42,400 --> 00:09:44,310 but follows the same principles. 152 00:09:44,310 --> 00:09:49,160 He keeps folding a piece of paper 153 00:09:49,160 --> 00:09:54,800 and tries to get these geometric shapes that really 154 00:09:54,800 --> 00:09:58,580 are able to by themselves capture the model. 155 00:09:58,580 --> 00:10:04,710 And I'm going to use some of that design technique 156 00:10:04,710 --> 00:10:07,690 later in a design example. 157 00:10:07,690 --> 00:10:09,620 He has a small but very distinguished 158 00:10:09,620 --> 00:10:18,370 repertoire because his process is less algorithmic-- I mean, 159 00:10:18,370 --> 00:10:25,100 he has algorithms, I'm sure, that are difficult to describe, 160 00:10:25,100 --> 00:10:29,520 but his process is actually very artistic. 161 00:10:29,520 --> 00:10:31,840 And while it's very exact, I think 162 00:10:31,840 --> 00:10:38,530 it's one of the most elegant examples of origami design. 163 00:10:38,530 --> 00:10:41,930 Here's another example of the traditional style. 164 00:10:41,930 --> 00:10:46,290 As you can see, there's slightly more curves and things in it, 165 00:10:46,290 --> 00:10:51,640 but it's fairly well characterized 166 00:10:51,640 --> 00:10:55,920 by these straight creases. 167 00:10:55,920 --> 00:11:00,570 Heavier paper for wet-folding. 168 00:11:00,570 --> 00:11:03,370 This model on the left here is box pleated. 169 00:11:03,370 --> 00:11:08,560 So as opposed to the 22.5 degrees structure, 170 00:11:08,560 --> 00:11:12,390 box pleating is characterized by only multiples of 45 degrees. 171 00:11:12,390 --> 00:11:15,160 So pi over 4. 172 00:11:19,070 --> 00:11:24,700 And so you see the grid here, this model 173 00:11:24,700 --> 00:11:27,860 is based on a fairly large grid, so you 174 00:11:27,860 --> 00:11:29,510 can get the detail that it needs. 175 00:11:32,020 --> 00:11:35,230 These are not uniaxial bases, again, 176 00:11:35,230 --> 00:11:38,080 but they're still limited by this stretch ability 177 00:11:38,080 --> 00:11:40,830 constraint. 178 00:11:40,830 --> 00:11:45,620 And those were styles that stemmed 179 00:11:45,620 --> 00:11:50,290 from the traditional crisp folding of say 180 00:11:50,290 --> 00:11:54,160 the crane and the crab and the frog and all 181 00:11:54,160 --> 00:11:55,640 these traditional designs. 182 00:11:55,640 --> 00:11:58,360 The non-traditional style is more 183 00:11:58,360 --> 00:12:03,224 an extension of Yoshizawa's work and shaping and curved folding 184 00:12:03,224 --> 00:12:04,390 and things like wet-folding. 185 00:12:08,100 --> 00:12:10,520 There is much shape that needs to be 186 00:12:10,520 --> 00:12:13,970 done to create the essence of the model. 187 00:12:17,690 --> 00:12:23,140 The model is encapsulated by not necessarily the structure 188 00:12:23,140 --> 00:12:28,600 as much, but of the final shaping, the undefined shaping 189 00:12:28,600 --> 00:12:31,290 that you kind of put into the model. 190 00:12:31,290 --> 00:12:35,160 Here's an example of an English folder 191 00:12:35,160 --> 00:12:38,230 named David Brill, who is an investment banker, 192 00:12:38,230 --> 00:12:40,700 if my memory serves me. 193 00:12:40,700 --> 00:12:43,070 He now lives on a golf course. 194 00:12:43,070 --> 00:12:48,850 And I think he's retired now, but he likes to fold paper. 195 00:12:48,850 --> 00:12:54,360 But you can see here, a good example 196 00:12:54,360 --> 00:12:57,710 of this style, thick paper. 197 00:13:03,530 --> 00:13:06,160 The character of the model is really 198 00:13:06,160 --> 00:13:12,260 defined by these curved tension folds, which 199 00:13:12,260 --> 00:13:17,770 is slightly different than at least the traditional style. 200 00:13:17,770 --> 00:13:22,850 And oftentimes, it's very, very difficult 201 00:13:22,850 --> 00:13:27,340 to replicate to any of these types of models, 202 00:13:27,340 --> 00:13:33,790 because it has so much to do with subjectivity as opposed 203 00:13:33,790 --> 00:13:37,360 to objectivity, as in the traditional style. 204 00:13:37,360 --> 00:13:40,090 Here's another good example, Michael LaFosse. 205 00:13:40,090 --> 00:13:47,510 He's a paper folder who actually resides here in Massachusetts. 206 00:13:47,510 --> 00:13:50,300 He's in Haverhill, "Have-er-ill," 207 00:13:50,300 --> 00:13:52,900 something like that, Massachusetts. 208 00:13:52,900 --> 00:13:57,310 He is unique in origami designers in the fact 209 00:13:57,310 --> 00:14:01,940 that he is also an avid paper maker. 210 00:14:01,940 --> 00:14:04,980 So he actually makes a lot of the media which he folds. 211 00:14:04,980 --> 00:14:08,090 And that gives this intimate relationship 212 00:14:08,090 --> 00:14:10,480 between the life cycle of the paper. 213 00:14:15,780 --> 00:14:20,330 He's able to make specialty paper that's 214 00:14:20,330 --> 00:14:23,230 really necessary to make some of the most complex works 215 00:14:23,230 --> 00:14:23,790 out there. 216 00:14:27,900 --> 00:14:29,530 He's gone to culinary school. 217 00:14:29,530 --> 00:14:31,510 He was a chef for a while. 218 00:14:31,510 --> 00:14:35,710 And he was also a marine biologist for a while. 219 00:14:35,710 --> 00:14:38,970 So these origami artists have come 220 00:14:38,970 --> 00:14:43,300 from many different walks of life. 221 00:14:43,300 --> 00:14:49,790 This next folder, Eric Joisel, he's a Frenchman, 222 00:14:49,790 --> 00:14:50,640 lives in Paris. 223 00:14:50,640 --> 00:14:52,780 He was a former clay sculptor. 224 00:14:52,780 --> 00:14:56,500 And actually, I think you can really see that in his work, 225 00:14:56,500 --> 00:15:05,470 the kind of solidness and really cohesiveness 226 00:15:05,470 --> 00:15:08,140 of his composition. 227 00:15:08,140 --> 00:15:14,490 All the detail and texturing are very well 228 00:15:14,490 --> 00:15:18,247 thought out in terms of the subject as a complete piece. 229 00:15:18,247 --> 00:15:19,580 Heavily influenced by Yoshizawa. 230 00:15:22,831 --> 00:15:27,600 A lot of this use of texture, incorporating texture 231 00:15:27,600 --> 00:15:33,270 into his models, he was a big pioneer in that area. 232 00:15:35,860 --> 00:15:40,070 This texturing is fairly obviously non-uniaxial. 233 00:15:40,070 --> 00:15:42,640 He doesn't go through a tree method 234 00:15:42,640 --> 00:15:45,170 and represent each one of these points 235 00:15:45,170 --> 00:15:46,680 as a stick in a stick figure. 236 00:15:49,640 --> 00:15:52,950 These flaps don't lie along an axis. 237 00:15:52,950 --> 00:15:55,880 They don't hinge perpendicular to that axis. 238 00:15:55,880 --> 00:16:02,590 Yet he's able to create these amazing forms in paper. 239 00:16:02,590 --> 00:16:04,940 He has stopped doing clay sculpture 240 00:16:04,940 --> 00:16:08,080 and does origami full time now. 241 00:16:08,080 --> 00:16:13,530 He's very well known for his depiction of the human form. 242 00:16:13,530 --> 00:16:17,690 This is taken from a collection of masks. 243 00:16:17,690 --> 00:16:19,980 He's done numerous, numerous masks 244 00:16:19,980 --> 00:16:22,100 that are really very expressive. 245 00:16:22,100 --> 00:16:26,840 He was one of the first people to really, for me at least, 246 00:16:26,840 --> 00:16:35,490 evoke emotion and convey emotion in his work. 247 00:16:35,490 --> 00:16:40,580 But you can see here, the structural crease pattern 248 00:16:40,580 --> 00:16:44,340 for this face is actually very, very simple. 249 00:16:44,340 --> 00:16:47,420 It's kind of represented by a few pleats. 250 00:16:47,420 --> 00:16:52,620 But the amount of work used to transform that very simple form 251 00:16:52,620 --> 00:16:57,790 into this very expressive, curved work of art 252 00:16:57,790 --> 00:16:59,200 is kind of astonishing. 253 00:17:02,130 --> 00:17:06,210 Here's a more recent work of the entire human form. 254 00:17:06,210 --> 00:17:16,130 You see how this is starting to come as some sort of blend 255 00:17:16,130 --> 00:17:19,369 between the traditional and nontraditional forms. 256 00:17:19,369 --> 00:17:22,109 It lies somewhere along the spectrum. 257 00:17:22,109 --> 00:17:24,920 But it's a very complex model, so it 258 00:17:24,920 --> 00:17:29,240 had needs to have this structural complexity. 259 00:17:29,240 --> 00:17:32,840 But at the same time, he shapes it to an extent 260 00:17:32,840 --> 00:17:34,960 that very few people can do. 261 00:17:40,100 --> 00:17:43,170 I'm paraphrasing a quote of his, but he's 262 00:17:43,170 --> 00:17:47,550 of the opinion that if you can reproduce 263 00:17:47,550 --> 00:17:52,560 exactly a piece of origami then it's not really art, 264 00:17:52,560 --> 00:17:58,190 because you're not putting anything more into the model, 265 00:17:58,190 --> 00:18:01,050 if it doesn't have something unique and original 266 00:18:01,050 --> 00:18:06,330 and something that can't be reproduced in the model. 267 00:18:06,330 --> 00:18:12,290 Here's two fantastic subjects in terms of art, to me. 268 00:18:12,290 --> 00:18:18,370 Very Escher-like and it's self-referencing. 269 00:18:18,370 --> 00:18:21,420 This is called the Self-made Man. 270 00:18:21,420 --> 00:18:23,960 And I forget the title of this work, 271 00:18:23,960 --> 00:18:27,050 but he's basically emerging from the paper. 272 00:18:27,050 --> 00:18:31,240 You see that his arm and leg are not actually finished. 273 00:18:31,240 --> 00:18:32,910 I think this is called Birth, actually. 274 00:18:35,680 --> 00:18:41,640 But really, using paper to express an artistic idea, 275 00:18:41,640 --> 00:18:45,720 very few people get to that stage of competency 276 00:18:45,720 --> 00:18:50,770 with the technical and being able to infuse 277 00:18:50,770 --> 00:18:52,250 that emotion into the subject. 278 00:18:52,250 --> 00:18:59,070 So Eric Joisel is a pioneer in that realm of origami art. 279 00:18:59,070 --> 00:19:03,890 Here are three very, very complex-- 280 00:19:03,890 --> 00:19:05,740 These are very recent works, probably 281 00:19:05,740 --> 00:19:08,840 within the last year or two. 282 00:19:08,840 --> 00:19:15,200 Lots of use of texturing to make the armor here. 283 00:19:15,200 --> 00:19:17,590 Lots of planning, tree theory included. 284 00:19:17,590 --> 00:19:19,310 These are mostly box pleated models, 285 00:19:19,310 --> 00:19:22,510 but you can't really tell from here because 286 00:19:22,510 --> 00:19:29,760 of his impeccable ability to shape a model. 287 00:19:29,760 --> 00:19:33,500 I'm going to remind you guys that everything 288 00:19:33,500 --> 00:19:36,230 I'm showing to you is a representational work. 289 00:19:36,230 --> 00:19:39,250 Each one of these is made from a single uncut square. 290 00:19:42,140 --> 00:19:44,380 Pretty much, I believe everything 291 00:19:44,380 --> 00:19:47,507 I'm going to show you today has that property. 292 00:19:47,507 --> 00:19:49,992 AUDIENCE: When people fold these, do they fold them 293 00:19:49,992 --> 00:19:51,980 by hand or do they need special tools? 294 00:19:51,980 --> 00:19:54,465 To me, this looks like it would be completely 295 00:19:54,465 --> 00:19:55,956 impossible to just fold it by hand. 296 00:20:01,321 --> 00:20:03,320 JASON KU: These are actually fairly large works. 297 00:20:03,320 --> 00:20:06,550 Each one stands maybe about that tall. 298 00:20:06,550 --> 00:20:09,620 So the paper's very large to begin. 