[00:00:05.15] hello I will briefly talk a little bit more about shape signature projects and [00:00:11.21] [00:00:11.21] then its potential towards extending the shape machine to incorporate the [00:00:16.09] [00:00:16.09] parametric shapes in the unique way or so so again once again the shape [00:00:22.06] [00:00:22.06] signature projects so far investigated from one to four line shape families [00:00:27.01] [00:00:27.01] here's the complete set of underlying configuration of construction lines that [00:00:31.16] [00:00:31.16] three line shape families can be arranged upon so starting from the very [00:00:36.12] [00:00:36.12] left from one construction line of the where threequel linear lines can be [00:00:42.20] [00:00:42.20] arranged upon and then two configurations of two construction lines [00:00:46.18] [00:00:46.18] followed by parallel ones across once and then four configurations of three [00:00:53.03] [00:00:53.03] construction lines three three parallels three having one intersection two [00:00:59.13] [00:00:59.13] intersections and three intersection which is the triangular configuration [00:01:02.07] [00:01:02.07] with the same on the very right hand side these seven shown here are [00:01:08.07] [00:01:08.07] representative instances so each of them can be characterized as long as they [00:01:13.14] [00:01:13.14] maintain the number of intersections we called its registration points so in [00:01:19.08] [00:01:19.08] general for any other end line shape families the number of construction line [00:01:23.21] [00:01:23.21] is less than an equal to number of maximum line of the shape factors so a [00:01:31.15] [00:01:31.15] finite number of three line shape families can be arranged upon each of [00:01:35.15] [00:01:35.15] these three to seven underline configuration based on the convention of [00:01:39.11] [00:01:39.11] the arrangement of maximum line that this fits best sped lena introduced [00:01:44.16] [00:01:44.16] earlier and total of five hundred and nineteen three line shape families are [00:01:51.08] [00:01:51.08] postulated and group s three three three on the right hand side the triangular [00:01:57.01] [00:01:57.01] configuration is the is the largest one of them all hosting three hundred and [00:02:04.00] [00:02:04.00] ninety shaped families including the triangle that we are all familiar with [00:02:09.22] [00:02:09.22] taking the group as 3 3 3 as an example here are the 13 parametric line segments [00:02:16.06] [00:02:16.06] or parts that makes the 390 shape families these 30 parts are defined [00:02:22.19] [00:02:22.19] based on their boundary condition with respect to the reservoirs registration [00:02:27.18] [00:02:27.18] points which is the intersection of the construction lines the boundaries of the [00:02:32.09] [00:02:32.09] parts are either fixed on the registration points of determined [00:02:36.10] [00:02:36.10] condition or to slide along the Associated construction line within the [00:02:40.09] [00:02:40.09] boundary you see prescribed by the neighboring registration point so you [00:02:44.08] [00:02:44.08] can either slide on both direction through both direction in one direction [00:02:48.18] [00:02:48.18] or for example if we see the case this one comma one this is a two fixed points [00:02:57.03] [00:02:57.03] on the second row in the very right hand side which if we put three of those [00:03:03.07] [00:03:03.07] together then mix the triangular so again this is here's the instances of [00:03:09.17] [00:03:09.17] 390 shaped families and from all of this [00:03:17.15] [00:03:19.07] yeah there's only one that is a determinant kick so again these are [00:03:24.20] [00:03:24.20] instances of a shaped family so all of these can be parameterize and then the [00:03:29.20] [00:03:29.20] triangle at the very bottom is the only one that is a determinant case and they [00:03:34.00] [00:03:34.00] all the others in determinants so under the shape signature here are here we see [00:03:40.12] [00:03:40.12] three construction lines in trying to look a figuration three registration [00:03:44.22] [00:03:44.22] points and three maximal lives constituting the shake and then it's [00:03:48.10] [00:03:48.10] notated as three ordered pairs of 1 comma 1 here are some sample variation [00:03:56.00] [00:03:56.00] of this family assignments of three vectors specify different kinds of [00:04:00.20] [00:04:00.20] triangles as we see here and then as long as the signature of 1 1 1 1 is kept [00:04:07.05] [00:04:07.05] any vector assignments will produce a triangle not collapsed case or anything [00:04:12.12] [00:04:12.12] else so this is this provides the constraints of being triangle so here's [00:04:19.12] [00:04:19.12] a an example of in dirt in in case a PE or flex shaped or a [00:04:25.13] [00:04:25.13] triangle with the extended line and for this case an additional parameter a [00:04:31.09] [00:04:31.09] should be assigned to stunt she ate a specific instance where a specifies the [00:04:37.06] [00:04:37.06] length of the extended part of the line which could be infinitely long here and [00:04:43.06] [00:04:43.06] here's another example of into indeterminate cases that features a [00:04:47.07] [00:04:47.07] break or emptiness within the shape even with the break this shape family belongs [00:04:53.00] [00:04:53.00] in the three in line shape truth because we see three next ones for this case an [00:04:59.20] [00:04:59.20] additional parameter B should be assigned to especially in a specific [00:05:03.22] [00:05:03.22] instance where you specify the size of a break B should be larger than zero [00:05:09.12] [00:05:09.12] otherwise the associated line will contact the registration point making a [00:05:13.17] [00:05:13.17] triangle which is the signature the one we saw before and then the B should be [00:05:18.20] [00:05:18.20] smaller than the distance between the two neighboring registration points [00:05:22.18] [00:05:22.18] otherwise the shape will become two line shape which again is belonging the [00:05:28.21] [00:05:28.21] different signature group so if the general lives any shape can be specified [00:05:34.23] [00:05:34.23] and uniquely described by the signature and three sets of assignments one kind [00:05:40.21] [00:05:40.21] is the vectors of the construction line the other one is correct parameters for [00:05:44.19] [00:05:44.19] the extended parts and then the third one is parameters for the breaks in [00:05:51.01] [00:05:51.01] comparison with the parameterization in u 0 J which is probably using the [00:05:56.03] [00:05:56.03] existing parametric modeler shape signature suggest a new theory of [00:06:00.19] [00:06:00.19] parametric modeling privilege in the visual aspects of the shapes in u1j over [00:06:07.08] [00:06:07.08] the numeric efficiency in engineering the model so here's the complete table [00:06:13.16] [00:06:13.16] including all 1 through 4 line in shape family groups starting from 1 1 line [00:06:20.07] [00:06:20.07] shaped group on the Left top consists of one shape group family all the way up to [00:06:25.02] [00:06:25.02] s 4 4 6 on the red third row on the right-hand side that consists of [00:06:30.22] [00:06:30.22] hundred and ninety five thousand and six hundred and twenty five shaped families [00:06:35.10] [00:06:35.10] the point is so far the complete set of families up to s 4 4 4 highlighted [00:06:44.11] [00:06:44.11] within the red are complete and they're partially for the four remaining groups [00:06:49.22] [00:06:49.22] the visualization of those are complete and then total of fourteen thousand [00:06:55.22] [00:06:55.22] seven hundred and fifty four shapes as instances representing the families are [00:07:00.16] [00:07:00.16] on display and various format in the ongoing exhibition to coin gallery [00:07:05.06] [00:07:05.06] hopefully you'll join us in the evening and the reception to see the shapes and [00:07:12.22]