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Questions tagged [polyhedra]

80 questions
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How to convert the half-spaces that constitute a convex hull to a set of extreme points?

I have a convex set in a Euclidean space (3D, but would like answers for nD) that is characterized by a finite set of half-spaces (normal vector + point). Is there a better algorithm to find the extreme points of the convex set other than compute…
Gyro Gearloose
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Determining if a point is inside a polyhedron

I'm attempting to determine if a specific point lies inside a polyhedron. In my current implementation, the method I'm working on take the point we're looking for an array of the faces of the polyhedron (triangles in this case, but it could be other…
gregghz
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Calculation of centroid & volume of a polyhedron when the vertices are given

Given the location of vertices of a convex polyhedron (3D), I need to calculate the centroid and volume of the polyhedron. Following code is available at Mathworks site. function C = centroid(P) k=convhulln(P); if length(unique(k(:)))
John Smith
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Projecting points from 4d-space into 3d-space in Mathematica

Suppose we have a set of points with the restriction that for each point all coordinates are non-negative, and the sum of coordinates is equal to 1. This restricts points to lie in a 3-dimensional simplex so it makes sense to try to map it back into…
Yaroslav Bulatov
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Smallest Rectangular Box that surrounds a polyhedron

I'm looking for an algorithm that finds the smallest box enclosing a polyhedron. My idea is as follows: find the largest side, and move the solid so that side aligns with the x axis. Find the next largest side that meets this side, and align it as…
Charles Taylor
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How do I determine if a polyhedron is convex?

I'm looking for an efficient algorithm that determines if a polyhedron is convex. I started by checking that the Euler characteristic is 2. And I'm also checking that every face is convex. But that still doesn't catch a lot of cases.
Charles Taylor
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Delaunay triangularization of Polyhedron (Python)

I'm trying to get the Delaunay Triangulation of a polyhedron in python so that I can calculate the centroid. I see that there is a Delaunay function in scipy.spatial and that it works in n-dimensions. The trouble is that the documentation shows 2D…
Steven Walton
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How to Combine Polyhedra?

Suppose I have a 2 Polyhedrons, partially overlapping in space. Each is defined by a list of connected Polygons, which in turn are defined by lists of line segments, (which are defined by 2 points). Is there a simple algorithm for creating the…
Charles Taylor
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MATLAB: Calculate volume of concave polyhedron from set of scattered 3D points

I have 20 to 30 randomly generated 3D points as vertices from which a polyhedron is defined. I have tried using DelaunayTri(points) to enumerate the facets and use the determinant of the cross product to calculate and sum the tetrahedral volumes,…
Slaiyer
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What is the *fastest* algorithm for detecting intersection between polyhedra?

Say there are n 3-dimensional objects (polyhedra). Is the fastest way to calculate the intersection of all objects O(n ^ 2)? Right now, I'm using a library that essentially forces T(n) to equal n ^ 2: for each object: // there are n objects get…
user3745189
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Exact Medial Axis, Surfaces, Skeletonizations of 3D Polyhedra

I am interested in finding software to compute the exact medial axis (or your term of choice!) of a 3D polyhedra. I imagine the output would be a list of triangular faces, possibly edges, and vertices, representing the junctions, sheets, and seams…
user695322
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calculating outward normal of a non-convex polyhedral

If all nodes of a polyhedron (may be non-convex) and their coordinates are known, the points of a face are given in order (anti-clockwise or clockwise around the outward normal), how do I obtain the outward normal vector of each face? Here is a…
Y. Zhong
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OpenGL Icosahedron Texture Mapping

I've got currently no solution for texture mapping an icosahedron without a seam from pole to pole. The texture mapping of this primitive seems to be a common problem, which is not completely solved yet. I've made a lot of research and I've tried a…
Stephan
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Given set of points, how to generate polyhedron in Javascript

I am doing a WEBGL visualization project in material science. What I am trying to accomplish right now is that, I have a set of 3D coordinates of atoms. They are bonded together. I would like to create a polyhedron for each molecule. I noticed that…
Randolph Zeng
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How do I break a polyhedron into tetrahedra in MATLAB?

I have a polyhedron, with a list of vertices (v) and surfaces (s). How do I break this polyhedron into a series of tetrahedra? I would particularly like to know if there are any built-in MATLAB commands for this.
Graviton
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