299 00:20:09,620 --> 00:20:12,140 But yeah, I believe he just uses his hands 300 00:20:12,140 --> 00:20:14,290 and this wet-folding technique to allow 301 00:20:14,290 --> 00:20:16,090 things to be held in place. 302 00:20:16,090 --> 00:20:21,140 I mean, many people, including Eric Joisel, use clips 303 00:20:21,140 --> 00:20:24,090 and braces and things like that to hold certain things in place 304 00:20:24,090 --> 00:20:26,990 while he's working on other areas of the model, 305 00:20:26,990 --> 00:20:28,310 but it's pretty much by hand. 306 00:20:28,310 --> 00:20:31,340 Some people use tweezers or things like that. 307 00:20:31,340 --> 00:20:33,070 But most of it is by hand. 308 00:20:33,070 --> 00:20:36,430 AUDIENCE: Does he add color or shade or those things? 309 00:20:36,430 --> 00:20:38,250 JASON KU: Sometimes. 310 00:20:38,250 --> 00:20:42,160 For example, that mask I think was speckled with paint 311 00:20:42,160 --> 00:20:46,090 after, before or after. 312 00:20:48,890 --> 00:20:55,140 There are different opinions on this idea of origami purity. 313 00:20:57,850 --> 00:21:00,490 I like Robert Lang's definition of origami, 314 00:21:00,490 --> 00:21:11,040 that it's any work whose primary structure 315 00:21:11,040 --> 00:21:13,550 is defined by folding. 316 00:21:13,550 --> 00:21:17,540 And that's a very broad definition of origami. 317 00:21:17,540 --> 00:21:19,820 But I think it works really well. 318 00:21:19,820 --> 00:21:26,400 So if the subject matter is still heavily characterized 319 00:21:26,400 --> 00:21:29,820 by the folding and not some other thing 320 00:21:29,820 --> 00:21:32,100 that you do to the model, I think 321 00:21:32,100 --> 00:21:34,400 most people are OK with that, as long as you're not 322 00:21:34,400 --> 00:21:37,650 trying to pass it off as something it's not. 323 00:21:40,360 --> 00:21:44,450 There are many origami designers to do multi-sheet things 324 00:21:44,450 --> 00:21:52,010 and do very complex works and very beautiful pieces of art. 325 00:21:52,010 --> 00:21:55,750 I think Joseph Wu is a great example of this, 326 00:21:55,750 --> 00:21:58,520 who I don't have pictures of his work. 327 00:21:58,520 --> 00:22:03,270 But he doesn't try to pass them off a single sheet origami. 328 00:22:03,270 --> 00:22:04,680 He is a very skilled designer. 329 00:22:04,680 --> 00:22:06,380 He could do it with a single sheet, 330 00:22:06,380 --> 00:22:08,380 but he finds that the solution is more elegant 331 00:22:08,380 --> 00:22:10,797 using multiple sheets. 332 00:22:10,797 --> 00:22:11,630 Any other questions? 333 00:22:14,270 --> 00:22:18,420 Just one more picture of some of Joisel's work. 334 00:22:18,420 --> 00:22:24,110 He actually made an entire orchestra of these little guys. 335 00:22:24,110 --> 00:22:25,130 This is two sheets. 336 00:22:25,130 --> 00:22:27,300 The saxophone is a different sheet. 337 00:22:27,300 --> 00:22:31,255 But again, he's not trying to pass them off 338 00:22:31,255 --> 00:22:40,440 as being the same sheet here, whereas in here, the weapons 339 00:22:40,440 --> 00:22:45,750 actually are from the same sheet of paper. 340 00:22:45,750 --> 00:22:49,870 And these multi-subject pieces, each one of these, it's 341 00:22:49,870 --> 00:22:51,730 not all three of them together as one sheet. 342 00:22:51,730 --> 00:22:54,740 Just to clarify. 343 00:22:54,740 --> 00:22:58,880 But these multi-subject, trying to represents 344 00:22:58,880 --> 00:23:01,910 clothes, and weapons, and the human, 345 00:23:01,910 --> 00:23:05,700 and all these types of things, is becoming more and more a way 346 00:23:05,700 --> 00:23:08,890 to a push the limits of origami design. 347 00:23:08,890 --> 00:23:13,500 So again, trying to breathe life into the paper is really what 348 00:23:13,500 --> 00:23:18,830 Yoshizawa's mantra was, and so is Eric Joisel's. 349 00:23:18,830 --> 00:23:19,330 All right. 350 00:23:19,330 --> 00:23:27,780 So I'm going to move on to this independent concept of really 351 00:23:27,780 --> 00:23:30,990 the ability that we have right now 352 00:23:30,990 --> 00:23:35,550 to pretty much-- We have the algorithms to make anything 353 00:23:35,550 --> 00:23:38,830 we want and really trying to capture 354 00:23:38,830 --> 00:23:43,575 that is this idea that I call this modern realism. 355 00:23:47,460 --> 00:23:54,790 The style, like Eric Joisel's work, 356 00:23:54,790 --> 00:23:56,700 kind of follow along the spectrum 357 00:23:56,700 --> 00:24:03,620 of this rigid structure and this free-form shaping, 358 00:24:03,620 --> 00:24:09,590 but really try to capture this realism of the subject. 359 00:24:09,590 --> 00:24:14,040 So I think Robert Lang is one of the foremost origami 360 00:24:14,040 --> 00:24:15,690 designers in this kind of area. 361 00:24:15,690 --> 00:24:21,000 He's a guy from California who is 362 00:24:21,000 --> 00:24:23,050 a pioneer of algorithmic origami design. 363 00:24:23,050 --> 00:24:25,540 You've heard his name a number of times. 364 00:24:29,100 --> 00:24:33,600 He has kind of codified tree theory, 365 00:24:33,600 --> 00:24:37,040 if not one of the pioneers of establishing 366 00:24:37,040 --> 00:24:38,950 that research himself. 367 00:24:38,950 --> 00:24:42,530 He wrote the program TreeMaker that you guys are all probably 368 00:24:42,530 --> 00:24:45,130 using to do your homework. 369 00:24:45,130 --> 00:24:52,520 He was at Caltech Ph.D., and was a laser physicist for NASA. 370 00:24:52,520 --> 00:24:57,050 And he decided maybe less than 10 years ago 371 00:24:57,050 --> 00:25:00,740 to quit and do origami full time. 372 00:25:00,740 --> 00:25:01,900 So that's what he does now. 373 00:25:04,430 --> 00:25:06,280 So here's a number of his works. 374 00:25:06,280 --> 00:25:10,520 Very complex, very exact. 375 00:25:10,520 --> 00:25:16,720 For example, he was a huge pioneer 376 00:25:16,720 --> 00:25:18,980 of what we call the Bug Wars. 377 00:25:18,980 --> 00:25:23,490 When we had these tools at our disposal 378 00:25:23,490 --> 00:25:28,340 to make very complex trees, we can 379 00:25:28,340 --> 00:25:31,080 represent very, very complex subjects. 380 00:25:31,080 --> 00:25:33,900 And that led to this Bug Wars of trying to one-up 381 00:25:33,900 --> 00:25:39,370 each other on how many legs you could make or things like that. 382 00:25:39,370 --> 00:25:41,630 So here's a centipede, for example, 383 00:25:41,630 --> 00:25:44,610 with lots and lots of legs. 384 00:25:44,610 --> 00:25:49,550 And the exactness to which we can specify the tree 385 00:25:49,550 --> 00:25:50,550 is phenomenal. 386 00:25:50,550 --> 00:25:55,680 For example, the scorpion here is a design 387 00:25:55,680 --> 00:25:59,450 that Robert Lang has approached-- 388 00:25:59,450 --> 00:26:02,540 a subject he's approached-- many, many, many times. 389 00:26:02,540 --> 00:26:05,910 This is a design that I particularly like. 390 00:26:05,910 --> 00:26:12,330 It's very clean in its folded and its structural forms. 391 00:26:12,330 --> 00:26:16,450 But he actually used TreeMaker and designed 392 00:26:16,450 --> 00:26:19,080 each of these pairs of legs to actually 393 00:26:19,080 --> 00:26:23,350 be increasing in length as they go back. 394 00:26:23,350 --> 00:26:27,870 So really being very exact with the proportions 395 00:26:27,870 --> 00:26:30,790 of the model, the proportions in the tree. 396 00:26:30,790 --> 00:26:32,730 And tree theory really allows you 397 00:26:32,730 --> 00:26:34,280 to do that, to capture that. 398 00:26:34,280 --> 00:26:36,520 Here's a slide for the mathematicians in here. 399 00:26:36,520 --> 00:26:38,600 This is not one square sheet of paper. 400 00:26:38,600 --> 00:26:42,070 This is probably the only model here that isn't. 401 00:26:42,070 --> 00:26:53,190 But it's what we call modular origami, making a single unit 402 00:26:53,190 --> 00:26:56,870 and sticking them all together in a very complex and elegant 403 00:26:56,870 --> 00:26:57,380 way. 404 00:26:57,380 --> 00:27:00,650 Here's a representation of some of the tessellation work 405 00:27:00,650 --> 00:27:03,900 that Robert Lang has been working on. 406 00:27:08,450 --> 00:27:12,800 This is a vase form. 407 00:27:12,800 --> 00:27:16,210 And all these, or at least these three, 408 00:27:16,210 --> 00:27:20,880 were very much characterized by using mathematics 409 00:27:20,880 --> 00:27:23,070 to find these forms. 410 00:27:23,070 --> 00:27:26,200 And while they're very heavily rooted in mathematics. 411 00:27:26,200 --> 00:27:29,380 Mathematics, as I'm sure all of us can appreciate, 412 00:27:29,380 --> 00:27:32,840 is an elegant subject in and of itself. 413 00:27:32,840 --> 00:27:34,920 There are elegant solutions to problems. 414 00:27:34,920 --> 00:27:38,090 And in origami it's particularly nice, 415 00:27:38,090 --> 00:27:41,400 because these elegant solutions often 416 00:27:41,400 --> 00:27:44,840 are very elegant and pleasing to the eye, as well. 417 00:27:44,840 --> 00:27:47,630 So this is also a Klein bottle. 418 00:27:47,630 --> 00:27:49,690 It's kind of a joke. 419 00:27:49,690 --> 00:27:53,610 But it topologically does intersect and things like that. 420 00:27:53,610 --> 00:27:57,500 So in an interesting work. 421 00:27:57,500 --> 00:28:01,310 I want to move on to a guy named Brian Chan, who 422 00:28:01,310 --> 00:28:03,270 is an alumni of MIT. 423 00:28:03,270 --> 00:28:08,560 He got his bachelor's, his master's, and his Ph.D. at MIT. 424 00:28:08,560 --> 00:28:13,420 He defended his Ph.D. in 2009, but he's still 425 00:28:13,420 --> 00:28:15,510 around Cambridge. 426 00:28:15,510 --> 00:28:22,230 He is a big pioneer of pushing the limits of complex folding. 427 00:28:22,230 --> 00:28:26,610 He's picked up origami design very quickly. 428 00:28:26,610 --> 00:28:29,040 And so it is possible to do. 429 00:28:29,040 --> 00:28:31,270 So I encourage all of you to try it. 430 00:28:31,270 --> 00:28:36,410 Here is an example of a very, very complex centipede that he 431 00:28:36,410 --> 00:28:39,885 designed kind of in response to Robert Lang's. 432 00:28:42,960 --> 00:28:53,640 There's a huge history of really trying 433 00:28:53,640 --> 00:28:55,760 to one-up each other in origami. 434 00:28:55,760 --> 00:29:00,090 And it really helps spur the creativity. 435 00:29:00,090 --> 00:29:05,970 And playful competition is very useful to any subject. 436 00:29:05,970 --> 00:29:08,700 These multi-subject things, like this 437 00:29:08,700 --> 00:29:13,510 rose, the stem and the petals itself, 438 00:29:13,510 --> 00:29:15,610 all from one square sheet of paper. 439 00:29:15,610 --> 00:29:17,390 He uses color change. 440 00:29:17,390 --> 00:29:20,050 One side of the paper is red; one side of the paper is green. 441 00:29:24,756 --> 00:29:26,880 There have been tons of people that design just the 442 00:29:26,880 --> 00:29:31,110 rose part of the rose, and then they make an additional stem 443 00:29:31,110 --> 00:29:32,360 and stick it on. 444 00:29:32,360 --> 00:29:35,280 This is the first one-piece model of that. 445 00:29:35,280 --> 00:29:39,140 And was somewhat influential in that respect. 446 00:29:39,140 --> 00:29:44,200 Here's a very complex, textured character 447 00:29:44,200 --> 00:29:45,790 from an anime TV show. 448 00:29:45,790 --> 00:29:47,120 I forget which one it's called. 449 00:29:47,120 --> 00:29:48,100 AUDIENCE: Rozen Maiden. 450 00:29:48,100 --> 00:29:49,750 JASON KU: Rozen Maiden Thank you. 451 00:29:49,750 --> 00:29:50,740 That is correct. 