{"id":8178,"date":"2023-11-23T08:42:20","date_gmt":"2023-11-23T08:42:20","guid":{"rendered":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/?p=8178"},"modified":"2023-11-23T08:45:33","modified_gmt":"2023-11-23T08:45:33","slug":"jingbo-liang-tiling","status":"publish","type":"post","link":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/2023\/11\/23\/jingbo-liang-tiling\/","title":{"rendered":"Jingbo Liang -Tiling"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>Part 1: 2D Tiles A\u00a0<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"794\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-4-1024x794.png\" alt=\"\" class=\"wp-image-8215\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-4-1024x794.png 1024w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-4-300x232.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-4-768x595.png 768w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-4-920x713.png 920w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-4-575x446.png 575w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-4-380x294.png 380w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-4.png 1031w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"626\" height=\"434\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-3.png\" alt=\"\" class=\"wp-image-8214\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-3.png 626w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-3-300x208.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-3-575x399.png 575w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-3-380x263.png 380w\" sizes=\"auto, (max-width: 626px) 100vw, 626px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">In the right picture, you can see the unit. Similar to the Part1:2D tiles B, Line a and Line e are replaced by Curve a and Line b and Line d are replaced by curve b. <\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Part 1:2D Tiles B<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"698\" height=\"457\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-1.png\" alt=\"\" class=\"wp-image-8180\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-1.png 698w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-1-300x196.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-1-575x376.png 575w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-1-380x249.png 380w\" sizes=\"auto, (max-width: 698px) 100vw, 698px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"367\" height=\"328\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-2.png\" alt=\"\" class=\"wp-image-8181\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-2.png 367w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-2-300x268.png 300w\" sizes=\"auto, (max-width: 367px) 100vw, 367px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the right picture, you can see the unit. There are five lines: a, b, c, d, e. The close curve formed by a, b, d, e is known as a parallogram. Line c was used to divide it into two triangles. It repeats itself along two vectors, v1 and v2 to form the 2D tiles.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Part 2:<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"701\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-10.png\" alt=\"\" class=\"wp-image-8223\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-10.png 700w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-10-300x300.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-10-150x150.png 150w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-10-575x576.png 575w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-10-380x381.png 380w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"434\" height=\"272\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-11.png\" alt=\"\" class=\"wp-image-8224\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-11.png 434w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-11-300x188.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-11-380x238.png 380w\" sizes=\"auto, (max-width: 434px) 100vw, 434px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the left picture, you can see the tiles I&#8217;m trying to create (cited from: https:\/\/link.aps.org\/accepted\/10.1103\/PhysRevB.99.100404). This 2D tile is made up of hexagons formed by two triangles colored red and blue. Codes are assigned to all intersection points. The tile repeats itself along two vectors, Vx and Vy. Two shaded triangles of one unit are shared with its repeated unit in the top. Thus, the unit I need to print is the star-like shape shown on the right. <\/li>\n\n\n\n<li>The geometrical changes in the z direction happen along the triangles rather than the hexagon. Because each intersection points are recorded. Curves formed by segments between any two intersection points can be formed by rs.AddCurve([point1,point2]). Then using rs.DivideCurve function to get points on each curve.  Turtle is used to trace points. I used another turtle to add the changes.  <\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"775\" height=\"530\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-12.png\" alt=\"\" class=\"wp-image-8225\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-12.png 775w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-12-300x205.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-12-768x525.png 768w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-12-575x393.png 575w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-12-380x260.png 380w\" sizes=\"auto, (max-width: 775px) 100vw, 775px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The hardest part is drawing a matrix of tiles in the plane. Turtle&#8217;s moving generated some unnecessary lines. I tried penup() and pendown(). However, it didn&#8217;t work. It&#8217;s something I need to think about more.<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"983\" height=\"757\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-13.png\" alt=\"\" class=\"wp-image-8226\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-13.png 983w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-13-300x231.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-13-768x591.png 768w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-13-920x708.png 920w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-13-575x443.png 575w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-13-380x293.png 380w\" sizes=\"auto, (max-width: 983px) 100vw, 983px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1002\" height=\"773\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-14.png\" alt=\"\" class=\"wp-image-8227\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-14.png 1002w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-14-300x231.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-14-768x592.png 768w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-14-920x710.png 920w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-14-575x444.png 575w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-14-380x293.png 380w\" sizes=\"auto, (max-width: 1002px) 100vw, 1002px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"704\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-15-1024x704.png\" alt=\"\" class=\"wp-image-8228\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-15-1024x704.png 1024w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-15-300x206.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-15-768x528.png 768w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-15-1536x1056.png 1536w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-15-2048x1408.png 2048w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-15-1140x784.png 1140w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-15-920x633.png 920w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-15-575x395.png 575w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-15-380x261.png 380w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"675\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-16-1024x675.png\" alt=\"\" class=\"wp-image-8229\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-16-1024x675.png 1024w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-16-300x198.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-16-768x506.png 768w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-16-1140x752.png 1140w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-16-920x606.png 920w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-16-575x379.png 575w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-16-380x251.png 380w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-16.png 1165w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Part 3:<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"555\" height=\"389\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-5.png\" alt=\"\" class=\"wp-image-8217\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-5.png 555w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-5-300x210.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-5-380x266.png 380w\" sizes=\"auto, (max-width: 555px) 100vw, 555px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"494\" height=\"359\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-7.png\" alt=\"\" class=\"wp-image-8219\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-7.png 494w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-7-300x218.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-7-380x276.png 380w\" sizes=\"auto, (max-width: 494px) 100vw, 494px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"596\" height=\"369\" src=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-6.png\" alt=\"\" class=\"wp-image-8218\" srcset=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-6.png 596w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-6-300x186.png 300w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-6-575x356.png 575w, https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/tile-6-380x235.png 380w\" sizes=\"auto, (max-width: 596px) 100vw, 596px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>I modified the &#8220;pot&#8221; from HW2 to make the surface. These tiles are from Part 1. Initially, my code didn&#8217;t work because the surface I generated used &#8220;polygon=rs.AddLine(points)&#8221;. You can fix it by using &#8220;polygon=rs.AddCurve(points)&#8221;. It&#8217;s hard to tell the difference visually. Their outputs are different, though. The first one adds a line, while the second adds a curve.<\/li>\n\n\n\n<li>Codes are <a href=\"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-content\/uploads\/2023\/11\/JingboLiangTiling.zip\">here<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Part 1: 2D Tiles A\u00a0 In the right picture, you can see the unit. Similar to the Part1:2D tiles B, Line a and Line e are replaced by Curve a and Line b and Line d are replaced by curve b. Part 1:2D Tiles B Part 2: Part 3:<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[43,1,24],"tags":[],"class_list":["post-8178","post","type-post","status-publish","format-standard","hentry","category-tiling_23","category-uncategorized","category-studentwork23"],"_links":{"self":[{"href":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-json\/wp\/v2\/posts\/8178","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-json\/wp\/v2\/comments?post=8178"}],"version-history":[{"count":5,"href":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-json\/wp\/v2\/posts\/8178\/revisions"}],"predecessor-version":[{"id":8233,"href":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-json\/wp\/v2\/posts\/8178\/revisions\/8233"}],"wp:attachment":[{"href":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-json\/wp\/v2\/media?parent=8178"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-json\/wp\/v2\/categories?post=8178"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/handandmachine.org\/classes\/computational_fabrication\/wp-json\/wp\/v2\/tags?post=8178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}