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Typescript library for generating multidimensional convex hulls and delaunay triangulations.","homepage":"https://github.com/DerSchmale/tympanum#readme","keywords":["helix3d","3d","geometry","hull"],"repository":{"type":"git","url":"git+https://github.com/DerSchmale/tympanum.git"},"bugs":{"url":"https://github.com/DerSchmale/tympanum/issues"},"license":"MIT","readme":"# Tympanum\r\n\r\nA Typescript library for generating multidimensional convex hulls and delaunay triangulations.\r\n\r\n# Documentation\r\n\r\n- [Reference documentation](https://derschmale.github.io/tympanum/docs/index.html)\r\n- [The original QuickHull algorithm](https://www.researchgate.net/publication/2641780_The_QuickHull_Algorithm_for_Convex_Hulls)\r\n\r\n# Examples:\r\n\r\n- [2D Quickhull](https://derschmale.github.io/tympanum/examples/convex_hull_2d/index.html)\r\n- [3D Quickhull](https://derschmale.github.io/tympanum/examples/convex_hull_3d/index.html)\r\n- [2D Delaunay Triangulation](https://derschmale.github.io/tympanum/examples/delaunay_2d/index.html)\r\n- [3D Delaunay Tetrahedralisation](https://derschmale.github.io/tympanum/examples/delaunay_3d/index.html)\r\n- [Delaunay facet search using visibility walking](https://derschmale.github.io/tympanum/examples/walk_2d/index.html)\r\n- [Point reconstruction with barycentric coordinates](https://derschmale.github.io/tympanum/examples/barycentric/index.html)\r\n\r\n## Basic Types\r\n\r\nTympanum has the following building blocks to form shapes:\r\n\r\nAny N-dimensional shape such as a simplex is a collection of Facets.\r\n- `Facet`: This is a polygonal face of dimension N-1: a line, a triangle, or a tetrahedron in 2D, 3D or 4D respectively. \r\n  Each facet is bounded by a set of ridges.\r\n- `Ridge`: This is an edge of dimension N-2: a point (vertex), a line (edge), or a triangle in 2D, 3D or 4D respectively.\r\n  A ridge has N-1 vertices (ie: 1 vertex, 2 line end points, 3 triangle corners).\r\n- `Vertex`: These are represented as an index into a list of points (fe: the list of points used to generate a convex \r\n  hull). This is so that we can easily map points to other data sets from which the points were extracted, or they can\r\n  be used to construct 3D meshes for use in WebGL.\r\n  \r\n## Convex Hull\r\n\r\nTo generate a convex hull using the quickHull algorithm:\r\n\r\n```\r\nimport { quickHull } from \"@derschmale/tympanum\";\r\n\r\nconst points = [];\r\n\r\nfor (let i = 0; i < 5000; ++i) {  \r\n    points[i] = [Math.random(), Math.random(), Math.random()];\r\n}\r\n\r\nconst hull = quickHull(points);\r\n\r\n```\r\n\r\n`hull` will contain an array of `Facet`.\r\n\r\n## Delaunay Triangulation\r\n\r\nTo generate the delaunay triangulation:\r\n\r\n```\r\nimport { delaunay } from \"@derschmale/tympanum\";\r\n\r\nconst points = [];\r\n\r\nfor (let i = 0; i < 500; ++i) {  \r\n    points[i] = [Math.random(), Math.random(), Math.random()];\r\n}\r\n\r\nconst triangulation = delaunay(points);\r\n\r\n```\r\n\r\n`triangulation` will contain an array of `Facet`, but of a higher dimension than the convex hull would.\r\n\r\nDelaunay triangulations allow searching for facets containing a point efficiently using the vibility walk algorithm:\r\n\r\n```\r\nimport { visibilityWalk } from \"@derschmale/tympanum\";\r\n\r\nconst pos = [ 0.5, 0.2, 0.7 ];\r\nconst facet = visibilityWalk(pos, triangulation, points);\r\n\r\n```\r\n\r\nWhen a facet has been found, we can calculate the point's barycentric coordinates. The barycentric coordinates can be \r\nused to interpolate values associated to each respective point.\r\n\r\n```\r\nimport { barycentricCoords } from \"@derschmale/tympanum\";\r\n\r\n// for example: every point has an RGB color assigned to it:\r\nlet colors = [];\r\n\r\n// any color at index N is associated with the point at points[N]\r\nfor (let i = 0; i < 5000; ++i) {  \r\n    colors[i] = { \r\n      r: Math.random() * 0xff, \r\n      g: Math.random() * 0xff, \r\n      b: Math.random() * 0xff\r\n    };\r\n}\r\n\r\nif (facet) {\r\n  const bary = barycentricCoords(pos, facet, points);\r\n  const color = { r: 0, g: 0, b: 0 };\r\n  \r\n  for (let i = 0; i < bary.length; ++i) {\r\n    // get the index of the point\r\n    let index = facet.verts[i];\r\n  \r\n    // get the color at that index\r\n    let c = colors[index];\r\n    \r\n    // add the weighted colors together\r\n    color.r += bary[i] * c.r; \r\n    color.g += bary[i] * c.g; \r\n    color.b += bary[i] * c.b; \r\n  }\r\n}\r\n\r\n```\r\n","readmeFilename":"README.md"}