452 00:29:50,740 --> 00:29:54,410 But you really can see his use of color change here. 453 00:29:54,410 --> 00:30:02,980 Again, being able to make this cross in the fabric here. 454 00:30:02,980 --> 00:30:10,450 The zigzags of lace, and this texturing of the dress, 455 00:30:10,450 --> 00:30:15,560 very, very complex, in its form. 456 00:30:15,560 --> 00:30:19,850 But these are all actually uniaxial bases, 457 00:30:19,850 --> 00:30:22,830 all come from this idea of tree theory, 458 00:30:22,830 --> 00:30:26,520 being able to map things on your subject 459 00:30:26,520 --> 00:30:29,330 to the sheet of paper in an algorithmic way. 460 00:30:29,330 --> 00:30:36,400 Here's a very complex, another anime work, a Neko Bus. 461 00:30:36,400 --> 00:30:39,480 Neko is, I believe, Japanese for cat. 462 00:30:39,480 --> 00:30:41,970 And it's very, very complex. 463 00:30:41,970 --> 00:30:44,000 Again, similar to the centipede. 464 00:30:44,000 --> 00:30:45,930 Lots and lots of points. 465 00:30:45,930 --> 00:30:48,780 But this tree is actually kind of represented 466 00:30:48,780 --> 00:30:51,260 by-- There's a head region and there's 467 00:30:51,260 --> 00:30:55,630 many points sticking out on both sides. 468 00:30:55,630 --> 00:30:59,530 And then this flap kind of comes over and attaches up here, 469 00:30:59,530 --> 00:31:02,640 and you've got the tail. 470 00:31:02,640 --> 00:31:07,670 Here's another example of a multi-subject model. 471 00:31:07,670 --> 00:31:09,530 Every year there's a design challenge 472 00:31:09,530 --> 00:31:11,610 in New York for origami. 473 00:31:11,610 --> 00:31:15,200 And this was the sailing ship category. 474 00:31:15,200 --> 00:31:17,740 And he kind of went another direction with it. 475 00:31:17,740 --> 00:31:19,310 He did make a sailing ship, but this 476 00:31:19,310 --> 00:31:24,540 is a kraken attacking the ship. 477 00:31:24,540 --> 00:31:27,160 He's got a little person in one of his tentacles. 478 00:31:27,160 --> 00:31:29,700 Part of the ship and the ship itself, 479 00:31:29,700 --> 00:31:33,950 and it's all one square sheet of paper without cutting. 480 00:31:33,950 --> 00:31:39,390 And if that wasn't enough, then the MIT seal, as well. 481 00:31:39,390 --> 00:31:41,140 One square sheet of paper without cutting. 482 00:31:41,140 --> 00:31:46,960 The mens and manus, so the mind and hand. 483 00:31:46,960 --> 00:31:53,830 And I believe this isn't traditionally a crane, 484 00:31:53,830 --> 00:31:55,070 but yeah. 485 00:31:55,070 --> 00:31:57,520 The last person I want to touch on 486 00:31:57,520 --> 00:32:00,720 is a guy named Satoshi Kamiya, who's 487 00:32:00,720 --> 00:32:07,390 represented as probably the foremost pioneer 488 00:32:07,390 --> 00:32:09,130 of super-complex origami. 489 00:32:09,130 --> 00:32:11,620 He is a little further on the spectrum 490 00:32:11,620 --> 00:32:14,810 on the traditional style than many 491 00:32:14,810 --> 00:32:19,090 of these other super-complex folders, 492 00:32:19,090 --> 00:32:23,990 characterized by kind of very exact, straight creases, 493 00:32:23,990 --> 00:32:30,670 this texturing for example, a unique balance between making 494 00:32:30,670 --> 00:32:37,040 a very cleanly folded-- The Japanese traditionally 495 00:32:37,040 --> 00:32:42,080 make very clean subjects in terms of exactness and form. 496 00:32:42,080 --> 00:32:44,800 Here's a little more shaping in the wet-folding. 497 00:32:44,800 --> 00:32:48,460 But again, this is one of my favorite works 498 00:32:48,460 --> 00:32:51,700 of his, another Lord of the Rings character. 499 00:32:54,860 --> 00:32:57,910 What's neat about this sea turtle actually, 500 00:32:57,910 --> 00:33:01,310 the diagrams for it were just published. 501 00:33:01,310 --> 00:33:06,950 I first all this work in 2001 or something like that. 502 00:33:06,950 --> 00:33:11,080 But it has these plates on the back, this texture, 503 00:33:11,080 --> 00:33:14,110 but it also has plates on the front of the model. 504 00:33:14,110 --> 00:33:15,970 So you can actually pick it up, and it 505 00:33:15,970 --> 00:33:20,220 looks very, very convincing. 506 00:33:20,220 --> 00:33:22,280 Here are some more models by him. 507 00:33:22,280 --> 00:33:25,200 Again, you can see a lot of this texturing here 508 00:33:25,200 --> 00:33:30,300 in this wasp, very clean folding. 509 00:33:30,300 --> 00:33:34,930 A dog, multi-headed dog, a caribou 510 00:33:34,930 --> 00:33:39,320 with very complicated antler patterns, and this dragon. 511 00:33:39,320 --> 00:33:43,000 And again, you see the crisp, clean folding, 512 00:33:43,000 --> 00:33:46,800 but at the same time very well-planned and well-designed 513 00:33:46,800 --> 00:33:50,330 3D structure to be shaped afterwards. 514 00:33:50,330 --> 00:33:52,890 Here's another work that I particularly enjoy. 515 00:33:55,960 --> 00:34:02,430 Really lending this texturing he applies throughout the model, 516 00:34:02,430 --> 00:34:06,730 and it's a very cohesive subject, 517 00:34:06,730 --> 00:34:07,870 from an artistic sense. 518 00:34:07,870 --> 00:34:10,800 It's very complete. 519 00:34:10,800 --> 00:34:12,840 There's the same level of detail everywhere 520 00:34:12,840 --> 00:34:15,860 on the model, which is very useful. 521 00:34:15,860 --> 00:34:18,300 And I'm going to kind of end this artistic side 522 00:34:18,300 --> 00:34:22,170 with a model which is widely regarded 523 00:34:22,170 --> 00:34:26,870 as the most complex single work in origami. 524 00:34:26,870 --> 00:34:31,580 This took Kamiya over the course of a year to fold. 525 00:34:31,580 --> 00:34:34,010 There's thousands of scales on this guy. 526 00:34:34,010 --> 00:34:37,260 And again, it's one square sheet of paper without cutting. 527 00:34:37,260 --> 00:34:41,701 You see that it's a very long model. 528 00:34:41,701 --> 00:34:43,159 You'd think that this subject would 529 00:34:43,159 --> 00:34:46,139 be much better represented by a long rectangle 530 00:34:46,139 --> 00:34:47,550 or something like that. 531 00:34:47,550 --> 00:34:50,750 But actually it's very symmetric. 532 00:34:50,750 --> 00:34:55,889 This crease pattern, which we'll look at later, 533 00:34:55,889 --> 00:34:58,800 actually has an asymmetric crease pattern 534 00:34:58,800 --> 00:35:03,020 and is quite ingenious in how he decides 535 00:35:03,020 --> 00:35:06,820 to accomplish this form and structure. 536 00:35:06,820 --> 00:35:10,220 If you're interested in learning more about the origami art 537 00:35:10,220 --> 00:35:15,160 side of things, there's this phenomenal document documentary 538 00:35:15,160 --> 00:35:18,350 which you can and purchase online. 539 00:35:18,350 --> 00:35:23,020 Or I've believe OrigaMIT has a copy of this, 540 00:35:23,020 --> 00:35:26,320 and we'll probably be screening it some time 541 00:35:26,320 --> 00:35:27,930 this semester or next. 542 00:35:27,930 --> 00:35:31,100 It's called Between the Folds. 543 00:35:31,100 --> 00:35:38,160 And it features, among others, both Erik and Marty Demaine, 544 00:35:38,160 --> 00:35:40,520 Robert Lang, and many more. 545 00:35:40,520 --> 00:35:44,860 And there's a picture of Stata from the film. 546 00:35:44,860 --> 00:35:48,705 Now we're going to move on a little bit to origami design. 547 00:35:52,960 --> 00:35:55,140 We've learned what the algorithms are 548 00:35:55,140 --> 00:35:59,030 behind a lot of origami design, but now we're 549 00:35:59,030 --> 00:36:04,660 going to see how that applies more directly to creating 550 00:36:04,660 --> 00:36:06,210 a representational work of art. 551 00:36:06,210 --> 00:36:08,720 If you're really serious about wanting 552 00:36:08,720 --> 00:36:13,340 to get into origami design, this book, Origami Design Secrets 553 00:36:13,340 --> 00:36:16,040 by Robert Lang, is really the first major book 554 00:36:16,040 --> 00:36:19,370 on the methods of origami design. 555 00:36:19,370 --> 00:36:23,560 Most origami books are traditionally about diagrams, 556 00:36:23,560 --> 00:36:25,550 trying to fold specific models. 557 00:36:25,550 --> 00:36:27,880 This is the first book really to lay out 558 00:36:27,880 --> 00:36:30,640 some of the ground rules of how you create models. 559 00:36:30,640 --> 00:36:34,570 And it goes through a number of the things we've talked about. 560 00:36:34,570 --> 00:36:40,050 So just to review a little bit about tree theory, the idea, 561 00:36:40,050 --> 00:36:45,150 the process is you start with a subject, like this picture 562 00:36:45,150 --> 00:36:49,980 I took at a Japanese museum of a little crab. 563 00:36:49,980 --> 00:36:52,770 You kind of draw a little stick figure 564 00:36:52,770 --> 00:36:57,610 of what that crab might look like in a one-dimensional form, 565 00:36:57,610 --> 00:36:59,550 characterized just by the lengths 566 00:36:59,550 --> 00:37:02,500 of these flaps and the connectedness. 567 00:37:02,500 --> 00:37:06,380 You go from here to here to an origami base, which 568 00:37:06,380 --> 00:37:09,380 has all of those flaps of the right length 569 00:37:09,380 --> 00:37:11,877 and connected in the right way. 570 00:37:11,877 --> 00:37:13,710 And then you shape it into an origami model. 571 00:37:13,710 --> 00:37:21,110 Now this method, this step here might seem hard to you guys. 572 00:37:21,110 --> 00:37:28,920 With a little experience, it's actually very reasonable 573 00:37:28,920 --> 00:37:32,530 to assume that someone fairly well versed 574 00:37:32,530 --> 00:37:34,020 in the vocabulary of origami will 575 00:37:34,020 --> 00:37:36,570 be able to accomplish that step. 576 00:37:36,570 --> 00:37:40,720 This step, again, this kind of child's play, somewhat. 577 00:37:40,720 --> 00:37:44,850 It's actually not, to do it really well, 578 00:37:44,850 --> 00:37:46,600 to represent this model as a stick figure, 579 00:37:46,600 --> 00:37:52,230 and we'll see that when we try to go through an example. 580 00:37:52,230 --> 00:37:54,950 This step is the one where algorithms and mathematics 581 00:37:54,950 --> 00:37:59,030 really help to do a lot of the work for us, 582 00:37:59,030 --> 00:38:04,550 and essentially is kind of the easy part from our perspective, 583 00:38:04,550 --> 00:38:07,680 because it's kind of methodical and there's 584 00:38:07,680 --> 00:38:09,360 algorithms involved to help us out. 585 00:38:13,250 --> 00:38:18,590 The most artistic and free things 586 00:38:18,590 --> 00:38:21,540 we can do with origami design are 587 00:38:21,540 --> 00:38:24,320 kind of this step in the shaping and this step 588 00:38:24,320 --> 00:38:26,200 in defining the proportions. 589 00:38:26,200 --> 00:38:31,990 In this step really you define what the abstraction you 590 00:38:31,990 --> 00:38:33,930 choose to characterize in your model. 591 00:38:33,930 --> 00:38:38,450 Like here, we are choosing to represent 592 00:38:38,450 --> 00:38:40,590 all four legs on either side. 593 00:38:40,590 --> 00:38:42,400 You don't have too. 594 00:38:42,400 --> 00:38:50,760 But we also decided to model the eyes and the claws as is. 595 00:38:50,760 --> 00:38:54,630 But an underbelly to a crab. 596 00:38:54,630 --> 00:38:57,820 We could have modeled that with the texture. 597 00:38:57,820 --> 00:39:03,220 We could have modeled the little mouth parts of the crab. 598 00:39:03,220 --> 00:39:05,930 There are many things we could choose to model on here 599 00:39:05,930 --> 00:39:08,590 that we don't choose to. 600 00:39:08,590 --> 00:39:10,820 So this is one level of abstraction. 