tetrahedra | 易学教程

How to draw a Tetrahedron mesh by matplotlib?

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问题 I want to plot a tetrahedron mesh by matplotlib , and the following are a simple tetrahedron mesh: xyz = np.array([ [-1,-1,-1], [ 1,-1,-1], [ 1, 1,-1], [-1, 1,-1], [-1,-1, 1], [ 1,-1, 1], [ 1, 1, 1], [-1, 1, 1]], dtype=np.float) tets = np.array([ [0,1,2,6], [0,5,1,6], [0,4,5,6], [0,7,4,6], [0,3,7,6], [0,2,3,6]], dtype=np.int) Of course, in practical applications, the number of tetrahedrons in a mesh can be large. I can't find any useful help information in google. So what is the better way to

Large, mostly empty data structure for tetrahedron faces

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问题 I'm trying to link the node id of every face in a tetrahedron with it's corresponding tetra id. tetras = [1 2 3 4 % Tetra 1 5 6 7 8] % Tetra 2 For tetra 1, there are four faces: faces = [1 2 3; 1 2 4; 1 3 4; 2 3 4] % Notice these are sorted Then I'd like to store these in a data structure: tet_for_face = cell(8,8,8) % 8 allows for the maximum node id tet_for_face{1,2,3} = 1; tet_for_face{1,2,4} = 1; tet_for_face{1,3,4} = 1; tet_for_face{2,3,4} = 1; This means that I can find the tetra ID of

Barycentric coordinates of a tetrahedron

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I would like to ask for help regarding barycentric coordinates of a tetrahedron: Following an approach I found here: http://www.cdsimpson.net/2014/10/barycentric-coordinates.html i implemented a C++ function for finding barycentric coordinates of a point in a tetrahedron: float ScTP(const Vec &a, const Vec &b, const Vec &c) { // computes scalar triple product return Dot(a, Cross(b, c)); } Vec4f bary_tet(Vec3f a, Vec3f b, Vec3f c, Vec3f d, Vec3f p) { float va, vb, vc, vd, v; Vec3f vap = p - a; Vec3f vbp = p - b; Vec3f vcp = p - c; Vec3f vdp = p - d; Vec3f vab = b - a; Vec3f vac = c - a; Vec3f

Barycentric coordinates of a tetrahedron

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问题 I would like to ask for help regarding barycentric coordinates of a tetrahedron: Following an approach I found here: http://www.cdsimpson.net/2014/10/barycentric-coordinates.html i implemented a C++ function for finding barycentric coordinates of a point in a tetrahedron: float ScTP(const Vec &a, const Vec &b, const Vec &c) { // computes scalar triple product return Dot(a, Cross(b, c)); } Vec4f bary_tet(Vec3f a, Vec3f b, Vec3f c, Vec3f d, Vec3f p) { float va, vb, vc, vd, v; Vec3f vap = p - a;

How to check whether the point is in the tetrahedron or not?

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问题 I know all coordinates of tetrahedron and the point I would like to determine. So does anyone know how to do it? I've tried to determine the point's belonging to each triangle of tetrahedron, and if it's true to all triangles then the point is in the tetrahedron. But it's absolutely wrong. 回答1: You define a tetrahedron by four vertices, A B C and D. Therefore you also can have the 4 triangles defining the surface of the tetrahedron. You now just check if a point P is on the other side of the