601 00:39:13,730 --> 00:39:16,150 And this comes with a lot of choice. 602 00:39:16,150 --> 00:39:20,040 Here, there's lots of algorithms and math to help us out. 603 00:39:20,040 --> 00:39:21,880 But as we'll see, there is actually 604 00:39:21,880 --> 00:39:24,200 a lot of choice going from here to here 605 00:39:24,200 --> 00:39:27,470 as well, artistic choice, and from here to here, again, 606 00:39:27,470 --> 00:39:37,300 probably the most blatant way that an artist can 607 00:39:37,300 --> 00:39:40,740 put his style in essence into an origami work. 608 00:39:44,170 --> 00:39:47,587 AUDIENCE: What is the extra fringe? 609 00:39:47,587 --> 00:39:48,420 JASON KU: Which one? 610 00:39:48,420 --> 00:39:48,980 This? 611 00:39:48,980 --> 00:39:51,310 AUDIENCE: Diagonal from the top. 612 00:39:51,310 --> 00:39:52,404 AUDIENCE: On the left. 613 00:39:52,404 --> 00:39:53,320 JASON KU: On the left. 614 00:39:53,320 --> 00:39:54,431 Oh, this? 615 00:39:54,431 --> 00:39:54,930 OK. 616 00:39:54,930 --> 00:40:01,260 So I modeled here the body of this crab 617 00:40:01,260 --> 00:40:02,900 as a flap coming from here. 618 00:40:02,900 --> 00:40:07,370 I kind of wanted a flap to cover the rest of this. 619 00:40:07,370 --> 00:40:11,260 And so that's why I've added this leg of the tree there. 620 00:40:16,700 --> 00:40:21,620 While branch edges-- this is a branch edge, it doesn't 621 00:40:21,620 --> 00:40:27,130 terminate-- will provide paper in that region, 622 00:40:27,130 --> 00:40:31,190 as we'll see later, branch edges of the tree, 623 00:40:31,190 --> 00:40:35,060 rivers in the space allocation, really 624 00:40:35,060 --> 00:40:38,970 don't lend themselves to being shaped very easily. 625 00:40:38,970 --> 00:40:42,400 And so if I isolate that body segment 626 00:40:42,400 --> 00:40:45,010 as a leaf edge for itself, then I 627 00:40:45,010 --> 00:40:49,700 can actually do control a little more 628 00:40:49,700 --> 00:40:52,520 about how I'm able to shape it. 629 00:40:52,520 --> 00:40:53,890 Good question. 630 00:40:53,890 --> 00:40:55,790 So we're going to review a little bit 631 00:40:55,790 --> 00:40:57,540 about uniaxial bases. 632 00:40:57,540 --> 00:41:03,520 This these are the definitions that Erik Demaine posed 633 00:41:03,520 --> 00:41:09,080 in the algorithm, I think in lecture four. 634 00:41:09,080 --> 00:41:12,750 Again, you have this uniaxial base. 635 00:41:12,750 --> 00:41:18,180 It has these characteristics that it's 636 00:41:18,180 --> 00:41:25,230 in the positive space above the z equals zero plane. 637 00:41:25,230 --> 00:41:28,670 And that's kind of represented here. 638 00:41:28,670 --> 00:41:35,300 The intersection with that plane is the projection. 639 00:41:35,300 --> 00:41:39,210 So if you shine the light above it, 640 00:41:39,210 --> 00:41:42,030 it would cast a shadow of a stick figure out, which 641 00:41:42,030 --> 00:41:43,610 is exactly kind of what we want. 642 00:41:43,610 --> 00:41:47,840 We want to make an origami base that associates itself 643 00:41:47,840 --> 00:41:50,000 with a stick figure. 644 00:41:50,000 --> 00:41:53,920 And then we partition the faces into flaps. 645 00:41:53,920 --> 00:41:55,295 So there's all these definitions. 646 00:41:59,340 --> 00:42:02,820 I think to put these in kind of layman's terms 647 00:42:02,820 --> 00:42:06,290 from an origami designer's point of view, what 648 00:42:06,290 --> 00:42:09,880 do these really mean? 649 00:42:09,880 --> 00:42:13,260 Really, the important characteristics that we want 650 00:42:13,260 --> 00:42:17,950 are that the flaps lie along or straddle a single line. 651 00:42:17,950 --> 00:42:21,480 Because if they do that, then we could just fold it in half 652 00:42:21,480 --> 00:42:23,510 and it will have that property of everything 653 00:42:23,510 --> 00:42:29,690 being above an axis and everything lying along an axis, 654 00:42:29,690 --> 00:42:33,620 and that the flaps hinge perpendicular to that axis. 655 00:42:33,620 --> 00:42:37,160 The reason why we need the flaps to hinge perpendicular 656 00:42:37,160 --> 00:42:40,290 to the axis is if they don't hinge perpendicular to the axis 657 00:42:40,290 --> 00:42:50,540 then you will not be able to create a projection 658 00:42:50,540 --> 00:42:53,910 to the plane that is a one-dimensional stick figure. 659 00:42:53,910 --> 00:42:56,880 If these hinges are tilted then that line 660 00:42:56,880 --> 00:42:59,540 will project to a line instead of a point, like we'd want. 661 00:42:59,540 --> 00:43:04,790 We'd want it to project to a single node on the tree. 662 00:43:04,790 --> 00:43:08,500 In any of these uniaxial bases, think 663 00:43:08,500 --> 00:43:12,210 about the base being thinned in the limiting case, that we 664 00:43:12,210 --> 00:43:20,150 can create folds parallel to this axis and thin this model 665 00:43:20,150 --> 00:43:22,830 until it's right along the axis. 666 00:43:22,830 --> 00:43:25,360 And then in that limiting case it 667 00:43:25,360 --> 00:43:27,800 is a stick figure, essentially. 668 00:43:27,800 --> 00:43:32,420 And once it is a stick figure, layering and orientation 669 00:43:32,420 --> 00:43:34,110 of the flaps really don't matter, 670 00:43:34,110 --> 00:43:38,460 because it is the stick figure. 671 00:43:38,460 --> 00:43:41,670 So this is kind of an informal definition, 672 00:43:41,670 --> 00:43:45,830 but we'll use these later in the lecture. 673 00:43:45,830 --> 00:43:47,180 So what is a flap? 674 00:43:47,180 --> 00:43:54,210 We kind of made this argument a couple lectures ago. 675 00:43:57,420 --> 00:44:00,550 So we want to model a flap, so that we can kind of stick it 676 00:44:00,550 --> 00:44:01,227 together. 677 00:44:01,227 --> 00:44:02,810 And this is kind of an intuitive sense 678 00:44:02,810 --> 00:44:07,400 of we take a sheet of paper, we thin it a little bit, 679 00:44:07,400 --> 00:44:12,510 we hinge it perpendicular to some axis. 680 00:44:12,510 --> 00:44:16,120 And when we do and we unfold the paper, 681 00:44:16,120 --> 00:44:18,120 we see that it takes up this kind 682 00:44:18,120 --> 00:44:19,975 of quarter octagon of paper. 683 00:44:24,000 --> 00:44:30,700 Now, if we continue to thin this, 684 00:44:30,700 --> 00:44:32,680 if we make it really, really thin, 685 00:44:32,680 --> 00:44:37,160 you see how deep the boundary, this fold that we make, 686 00:44:37,160 --> 00:44:41,960 will little closer and closer approximate a circle. 687 00:44:41,960 --> 00:44:43,600 Everyone see that? 688 00:44:43,600 --> 00:44:45,300 It's kind of like an umbrella. 689 00:44:45,300 --> 00:44:46,950 I like this analogy with an umbrella. 690 00:44:46,950 --> 00:44:49,335 That you have a single point that's 691 00:44:49,335 --> 00:44:50,710 the center the umbrella, and when 692 00:44:50,710 --> 00:44:55,980 you close the umbrella, all of the umbrella 693 00:44:55,980 --> 00:44:59,180 kind of maps to a single line. 694 00:44:59,180 --> 00:45:06,450 And so it's neat to see on the paper. 695 00:45:06,450 --> 00:45:08,340 It's kind of what you could think 696 00:45:08,340 --> 00:45:12,150 of as a projection to this tree. 697 00:45:12,150 --> 00:45:19,690 Lines on the unfolded square, these lines 698 00:45:19,690 --> 00:45:22,800 at the edges of the circle, map to a single point 699 00:45:22,800 --> 00:45:30,400 on this flap, or infinitely thin flap, or essentially the tree. 700 00:45:30,400 --> 00:45:38,150 This is kind of a leaf edge of our tree. 701 00:45:38,150 --> 00:45:43,170 And so everything along this line maps to a single point, 702 00:45:43,170 --> 00:45:44,830 is compressed onto a single point. 703 00:45:44,830 --> 00:45:50,280 You can do that with any point going up this flap. 704 00:45:50,280 --> 00:45:53,620 We can actually pick off a point here, 705 00:45:53,620 --> 00:45:59,840 and we see a line of constant elevation with respect 706 00:45:59,840 --> 00:46:02,010 to this flap. 707 00:46:02,010 --> 00:46:07,540 And so now we've created a very, very simple tree. 708 00:46:07,540 --> 00:46:13,710 Instead of one leaf edge extending off 709 00:46:13,710 --> 00:46:18,400 of the rest of the model, we have a branch edge, and then 710 00:46:18,400 --> 00:46:19,880 a leaf edge. 711 00:46:19,880 --> 00:46:27,730 And this branch edge is corresponding to this strip 712 00:46:27,730 --> 00:46:29,660 of paper here of constant width. 713 00:46:29,660 --> 00:46:31,660 That's what we call a river. 714 00:46:31,660 --> 00:46:35,540 And we see that a circle is just a limiting case of a river. 715 00:46:35,540 --> 00:46:40,240 Rivers separates two parts of the model off from each other 716 00:46:40,240 --> 00:46:41,480 by a constant distance. 717 00:46:41,480 --> 00:46:44,560 That's what that constant thickness strip of paper means. 718 00:46:44,560 --> 00:46:47,750 And the circle is really just a limiting case 719 00:46:47,750 --> 00:46:54,625 off that river that separates only a single point away 720 00:46:54,625 --> 00:46:55,750 from the rest of the model. 721 00:47:00,120 --> 00:47:01,620 That's all I want to say about that. 722 00:47:01,620 --> 00:47:09,790 And we can actually tile these rivers 723 00:47:09,790 --> 00:47:12,360 onto a plane to create arbitrary trees. 724 00:47:12,360 --> 00:47:15,976 So here's an example of the correspondence. 725 00:47:18,550 --> 00:47:22,880 I call these circle/river packings. 726 00:47:22,880 --> 00:47:25,980 That's the common term in origami design. 727 00:47:25,980 --> 00:47:27,360 This is a circle/river packing. 728 00:47:27,360 --> 00:47:30,960 It's kind of a space allocation. 729 00:47:30,960 --> 00:47:33,920 It's an idealization. 730 00:47:33,920 --> 00:47:35,610 The model we make is actually not 731 00:47:35,610 --> 00:47:38,090 going to be infinitely thin. 732 00:47:38,090 --> 00:47:44,102 So each flap is going to take up more space than these circles. 733 00:47:44,102 --> 00:47:45,310 But it's a good idealization. 734 00:47:49,350 --> 00:47:53,480 This circle/river packing or this space allocation 735 00:47:53,480 --> 00:47:56,140 actually maps uniquely to as a tree. 736 00:47:56,140 --> 00:48:01,190 So if we go through it, this point, 737 00:48:01,190 --> 00:48:07,050 this circle here might map to this line on the tree. 738 00:48:07,050 --> 00:48:11,840 It can actually also map to this line, this edge or this edge, 739 00:48:11,840 --> 00:48:13,860 as well. 740 00:48:13,860 --> 00:48:18,255 Because I don't really care how these flaps are oriented. 741 00:48:20,840 --> 00:48:23,340 The tree is just supposed to preserve 742 00:48:23,340 --> 00:48:24,730 length and connectedness. 743 00:48:24,730 --> 00:48:28,000 It doesn't really have to do with where they're mapped. 744 00:48:28,000 --> 00:48:31,340 And so we'll see some examples of that later. 745 00:48:31,340 --> 00:48:37,420 But we can kind of go through this tree 746 00:48:37,420 --> 00:48:42,900 and see all the different aspects of it, 747 00:48:42,900 --> 00:48:47,440 how the edges correspond to circles and rivers 748 00:48:47,440 --> 00:48:48,720 on the packing. 749 00:48:48,720 --> 00:48:50,890 And we're going to do a little bit of practice 750 00:48:50,890 --> 00:48:56,450 for that, because I think that was one of the day 751 00:48:56,450 --> 00:48:59,390 hardest parts for me starting out in origami design, 752 00:48:59,390 --> 00:49:03,600 was being able to be comfortable with going from a tree 753 00:49:03,600 --> 00:49:07,450 to a space allocation, from a space allocation to a tree. 754 00:49:07,450 --> 00:49:11,490 Getting that concept in my head was kind of difficult. 755 00:49:11,490 --> 00:49:14,320 So how about we practice a little bit. 756 00:49:14,320 --> 00:49:18,950 We have this space allocation of maybe two circles, a river, 757 00:49:18,950 --> 00:49:22,890 and three more circles. 758 00:49:22,890 --> 00:49:28,550 I'll just give you a second to see which one of these trees 759 00:49:28,550 --> 00:49:34,190 is represented by this space allocation. 760 00:49:34,190 --> 00:49:38,100 Or should I say how many of these. 761 00:49:38,100 --> 00:49:42,170 Because some of these trees might be equivalent. 762 00:49:42,170 --> 00:49:46,420 So we're going to start with the upper right one here. 763 00:49:51,090 --> 00:49:54,610 Does it correspond to this space allocation? 764 00:49:54,610 --> 00:49:55,240 Yes or no? 765 00:49:55,240 --> 00:49:55,970 No. 766 00:49:55,970 --> 00:49:57,224 Why? 767 00:49:57,224 --> 00:49:58,156 AUDIENCE: [INAUDIBLE] 768 00:49:58,156 --> 00:49:58,780 JASON KU: Yeah. 769 00:49:58,780 --> 00:50:00,320 So the topology's kind of wrong. 770 00:50:00,320 --> 00:50:03,250 You've got three equal length flaps up here, 771 00:50:03,250 --> 00:50:04,320 which is what we want. 772 00:50:04,320 --> 00:50:07,420 We want three equal length flaps separated off 773 00:50:07,420 --> 00:50:12,430 from the rest of the model by a river of the same length. 774 00:50:12,430 --> 00:50:13,560 That makes sense. 775 00:50:13,560 --> 00:50:18,860 But instead of separating off two flaps, two leaf 776 00:50:18,860 --> 00:50:21,930 edges of maybe twice the length, it 777 00:50:21,930 --> 00:50:26,510 separates three of the same length, which doesn't quite 778 00:50:26,510 --> 00:50:27,040 work out. 779 00:50:27,040 --> 00:50:29,700 So the distances and the connectivity's 780 00:50:29,700 --> 00:50:32,830 kind of off here, just terms of the numbers. 781 00:50:32,830 --> 00:50:34,315 So this one's wrong. 782 00:50:34,315 --> 00:50:36,860 How about this one? 783 00:50:36,860 --> 00:50:37,360 Yes. 784 00:50:37,360 --> 00:50:37,940 Right? 785 00:50:37,940 --> 00:50:41,000 It has the right topology. 786 00:50:41,000 --> 00:50:42,810 This one? 787 00:50:42,810 --> 00:50:44,600 No, again. 788 00:50:44,600 --> 00:50:46,660 The wrong typology. 789 00:50:46,660 --> 00:50:52,510 There is, again, three separated from two by a branch edge. 790 00:50:52,510 --> 00:50:57,100 But it doesn't have the right lengths 791 00:50:57,100 --> 00:50:58,800 associated with this space allocation. 792 00:50:58,800 --> 00:51:00,710 And how about this one? 793 00:51:00,710 --> 00:51:01,210 Yes. 794 00:51:01,210 --> 00:51:03,030 Right? 795 00:51:03,030 --> 00:51:07,230 I've transformed this tree from here to here. 796 00:51:07,230 --> 00:51:11,700 I just moved them around with respect to each other. 797 00:51:11,700 --> 00:51:16,200 They're equivalent, in terms of how we choose our tree. 798 00:51:16,200 --> 00:51:20,190 And this will be important when we actually use TreeMaker. 799 00:51:23,330 --> 00:51:28,220 Because it doesn't matter how we orient things in our tree, 800 00:51:28,220 --> 00:51:33,570 we can manipulate where we put our circles on the paper 801 00:51:33,570 --> 00:51:35,150 to get the same tree. 802 00:51:35,150 --> 00:51:38,640 The mapping from here to a tree is unique. 803 00:51:38,640 --> 00:51:41,020 Mapping from a tree to a space allocation 804 00:51:41,020 --> 00:51:45,395 is not, which leads to interesting design choices 805 00:51:45,395 --> 00:51:49,780 that you can make in designing an origami model. 806 00:51:49,780 --> 00:51:52,440 Yeah, those two. 807 00:51:52,440 --> 00:51:53,630 One more time. 808 00:51:53,630 --> 00:51:56,130 We'll go through this one a little quicker. 809 00:51:56,130 --> 00:51:59,460 I'll give you maybe five seconds or so. 810 00:52:02,840 --> 00:52:06,550 So we're going to start with this one, the first one. 811 00:52:06,550 --> 00:52:10,380 Does that map to this space allocation? 812 00:52:10,380 --> 00:52:12,390 AUDIENCE: [INAUDIBLE] 813 00:52:12,390 --> 00:52:14,040 JASON KU: Yes, it does. 814 00:52:14,040 --> 00:52:21,050 We have two equal length set off from the same length to equal, 815 00:52:21,050 --> 00:52:22,580 and then one twice as big. 816 00:52:22,580 --> 00:52:28,780 And see how I've actually added a redundant node here. 817 00:52:28,780 --> 00:52:34,220 I've split this leaf edge into a branch edge and a leaf edge. 818 00:52:34,220 --> 00:52:37,370 That's kind of a redundant node that I don't really need. 819 00:52:37,370 --> 00:52:40,210 It doesn't really change the topology of this at all. 820 00:52:40,210 --> 00:52:44,250 It would just map to a line right here. 821 00:52:44,250 --> 00:52:45,360 Everyone see that? 822 00:52:45,360 --> 00:52:47,330 How about this one? 823 00:52:47,330 --> 00:52:47,830 No. 824 00:52:47,830 --> 00:52:48,580 Right? 825 00:52:48,580 --> 00:52:51,470 For a number of reasons that I won't go into. 826 00:52:51,470 --> 00:52:53,910 How about this one? 827 00:52:53,910 --> 00:52:54,410 No. 828 00:52:54,410 --> 00:52:58,430 Again, the distances and the topology are wrong. 829 00:52:58,430 --> 00:52:59,970 This one? 830 00:52:59,970 --> 00:53:01,500 No. 831 00:53:01,500 --> 00:53:05,110 This is actually one of the trees from the slide before. 832 00:53:05,110 --> 00:53:06,530 And this one? 833 00:53:06,530 --> 00:53:07,660 Yes. 834 00:53:07,660 --> 00:53:10,870 This is actually just a manipulation of that tree. 835 00:53:10,870 --> 00:53:12,170 So yay! 836 00:53:12,170 --> 00:53:13,790 We're awesome. 837 00:53:13,790 --> 00:53:16,670 Now, going the other way is not necessarily unique. 838 00:53:19,590 --> 00:53:22,000 So there would be multiple answers here. 839 00:53:25,230 --> 00:53:31,670 Is this a correct representation of this tree? 840 00:53:31,670 --> 00:53:33,644 Yes or no? 841 00:53:33,644 --> 00:53:34,440 AUDIENCE: No. 842 00:53:34,440 --> 00:53:36,315 JASON KU: It has the correct topology, right? 843 00:53:36,315 --> 00:53:39,580 It has three equal length flaps separated off by a river 844 00:53:39,580 --> 00:53:40,840 from three equal length flaps. 845 00:53:40,840 --> 00:53:41,881 That's what we have here. 846 00:53:41,881 --> 00:53:47,000 But this river is actually twice as long as any of these flaps. 847 00:53:47,000 --> 00:53:49,810 So this is actually a little bit shorter 848 00:53:49,810 --> 00:53:52,300 than the length of any of these flaps, 849 00:53:52,300 --> 00:53:55,150 not really working for us there. 850 00:53:55,150 --> 00:53:57,420 How about this one? 851 00:53:57,420 --> 00:53:59,460 No, for pretty much the same reason. 852 00:53:59,460 --> 00:54:03,260 It actually has a very similar, if not identical, tree 853 00:54:03,260 --> 00:54:05,830 to this one. 854 00:54:05,830 --> 00:54:07,770 How about this one? 855 00:54:07,770 --> 00:54:11,230 No, topological problems there. 856 00:54:11,230 --> 00:54:12,780 This one? 857 00:54:12,780 --> 00:54:13,540 Yes. 858 00:54:13,540 --> 00:54:16,740 So it's got three equal length flaps separated off 859 00:54:16,740 --> 00:54:20,850 by a large 2x river, I guess. 860 00:54:20,850 --> 00:54:21,460 And this one? 861 00:54:24,050 --> 00:54:26,210 No, for the same reason here. 862 00:54:26,210 --> 00:54:30,080 And here we can actually see three different packings 863 00:54:30,080 --> 00:54:37,020 of a very similar, if not same, tree. 864 00:54:37,020 --> 00:54:39,770 And this goes to show you that there 865 00:54:39,770 --> 00:54:41,880 could be many different ways we could 866 00:54:41,880 --> 00:54:45,770 put these disks on a sheet of paper that could either improve 867 00:54:45,770 --> 00:54:48,490 efficiency or be more useful. 868 00:54:48,490 --> 00:54:52,950 For example, this packing has a central flap. 869 00:54:52,950 --> 00:54:55,820 We may or may not want that central flap. 870 00:54:55,820 --> 00:55:00,300 You can see that a central flap will use more paper 871 00:55:00,300 --> 00:55:05,020 than a flap at the corner or the edge of the paper, 872 00:55:05,020 --> 00:55:09,060 because it has 360 degrees of paper 873 00:55:09,060 --> 00:55:11,920 that you have to fold as opposed to 180 874 00:55:11,920 --> 00:55:16,430 or even just 90 degrees of paper. 875 00:55:16,430 --> 00:55:18,430 So typically in origami design, if you 876 00:55:18,430 --> 00:55:22,110 have a flap you need a little bit of bulk in, a little more 877 00:55:22,110 --> 00:55:24,010 paper, you might want to consider 878 00:55:24,010 --> 00:55:25,960 making that a central flap. 879 00:55:25,960 --> 00:55:29,890 If you want to make a very thin, maybe an antenna or something, 880 00:55:29,890 --> 00:55:32,510 a corner flap might be a better choice. 881 00:55:35,160 --> 00:55:37,680 So correct, in that sense. 882 00:55:37,680 --> 00:55:40,890 Now again, I want to stress the fact 883 00:55:40,890 --> 00:55:42,630 that this is an idealization. 884 00:55:42,630 --> 00:55:43,860 These are circles. 885 00:55:43,860 --> 00:55:51,076 They don't really account for all the paper in the square. 886 00:55:51,076 --> 00:55:53,960 This paper between the circles and the rivers 887 00:55:53,960 --> 00:55:55,760 is not really used. 888 00:55:55,760 --> 00:56:01,030 Pretty much everything in this no man's land here 889 00:56:01,030 --> 00:56:06,940 actually maps to a single point in the tree right. 890 00:56:06,940 --> 00:56:11,210 This is a bad example, so I'll use this correspondence. 891 00:56:11,210 --> 00:56:13,940 This kind of looks like a bikini or something like that. 892 00:56:13,940 --> 00:56:16,960 That's neither here nor there. 893 00:56:16,960 --> 00:56:23,290 But this space all maps to one of these branch nodes. 894 00:56:23,290 --> 00:56:24,640 Everyone see that? 895 00:56:24,640 --> 00:56:31,680 Because in the situation where we thin this model infinitely, 896 00:56:31,680 --> 00:56:34,230 this is kind of extra space that we kind of just 897 00:56:34,230 --> 00:56:36,090 don't even deal with. 898 00:56:36,090 --> 00:56:39,020 In reality, that extra space will 899 00:56:39,020 --> 00:56:43,450 have to go into either the rivers or the circles 900 00:56:43,450 --> 00:56:44,560 in the packing. 901 00:56:44,560 --> 00:56:50,230 So the reason why uniaxial bases are nice in this model 902 00:56:50,230 --> 00:56:56,720 is because since all they hinge creases of the model, basically 903 00:56:56,720 --> 00:56:59,260 the boundary of the flap with the model, 904 00:56:59,260 --> 00:57:10,530 hinge 90 degrees to some axis, then its projection maps 905 00:57:10,530 --> 00:57:11,780 to a single point. 906 00:57:11,780 --> 00:57:15,840 So if we cut off all the flaps along the hinge creases, 907 00:57:15,840 --> 00:57:19,695 we should actually get a very similar mapping 908 00:57:19,695 --> 00:57:20,570 to what we have here. 909 00:57:20,570 --> 00:57:26,370 And here's an example of a fairly complex model. 910 00:57:26,370 --> 00:57:29,790 But you can see, I've just highlighted the locus 911 00:57:29,790 --> 00:57:33,370 of possible hinge creases on this model. 912 00:57:33,370 --> 00:57:35,320 There's a unique way to do this. 913 00:57:35,320 --> 00:57:36,410 I won't go into it. 914 00:57:36,410 --> 00:57:40,780 But there is a unique way to add these hinge creases. 915 00:57:40,780 --> 00:57:45,030 But as you can see, the idea is very similar. 916 00:57:45,030 --> 00:57:48,860 But instead of having these curves of constant width, 917 00:57:48,860 --> 00:57:52,550 you have these discrete angular curves of constant width. 918 00:57:52,550 --> 00:57:57,330 So for example here, you have a river of constant width 919 00:57:57,330 --> 00:58:01,080 that changes directions at a discrete corner, 920 00:58:01,080 --> 00:58:03,710 but it's still a strip of constant width. 921 00:58:03,710 --> 00:58:05,250 Everyone see that? 922 00:58:05,250 --> 00:58:09,239 So maybe we could go ahead and see-- 923 00:58:09,239 --> 00:58:11,030 If we had this crease pattern and we didn't 924 00:58:11,030 --> 00:58:13,230 know what the model was, we could actually 925 00:58:13,230 --> 00:58:17,430 pick off the tree and figure out what this model is. 926 00:58:17,430 --> 00:58:23,660 So maybe we start with these two points down here. 927 00:58:23,660 --> 00:58:25,970 They're all points separated off the rest of the model 928 00:58:25,970 --> 00:58:27,600 by a certain distance. 929 00:58:27,600 --> 00:58:35,630 And that distance here, all these lines that are connected 930 00:58:35,630 --> 00:58:39,850 must be at the same location, the same node on the tree, 931 00:58:39,850 --> 00:58:43,110 because all those hinge creases must map to a single point. 932 00:58:43,110 --> 00:58:48,320 So these two flaps connect with each other 933 00:58:48,320 --> 00:58:51,810 because they share this set of hinge creases. 934 00:58:51,810 --> 00:58:54,000 And so that's that point right there. 935 00:58:54,000 --> 00:58:59,290 I'm going to ignore these two flaps at the bottom for now. 936 00:58:59,290 --> 00:59:01,980 We have this big long river. 937 00:59:01,980 --> 00:59:05,140 I'm just going to deal with the big points first. 938 00:59:05,140 --> 00:59:07,690 And that connects to two more big points. 939 00:59:10,260 --> 00:59:11,350 Everyone see that? 940 00:59:11,350 --> 00:59:13,080 I don't want to go too fast. 941 00:59:13,080 --> 00:59:15,790 And actually, you can do that. 942 00:59:15,790 --> 00:59:19,260 You can just keep doing that, and methodically picking off 943 00:59:19,260 --> 00:59:22,120 distances on this hinge crease representation, 944 00:59:22,120 --> 00:59:26,230 this is discrete space allocation 945 00:59:26,230 --> 00:59:28,865 and fill in the whole tree. 946 00:59:31,590 --> 00:59:35,960 Anyone can think of what this might be? 947 00:59:35,960 --> 00:59:41,910 Maybe a four-legged animal with antlers, like maybe a moose. 948 00:59:41,910 --> 00:59:45,020 So this is a model I designed, I think, 949 00:59:45,020 --> 00:59:47,732 my freshman year as an undergrad. 950 00:59:47,732 --> 00:59:49,232 AUDIENCE: What happens when you have 951 00:59:49,232 --> 00:59:50,930 the squares inside the squares? 952 00:59:58,545 --> 01:00:00,170 JASON KU: That's an excellent question. 953 01:00:00,170 --> 01:00:02,320 First, I want to answer one other question 954 01:00:02,320 --> 01:00:03,660 before I get to that one. 955 01:00:03,660 --> 01:00:12,610 Here, these polygons, these squares, 956 01:00:12,610 --> 01:00:16,480 you could think of maybe putting a circle in them. 957 01:00:16,480 --> 01:00:21,440 And the square is taking up more paper than the circle, 958 01:00:21,440 --> 01:00:24,490 and so the flap that this represents 959 01:00:24,490 --> 01:00:28,200 would be the largest circle that would be fully contained 960 01:00:28,200 --> 01:00:29,880 in that square. 961 01:00:29,880 --> 01:00:31,680 And that would be the length of that flap. 962 01:00:31,680 --> 01:00:35,110 What does it mean to have instead of this point separated 963 01:00:35,110 --> 01:00:38,000 off from the rest of the model have a line separated off 964 01:00:38,000 --> 01:00:40,670 from the rest of the model? 965 01:00:40,670 --> 01:00:46,440 Can anyone guess why would you want 966 01:00:46,440 --> 01:00:49,710 that as an origami designer? 967 01:00:49,710 --> 01:00:51,730 Well, you might want that property 968 01:00:51,730 --> 01:00:56,210 if you want not just a point separated 969 01:00:56,210 --> 01:00:58,070 off from the rest of the model, but a line. 970 01:00:58,070 --> 01:00:59,800 You might want thickness. 971 01:00:59,800 --> 01:01:02,410 It's a qualification of thickness 972 01:01:02,410 --> 01:01:07,480 of that flap at the extreme distance away from the model. 973 01:01:10,390 --> 01:01:13,510 And I don't have this example with me. 974 01:01:13,510 --> 01:01:16,660 I talked about it yesterday at the OrigaMIT lecture. 975 01:01:16,660 --> 01:01:20,360 But let's say you wanted to model a butterfly wing. 976 01:01:20,360 --> 01:01:25,420 It's not well characterized by a stick. 977 01:01:25,420 --> 01:01:28,430 Its thickness is kind of important. 978 01:01:28,430 --> 01:01:31,530 So how I designed a butterfly wing 979 01:01:31,530 --> 01:01:34,230 is I separated a line off from the rest 980 01:01:34,230 --> 01:01:38,900 of the model, something similar to this, 981 01:01:38,900 --> 01:01:41,600 so that I would have enough paper to kind of spread out 982 01:01:41,600 --> 01:01:44,740 that idealized single point. 983 01:01:44,740 --> 01:01:49,880 I could spread the end of that point to have some thickness 984 01:01:49,880 --> 01:01:53,990 and to make a full butterfly wing. 985 01:01:53,990 --> 01:01:56,080 And what you're saying is what does it 986 01:01:56,080 --> 01:02:00,170 mean to have these points, these single leaf edges, 987 01:02:00,170 --> 01:02:02,720 separated off kind of surrounded by river? 988 01:02:05,330 --> 01:02:06,460 You see what that means? 989 01:02:06,460 --> 01:02:08,240 Yep, this is just a river. 990 01:02:08,240 --> 01:02:12,510 Rivers, again, don't have to go all the way across a model. 991 01:02:12,510 --> 01:02:14,180 They can also connect. 992 01:02:14,180 --> 01:02:16,860 You're separating these two points off 993 01:02:16,860 --> 01:02:20,630 from the rest of the model by a certain constant distance. 994 01:02:20,630 --> 01:02:21,970 So excellent question. 995 01:02:27,030 --> 01:02:32,580 And as I promised before, I want to take look a little bit 996 01:02:32,580 --> 01:02:36,380 about the structure of this model. 997 01:02:36,380 --> 01:02:38,850 It looks very symmetric, right? 998 01:02:38,850 --> 01:02:41,960 And you'd think that maybe it would be well represented 999 01:02:41,960 --> 01:02:45,590 by a rectangle of paper instead of a square. 1000 01:02:45,590 --> 01:02:48,010 How do you fit this into a square 1001 01:02:48,010 --> 01:02:49,335 by still having this detail? 1002 01:02:52,930 --> 01:02:54,930 How do you think this texture was made? 1003 01:02:57,990 --> 01:02:58,490 Anybody? 1004 01:03:02,060 --> 01:03:06,424 It's kind of just pleating the paper back and forth. 1005 01:03:06,424 --> 01:03:09,240 If you've ever taken a sheet of paper 1006 01:03:09,240 --> 01:03:13,080 and pleated it to form a texture, 1007 01:03:13,080 --> 01:03:14,550 kind of a one-dimensional problem, 1008 01:03:14,550 --> 01:03:16,130 but you're pleating it. 1009 01:03:16,130 --> 01:03:17,805 But after you pleat it, it's smaller. 1010 01:03:22,250 --> 01:03:24,956 If we take a look at the crease pattern here-- 1011 01:03:24,956 --> 01:03:26,330 This is actually a crease pattern 1012 01:03:26,330 --> 01:03:30,910 to an earlier version of this model. 1013 01:03:30,910 --> 01:03:33,000 This is slightly less detailed, if you 1014 01:03:33,000 --> 01:03:36,860 can imagine, than this model right here. 1015 01:03:40,620 --> 01:03:42,770 What do you think this is? 1016 01:03:42,770 --> 01:03:45,560 Maybe the scales, right? 1017 01:03:45,560 --> 01:03:48,070 This is the head region. 1018 01:03:48,070 --> 01:03:52,540 We can actually do a rough version, 1019 01:03:52,540 --> 01:03:55,370 perform a rough version of this kind of hinge crease 1020 01:03:55,370 --> 01:03:58,500 representation, and get an idea for the structure 1021 01:03:58,500 --> 01:04:00,270 of this model. 1022 01:04:00,270 --> 01:04:04,710 So here, we see the tail. 1023 01:04:04,710 --> 01:04:06,030 I'll talk about this later. 1024 01:04:06,030 --> 01:04:08,972 We have the two back feet separated off 1025 01:04:08,972 --> 01:04:10,680 from the rest of the model by a distance. 1026 01:04:10,680 --> 01:04:13,040 That's this distance here. 1027 01:04:13,040 --> 01:04:15,570 Two more feet. 1028 01:04:15,570 --> 01:04:18,100 This is kind of the neck region. 1029 01:04:18,100 --> 01:04:20,400 And here's the head. 1030 01:04:20,400 --> 01:04:20,900 OK. 1031 01:04:20,900 --> 01:04:22,580 So this looks kind of weird. 1032 01:04:22,580 --> 01:04:26,670 I haven't really been specific about the details here. 1033 01:04:26,670 --> 01:04:29,030 But what does that pleating do? 1034 01:04:29,030 --> 01:04:32,230 Well, it shrinks the useful area of the paper, 1035 01:04:32,230 --> 01:04:33,700 because I pleated it. 1036 01:04:33,700 --> 01:04:36,480 So that's why here the length of this flap 1037 01:04:36,480 --> 01:04:38,660 is this distance here. 1038 01:04:38,660 --> 01:04:39,980 That's the length of the tail. 1039 01:04:42,790 --> 01:04:46,260 But when I make pleats, this thing shrinks. 1040 01:04:46,260 --> 01:04:49,170 And it actually shrinks to this distance. 1041 01:04:49,170 --> 01:04:54,340 This whole thing is cut in half. 1042 01:04:54,340 --> 01:04:58,080 So we make these pleats, it shrinks, 1043 01:04:58,080 --> 01:05:01,830 and then it can lie along this segment. 1044 01:05:01,830 --> 01:05:09,180 Then this area here also shrinks by half. 1045 01:05:09,180 --> 01:05:11,020 So the length is here. 1046 01:05:11,020 --> 01:05:16,270 And it is able to cover this aspect, this part 1047 01:05:16,270 --> 01:05:19,610 of this middle river with texture. 1048 01:05:23,584 --> 01:05:25,500 Please ask questions, because this is complex. 1049 01:05:25,500 --> 01:05:27,708 AUDIENCE: [? What's the ?] distance between the front 1050 01:05:27,708 --> 01:05:28,447 and back legs? 1051 01:05:28,447 --> 01:05:29,030 JASON KU: Yes. 1052 01:05:29,030 --> 01:05:31,709 So this is the distance between the front and back legs. 1053 01:05:31,709 --> 01:05:33,250 But we have to cover it with texture. 1054 01:05:33,250 --> 01:05:34,810 There's no texture here. 1055 01:05:34,810 --> 01:05:38,980 So what we do is create this extra flap here 1056 01:05:38,980 --> 01:05:46,440 where the back legs are with a length of half of this, 1057 01:05:46,440 --> 01:05:48,840 and cover it with texture. 1058 01:05:48,840 --> 01:05:50,850 So that's what he's done here. 1059 01:05:50,850 --> 01:05:54,760 And so the same goes for here. 1060 01:05:54,760 --> 01:05:59,150 It's not quite half down here, but this covers up 1061 01:05:59,150 --> 01:06:00,876 the rest of that section. 1062 01:06:00,876 --> 01:06:02,250 And there's actually some overlap 1063 01:06:02,250 --> 01:06:04,610 so that they can mesh correctly. 1064 01:06:04,610 --> 01:06:09,020 Then here, we have enough paper to provide texture to the neck 1065 01:06:09,020 --> 01:06:10,760 region, and then there's the head. 1066 01:06:10,760 --> 01:06:14,880 It's kind of an ingenious way of actually the top and bottom, 1067 01:06:14,880 --> 01:06:17,780 this top texture and this bottom texture, 1068 01:06:17,780 --> 01:06:21,760 folding up onto this line segment which represents 1069 01:06:21,760 --> 01:06:26,100 the length of the dragon, and still 1070 01:06:26,100 --> 01:06:30,750 having space for these toes and feet. 1071 01:06:30,750 --> 01:06:35,850 It's an ingenious way to distribute the paper, 1072 01:06:35,850 --> 01:06:36,930 in this case. 1073 01:06:36,930 --> 01:06:39,090 Here we can understand another reason 1074 01:06:39,090 --> 01:06:41,940 why we might want to separate a line off 1075 01:06:41,940 --> 01:06:45,570 from the rest of the model, because then that line has 1076 01:06:45,570 --> 01:06:47,750 some thickness, you have a certain amount of space 1077 01:06:47,750 --> 01:06:49,730 out there, and you can actually then 1078 01:06:49,730 --> 01:06:53,510 create more points from that line being 1079 01:06:53,510 --> 01:06:55,520 out at a certain distance. 1080 01:06:55,520 --> 01:06:59,220 We can create a number of little points, which are then toes. 1081 01:07:02,810 --> 01:07:06,600 So I thought that was pretty cool. 1082 01:07:06,600 --> 01:07:09,300 One of my favorite examples of structure. 1083 01:07:09,300 --> 01:07:10,270 AUDIENCE: [INAUDIBLE] 1084 01:07:13,670 --> 01:07:15,450 JASON KU: These were all drawn by hand 1085 01:07:15,450 --> 01:07:18,335 using a program very similar to Adobe Illustrator. 1086 01:07:20,880 --> 01:07:24,490 So yeah, it's very tedious, and lots of copying and pasting. 1087 01:07:24,490 --> 01:07:28,890 But you should see the more complicated version 1088 01:07:28,890 --> 01:07:31,070 of this pattern. 1089 01:07:31,070 --> 01:07:35,290 Because as you can see on this model here, 1090 01:07:35,290 --> 01:07:40,720 there are actually scales on the feet part itself. 1091 01:07:40,720 --> 01:07:47,990 These claws actually are longer in proportion to everything 1092 01:07:47,990 --> 01:07:49,450 else in the model. 1093 01:07:49,450 --> 01:07:51,190 So we actually add some more things. 1094 01:07:51,190 --> 01:07:54,380 There's also a strip of paper here 1095 01:07:54,380 --> 01:07:55,730 that has spines on the back. 1096 01:07:55,730 --> 01:07:59,790 This crease pattern doesn't represent those things. 1097 01:07:59,790 --> 01:08:03,369 So this is a simplified version, if you will. 1098 01:08:03,369 --> 01:08:05,452 AUDIENCE: What was the starting size of the paper? 1099 01:08:05,452 --> 01:08:08,790 AUDIENCE: Yeah, how big is it? 1100 01:08:08,790 --> 01:08:11,030 JASON KU: It's actually an amazingly efficient use 1101 01:08:11,030 --> 01:08:12,770 of paper. 1102 01:08:12,770 --> 01:08:15,600 The length of the dragon is pretty much 1103 01:08:15,600 --> 01:08:19,210 this length right here, which is actually 1104 01:08:19,210 --> 01:08:21,650 quite impressive for the amount of detail there is. 1105 01:08:24,819 --> 01:08:26,290 The shrinkage factor is something 1106 01:08:26,290 --> 01:08:28,510 like to the length of the squared 1107 01:08:28,510 --> 01:08:31,454 to the length of the dragon is not even a half. 1108 01:08:35,910 --> 01:08:38,990 The overall structure of this model is actually quite simple. 1109 01:08:43,229 --> 01:08:47,420 The model itself is maybe about this big. 1110 01:08:47,420 --> 01:08:50,109 So I'm guessing the size of the square 1111 01:08:50,109 --> 01:08:53,229 was something like a meter, if not a little larger. 1112 01:08:57,399 --> 01:09:00,220 It's a long time to work with a single sheet of paper. 1113 01:09:00,220 --> 01:09:00,720 All right. 1114 01:09:00,720 --> 01:09:04,240 So we're going to very quickly, maybe for the next 10, 15 1115 01:09:04,240 --> 01:09:08,270 minutes, go through a design example of a crab. 1116 01:09:08,270 --> 01:09:12,990 And so we're going to kind of go through it quickly. 1117 01:09:12,990 --> 01:09:15,020 To help you do your homework, I just 1118 01:09:15,020 --> 01:09:19,370 want to let you know about some details of TreeMaker that 1119 01:09:19,370 --> 01:09:21,720 might be useful to you to be able to make 1120 01:09:21,720 --> 01:09:24,380 a cleaner or nicer crease pattern. 1121 01:09:24,380 --> 01:09:30,319 So to go to a TreeMaker example, I'm going to open up TreeMaker. 1122 01:09:36,910 --> 01:09:42,664 I need to bring TreeMaker over here. 1123 01:09:45,450 --> 01:09:46,790 So we have TreeMaker. 1124 01:09:49,969 --> 01:09:51,510 And let's say we want to make a crab. 1125 01:09:51,510 --> 01:09:54,979 So how do you want to draw this tree? 1126 01:09:54,979 --> 01:09:57,020 Maybe I'll just draw the tree that we had before. 1127 01:09:59,920 --> 01:10:08,870 First we have four legs all of equal length. 1128 01:10:12,800 --> 01:10:16,230 We could have them all coming from the same spot. 1129 01:10:16,230 --> 01:10:39,670 But traditionally, if we take a look at a crab-- 1130 01:10:39,670 --> 01:10:43,840 That's a cartoony version of a crab, 1131 01:10:43,840 --> 01:10:49,580 but we see that these maybe our axis of our model is here. 1132 01:10:49,580 --> 01:10:55,570 These legs actually don't need to split at the axis. 1133 01:10:55,570 --> 01:10:59,830 We could actually model this as in the tree, 1134 01:10:59,830 --> 01:11:05,150 maybe we have our body segment, and maybe we 1135 01:11:05,150 --> 01:11:10,260 separate these four flaps off from the axis 1136 01:11:10,260 --> 01:11:13,120 by a certain distance so that we actually can save paper. 1137 01:11:13,120 --> 01:11:16,810 We don't have to make each one of these flaps this long. 1138 01:11:16,810 --> 01:11:18,050 You see? 1139 01:11:18,050 --> 01:11:21,420 So I'm going to add a little line segment there. 1140 01:11:21,420 --> 01:11:27,510 Repeat on the other side. 1141 01:11:27,510 --> 01:11:28,265 You get the idea. 1142 01:11:31,030 --> 01:11:34,050 Then maybe you have some modeling 1143 01:11:34,050 --> 01:11:36,770 of the thickness of the model. 1144 01:11:36,770 --> 01:11:38,640 Then we have claws. 1145 01:11:42,700 --> 01:11:46,800 One nice thing about this is we could view just the tree. 1146 01:11:46,800 --> 01:11:48,690 That might make things a little easier. 1147 01:11:48,690 --> 01:11:50,440 There's lots of these view characteristics 1148 01:11:50,440 --> 01:11:52,180 that we're going to take advantage of. 1149 01:11:55,570 --> 01:11:59,540 And maybe we want to represent the eyes. 1150 01:12:02,080 --> 01:12:07,640 Now, the lengths of these edges in the program 1151 01:12:07,640 --> 01:12:10,670 don't really mean anything. 1152 01:12:10,670 --> 01:12:12,990 So take that into note first. 1153 01:12:12,990 --> 01:12:15,450 You actually I've to click on each edge 1154 01:12:15,450 --> 01:12:18,760 and specify its length relative to all the others. 1155 01:12:18,760 --> 01:12:21,570 So maybe we want to make the claws 1156 01:12:21,570 --> 01:12:30,820 half as long as the branch connecting them. 1157 01:12:36,050 --> 01:12:37,170 Bear with me. 1158 01:12:39,830 --> 01:12:42,580 There's no good way of automating this process 1159 01:12:42,580 --> 01:12:43,900 at this point. 1160 01:12:43,900 --> 01:12:45,510 And maybe we make the eyes-- they're 1161 01:12:45,510 --> 01:12:47,930 pretty short-- so we maybe make them 1162 01:12:47,930 --> 01:12:49,785 a quarter of the length of those. 1163 01:12:53,740 --> 01:12:58,000 The body segment, I don't know. 1164 01:12:58,000 --> 01:13:00,150 Also a quarter. 1165 01:13:00,150 --> 01:13:01,810 This is really kind of arbitrary, 1166 01:13:01,810 --> 01:13:05,320 but you can play around with these dimensions. 1167 01:13:05,320 --> 01:13:08,640 And these guys, also a quarter. 1168 01:13:08,640 --> 01:13:13,230 And the back legs can also be one. 1169 01:13:13,230 --> 01:13:14,630 Something like that. 1170 01:13:14,630 --> 01:13:15,660 All right. 1171 01:13:15,660 --> 01:13:23,410 When we've got that, we see that we actually have circles there. 1172 01:13:23,410 --> 01:13:25,260 Now, these circles are kind of crossing. 1173 01:13:25,260 --> 01:13:29,030 We don't want that, because paper 1174 01:13:29,030 --> 01:13:31,430 can't go to two points at once. 1175 01:13:31,430 --> 01:13:33,260 What we can do now is scale everything. 1176 01:13:36,030 --> 01:13:40,410 So it tries to pack all the circles such 1177 01:13:40,410 --> 01:13:45,250 that none of the conditions are being violated. 1178 01:13:45,250 --> 01:13:50,210 So this is a valid packing, except these points 1179 01:13:50,210 --> 01:13:54,580 in the middle here, this whole polygon is constrained. 1180 01:13:54,580 --> 01:13:57,750 The green line segments here are active paths. 1181 01:13:57,750 --> 01:14:04,250 Basically, the distance between these points on the tree 1182 01:14:04,250 --> 01:14:06,440 and these points on the paper are minimized, 1183 01:14:06,440 --> 01:14:08,140 or they're equal. 1184 01:14:08,140 --> 01:14:10,670 So there must be a crease there. 1185 01:14:10,670 --> 01:14:15,500 That is a key statement of uniaxial bases, 1186 01:14:15,500 --> 01:14:18,310 is that there must be a crease along active paths. 1187 01:14:18,310 --> 01:14:22,750 Now, these two points can actually stand to get larger. 1188 01:14:28,700 --> 01:14:31,370 That's evident to the fact that we can move these around 1189 01:14:31,370 --> 01:14:33,180 and it's not violating any conditions. 1190 01:14:33,180 --> 01:14:35,770 Well, if I move it over here, it's violating a condition. 1191 01:14:35,770 --> 01:14:37,470 Whenever a condition is violated then 1192 01:14:37,470 --> 01:14:40,610 you have these red lines that yell at you. 1193 01:14:40,610 --> 01:14:44,980 But we can move this around in this area 1194 01:14:44,980 --> 01:14:46,700 without violating any conditions. 1195 01:14:46,700 --> 01:14:49,400 So it's not happy. 1196 01:14:49,400 --> 01:14:53,110 It's not completely crystallized or well-constrained, 1197 01:14:53,110 --> 01:14:54,660 so it's going to yell at us when we 1198 01:14:54,660 --> 01:14:59,020 try to build the crease pattern. 1199 01:14:59,020 --> 01:15:02,500 TreeMaker was not able to construct all polygons 1200 01:15:02,500 --> 01:15:06,230 because a polygon was either non-convex or contained 1201 01:15:06,230 --> 01:15:07,890 one or more nodes in its interiors. 1202 01:15:07,890 --> 01:15:09,789 So these have nodes in its interior, 1203 01:15:09,789 --> 01:15:11,455 so was not able to fill in this polygon. 1204 01:15:14,530 --> 01:15:16,750 What we can do about that is we don't 1205 01:15:16,750 --> 01:15:20,120 mind if these points get a little bigger. 1206 01:15:20,120 --> 01:15:22,000 Or we could add an extra point. 1207 01:15:22,000 --> 01:15:25,830 So we never modeled a body segment here. 1208 01:15:25,830 --> 01:15:27,750 So maybe we just add in a body segment. 1209 01:15:30,470 --> 01:15:32,230 So scale everything here. 1210 01:15:35,230 --> 01:15:36,430 We still have this problem. 1211 01:15:36,430 --> 01:15:39,390 This guy is unconstrained. 1212 01:15:39,390 --> 01:15:42,730 So what I'm going to do is make this guy a little bigger 1213 01:15:42,730 --> 01:15:45,020 by selecting the node and the edge. 1214 01:15:45,020 --> 01:15:47,980 You have to do both. 1215 01:15:47,980 --> 01:15:50,540 I can go here and scale just this selection. 1216 01:15:50,540 --> 01:15:53,320 And it'll increase it by itself. 1217 01:15:57,030 --> 01:16:01,750 Actually, nicely, this is somewhat of a symmetric crease 1218 01:16:01,750 --> 01:16:03,770 pattern, which didn't occur before. 1219 01:16:12,650 --> 01:16:15,230 So you see these lighter edges of the tree 1220 01:16:15,230 --> 01:16:17,300 are fully constrained edges. 1221 01:16:17,300 --> 01:16:19,680 These darker ones are not fully constrained edges. 1222 01:16:19,680 --> 01:16:22,780 So this guy can actually also increase a little bit. 1223 01:16:22,780 --> 01:16:27,340 So I'm going to scale selection. 1224 01:16:27,340 --> 01:16:29,190 Now everything should be good. 1225 01:16:29,190 --> 01:16:31,260 I can build the crease pattern. 1226 01:16:31,260 --> 01:16:33,050 Guh! 1227 01:16:33,050 --> 01:16:36,980 It built it, so whatever. 1228 01:16:36,980 --> 01:16:39,540 So this is a foldable crease pattern 1229 01:16:39,540 --> 01:16:42,280 that will form what we want it to. 1230 01:16:42,280 --> 01:16:46,760 We can also go to this creases view, 1231 01:16:46,760 --> 01:16:50,370 and it will show the creases of the model. 1232 01:16:50,370 --> 01:16:52,980 It was not able to find valid mountain-valleys. 1233 01:16:58,730 --> 01:16:59,910 Anyway. 1234 01:16:59,910 --> 01:17:02,310 So to make this cleaner, you might 1235 01:17:02,310 --> 01:17:05,210 want to deal with symmetry. 1236 01:17:05,210 --> 01:17:11,090 So there's an ability to select diagonal symmetry 1237 01:17:11,090 --> 01:17:18,230 and either add conditions to make a node fixed 1238 01:17:18,230 --> 01:17:21,610 to the symmetry line, so add additional constraints 1239 01:17:21,610 --> 01:17:23,650 to our system to make it cleaner. 1240 01:17:23,650 --> 01:17:25,980 We can fix them to the symmetry line. 1241 01:17:25,980 --> 01:17:28,250 We can fix it to the corner or the paper edge, 1242 01:17:28,250 --> 01:17:30,060 fix to any arbitrary position. 1243 01:17:30,060 --> 01:17:31,810 Or we can select two nodes and pair them 1244 01:17:31,810 --> 01:17:35,760 about the symmetry line, which is a very useful thing to do. 1245 01:17:46,882 --> 01:17:48,590 I don't know if it will yell at me again. 1246 01:17:48,590 --> 01:17:51,850 Yeah, it didn't do anything. 1247 01:17:51,850 --> 01:17:54,290 What I'm going to do is go in here. 1248 01:17:54,290 --> 01:17:56,330 There's lots of things you could do here. 1249 01:17:56,330 --> 01:18:01,990 We could perturb all the nodes, so they 1250 01:18:01,990 --> 01:18:04,280 move if by a slight distance. 1251 01:18:04,280 --> 01:18:06,850 And maybe if we try scaling it again, 1252 01:18:06,850 --> 01:18:08,255 it'll find a valid solution. 1253 01:18:19,560 --> 01:18:25,440 This was unfortunate. 1254 01:18:25,440 --> 01:18:27,490 Scale everything. 1255 01:18:34,100 --> 01:18:35,570 Kill the strain on this. 1256 01:18:51,730 --> 01:18:53,052 Yes? 1257 01:18:53,052 --> 01:18:54,010 AUDIENCE: I'm confused. 1258 01:18:54,010 --> 01:18:56,010 Is it failing because the problem 1259 01:18:56,010 --> 01:18:59,550 is over-constrained or under-constrained? 1260 01:18:59,550 --> 01:19:01,730 JASON KU: It's not failing because of either. 1261 01:19:01,730 --> 01:19:07,340 It's failing because certain creases 1262 01:19:07,340 --> 01:19:08,780 get very close together. 1263 01:19:08,780 --> 01:19:10,380 Now it's failing because it can't 1264 01:19:10,380 --> 01:19:14,362 find a correct valley-mountain assignment 1265 01:19:14,362 --> 01:19:15,320 for the crease pattern. 1266 01:19:15,320 --> 01:19:19,040 So it's able to build the creases fine. 1267 01:19:19,040 --> 01:19:24,170 So build crease pattern, fine. 1268 01:19:24,170 --> 01:19:27,120 It just wasn't able to construct a mountain-valley assignment, 1269 01:19:27,120 --> 01:19:29,190 which in the creases view would usually give you 1270 01:19:29,190 --> 01:19:30,523 mountain and valley assignments. 1271 01:19:30,523 --> 01:19:32,850 AUDIENCE: That means it's not possible? 1272 01:19:32,850 --> 01:19:34,142 JASON KU: It couldn't find it. 1273 01:19:34,142 --> 01:19:35,475 It's not that it's not possible. 1274 01:19:35,475 --> 01:19:38,830 It just couldn't find it. 1275 01:19:38,830 --> 01:19:40,290 I want to say one other thing. 1276 01:19:45,860 --> 01:19:47,650 Kill the crease pattern. 1277 01:19:47,650 --> 01:19:52,070 We have a polygon bounded by active paths that's 1278 01:19:52,070 --> 01:19:54,060 not triangular. 1279 01:19:54,060 --> 01:20:00,682 But we can actually split it any of these up into triangles. 1280 01:20:00,682 --> 01:20:02,640 I'm just going to mention that you can do this. 1281 01:20:02,640 --> 01:20:05,820 You click on one of these polygons, 1282 01:20:05,820 --> 01:20:09,350 go here, stub, triangulate tree. 1283 01:20:09,350 --> 01:20:12,550 It adds random points. 1284 01:20:12,550 --> 01:20:15,084 And now all the polygons are triangles, 1285 01:20:15,084 --> 01:20:16,375 and that's much easier to fold. 1286 01:20:19,090 --> 01:20:21,136 Or not. 1287 01:20:21,136 --> 01:20:22,260 That's how you would do it. 1288 01:20:22,260 --> 01:20:25,510 Anyway, I'm running out of time, so I'm 1289 01:20:25,510 --> 01:20:27,290 going to go back to the presentation. 1290 01:20:27,290 --> 01:20:29,890 But if you need any help with these, 1291 01:20:29,890 --> 01:20:35,290 or the tutorial with this program, I'm around. 1292 01:20:35,290 --> 01:20:39,990 You can contact me through the OrigaMIT website, 1293 01:20:39,990 --> 01:20:44,720 or you can come to it an OrigaMIT workshop on Sunday 1294 01:20:44,720 --> 01:20:47,900 and ask me questions then. 1295 01:20:47,900 --> 01:20:53,125 So I'm going to quickly just go right back to the presentation. 1296 01:20:55,820 --> 01:20:59,330 Play slide show. 1297 01:20:59,330 --> 01:20:59,830 Nope. 1298 01:21:09,300 --> 01:21:10,606 Technical difficulties. 1299 01:21:19,060 --> 01:21:21,440 Play slide show. 1300 01:21:21,440 --> 01:21:25,880 So that was the example of TreeMaker. 1301 01:21:25,880 --> 01:21:29,180 Here's an example of a non-TreeMaker example 1302 01:21:29,180 --> 01:21:32,540 that I designed this weekend of a crab. 1303 01:21:32,540 --> 01:21:37,210 I actually designed this model it 1304 01:21:37,210 --> 01:21:39,550 after I had drawn this picture. 1305 01:21:39,550 --> 01:21:44,820 And I wanted to incorporate some of the elements of this picture 1306 01:21:44,820 --> 01:21:46,140 into my design process. 1307 01:21:46,140 --> 01:21:49,190 So one of the first I actually started 1308 01:21:49,190 --> 01:21:50,740 was designing the back so that it 1309 01:21:50,740 --> 01:21:52,200 would have this kind of structure 1310 01:21:52,200 --> 01:21:59,410 with this polygon there, kind of a Komatsu-like design process, 1311 01:21:59,410 --> 01:22:04,626 and trying to make the final form polygons 1312 01:22:04,626 --> 01:22:06,500 and incorporate those into my crease pattern. 1313 01:22:06,500 --> 01:22:10,320 So that's what this area is right here. 1314 01:22:10,320 --> 01:22:18,930 It has a very similar structure to the tree we drew already. 1315 01:22:18,930 --> 01:22:22,810 We have the four points for the legs, the body segment. 1316 01:22:22,810 --> 01:22:26,030 These are going to be the eyes. 1317 01:22:26,030 --> 01:22:27,940 And so there are some extra points just 1318 01:22:27,940 --> 01:22:31,210 to make things easier to fold. 1319 01:22:31,210 --> 01:22:32,340 The claws. 1320 01:22:32,340 --> 01:22:33,340 Here's the body segment. 1321 01:22:33,340 --> 01:22:37,270 There's these extra two things on either side. 1322 01:22:37,270 --> 01:22:39,650 And I made those so that there could 1323 01:22:39,650 --> 01:22:43,420 be an underbelly to the crab, and that I 1324 01:22:43,420 --> 01:22:46,150 could add some texture in and things like that. 1325 01:22:46,150 --> 01:22:49,400 But you can see some of the constraints 1326 01:22:49,400 --> 01:22:52,980 that I've put on it are that I want this to be 22.5 degree 1327 01:22:52,980 --> 01:22:56,930 folding, which is hard to implement in TreeMaker. 1328 01:22:56,930 --> 01:23:00,880 I've also shown some of the thinning 1329 01:23:00,880 --> 01:23:05,740 to make these points thinner on the right. 1330 01:23:05,740 --> 01:23:08,290 So if we actually pick out the tree 1331 01:23:08,290 --> 01:23:12,270 for this hinge representation, we 1332 01:23:12,270 --> 01:23:14,090 get something that kind of looks like this. 1333 01:23:14,090 --> 01:23:15,910 So we have our legs. 1334 01:23:15,910 --> 01:23:16,910 Here's our body segment. 1335 01:23:16,910 --> 01:23:21,650 Here are the flaps that I make into the underbelly, eyes, 1336 01:23:21,650 --> 01:23:23,580 and the claws. 1337 01:23:23,580 --> 01:23:26,269 And here's the folded proof of concept version 1338 01:23:26,269 --> 01:23:27,310 that I folded last night. 1339 01:23:27,310 --> 01:23:29,140 It's actually a really crappy picture. 1340 01:23:29,140 --> 01:23:29,990 I apologize. 1341 01:23:29,990 --> 01:23:32,580 But it's up here. 1342 01:23:32,580 --> 01:23:36,590 I fold it like 10:00 last night, because I thought 1343 01:23:36,590 --> 01:23:39,460 it would be useful for you guys to see what a folded one might 1344 01:23:39,460 --> 01:23:40,450 look like. 1345 01:23:40,450 --> 01:23:45,090 But it actually turns out to be somewhat non-uniaxial. 1346 01:23:47,780 --> 01:23:50,660 And you can see some of the texturing on the underbelly, 1347 01:23:50,660 --> 01:23:53,460 if you take a look at it and come up here. 1348 01:23:57,390 --> 01:24:02,280 So that's kind of describing some of the design 1349 01:24:02,280 --> 01:24:08,880 process of a real work that uses the concepts of uniaxial bases, 1350 01:24:08,880 --> 01:24:11,870 that I can make this hinge crease representation, 1351 01:24:11,870 --> 01:24:15,500 but then use some shaping to modify it. 1352 01:24:15,500 --> 01:24:18,780 If you're interested in learning about anything related 1353 01:24:18,780 --> 01:24:22,400 to origami, there's an excellent online forum 1354 01:24:22,400 --> 01:24:26,700 that you can ask questions or show off work that you do 1355 01:24:26,700 --> 01:24:28,230 or anything like that. 1356 01:24:28,230 --> 01:24:33,175 And if you want to do something slightly more local-- 1357 01:24:33,175 --> 01:24:34,960 this is shameless self-promotion-- 1358 01:24:34,960 --> 01:24:39,850 but the origami club at MIT welcomes you with open arms. 1359 01:24:39,850 --> 01:24:41,930 We meet every Sunday in the Student Center 1360 01:24:41,930 --> 01:24:42,950 from 2:00 to 4:00 PM. 1361 01:24:42,950 --> 01:24:46,340 You can find all sorts of details on our website. 1362 01:24:46,340 --> 01:24:48,790 So that's about it. 1363 01:24:48,790 --> 01:24:51,449 AUDIENCE: Are those origami letters? 1364 01:24:51,449 --> 01:24:52,490 JASON KU: Those are, yes. 1365 01:24:55,450 --> 01:24:59,780 Each one of these letters was a model. 1366 01:24:59,780 --> 01:25:06,320 They're all the same model I designed, in which you have a 3 1367 01:25:06,320 --> 01:25:10,180 by 4 grid of flippable squares of color change 1368 01:25:10,180 --> 01:25:14,620 that you can flip to either be in the all white state 1369 01:25:14,620 --> 01:25:18,330 or all black state. 1370 01:25:18,330 --> 01:25:24,220 And you could also do some of these half pixeling. 1371 01:25:24,220 --> 01:25:29,760 But you can basically make any of these letters-- 1372 01:25:29,760 --> 01:25:32,990 I have a whole alphabet of things-- from a single model. 1373 01:25:32,990 --> 01:25:34,000 I was lazy. 1374 01:25:34,000 --> 01:25:36,170 I didn't want to design 26 models. 1375 01:25:36,170 --> 01:25:37,640 I just want to design one model. 1376 01:25:37,640 --> 01:25:41,610 So that that's what those are. 1377 01:25:41,610 --> 01:25:43,370 So that concludes the lecture. 1378 01:25:43,370 --> 01:25:45,980 We're just about at time.