Questions tagged [computational-geometry]

Questions on constructing graphical objects using relatively complex computations relating to the mathematical structures defining those objects. Examples include convex hulls, Voronoi diagrams, Delaunay triangulations, mathematical constructions, symmetries, genuses of curves and graphs and programmatic constructions of polyhedra.

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Intersection Region of two Conic Hull

I have the following semi-infinite conic hull, r1=ConicHullRegion[{{0,0,0}},{{-1,0,0},{0,-1,0},{1,0,1}}]; r2=ConicHullRegion[{{0,0,0}},{{-1,0,0},{0,-1,0},{0,1,1}}]; ...
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1answer
71 views

Create concentric circles with numbers inside

Hello there if you can give me a hand I want to create and export to pdf the following figure, which if you realize forms the multiplication table. The idea is to be able to control the central number ...
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2answers
286 views

Cube cutting problem

Show[Graphics3D[{Cuboid[]}], ContourPlot3D[{x==1/3,y==1/4,z==1/5},{x,-0.2,1.2},{y,-0.2,1.2},{z,-0.2,1.2}]] Three planes divide the unit cube into 8 small cubes, ...
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Does Mathematica have a built-in n-dimensional hypervolume indicator?

Mathematica has so many functions hidden away in obscure packages that I thought I'd ask before starting to code one myself. Thanks in advance.
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4answers
324 views

Speed up the intersection of the diagonals of a regular polygon

I need to calculate all the intersection points of the diagonals of a regular polygon, following code is really slow, when n=15, it take about 30sec. I also tried using ...
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1answer
118 views

Checking Membership in Boundary of Conical Hull

I want to check whether a given point is also a member of the edges of a given conical hull. For example, I have: ...
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0answers
34 views

Increase precision of ConvexHullMesh

I want to generate a set of equations for all planes in the convex hull as specified in this question. The problem is that the generated set of equations don't correctly cover all the points. I run a ...
4
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1answer
85 views

Find intersection points of arbitrary BSpline curve

I'm researching some computational geometry and am trying to find a method of determining the {x,y} intersection of a circle and BSplineCurve for further processing. ...
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2answers
88 views

How to find the shortest distance between two regions?

I need to find the shortest distance between the two regions and the two points of the shortest distance, but the following code cannot achieve this requirement: ...
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0answers
31 views

Dump Curvature Information for 3d Models

Is anyone aware of any utility to generate and dump Principal, Gaussian and Mean Curvatures for a 3D Model or a set of points? I have reserched following tools - meshlab cloudcompare They are able to ...
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1answer
63 views

For an enclosed surface region, how to find the furthest point on that surface to another point that is not on that surface?

I have an enclosed 3D surface (a distorted sphere surface region, which is got by finding an enclosed contour of a 3D volumetric data, and apply RegionBoundary[BoundaryDiscretizeGraphics[ ]] to get ...
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0answers
68 views

Find the intersection coordinate of a line and a 3D surface defined by a contour plot

I have two points, for instance {1, 1, 1} and {10, 11, 15} that connected to form a line. I also have an enclosed surface region ...
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2answers
202 views

How to fill in interior in a mesh region

Say I have a mesh region which encloses a region. How do I get a mesh region where this region is filled? Take for example the meshregion below: ...
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2answers
80 views

Finding plane equations of planes in a convex hull

I'm new to mathematica and I need to get the equations for the set of planes which are part of a convex hull that I have calculated using ConvexHullMesh. It is a ...
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2answers
464 views

Finding the intersection(s) of a 3D parametric surface and a line

I have some 3D parametric curve par and some line line. I want to find parameters u,v and t for the intersection points of par and line. I tried to do that with NSolve in many different ways and ...
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0answers
46 views

Why does ConvexHullMesh give inconsistent output stuctures?

I know much of the stuff in ConvexHullMesh needs some TLC convexhullmesh-inconsistency But, can anyone see why this would produce inconsistent output: Case 1 (expected behavior): ...
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1answer
58 views

How to modify a particular step length in a 3D random walk?

Suppose I simulate a random walk in 3D using AnglePath3D[]: ...
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0answers
27 views

How to reorient a Sphere[] and associated point based on some arbitrary axis?

Suppose I have a unit Sphere[] sitting at the center {0,0,0}, with a point on its "north pole", like this one: ...
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1answer
46 views

VoronoiMesh with boundary edges removed

I would like to create a Voronoi diagram without the boundary edges highlighted. This code gVD = VoronoiMesh[X, MeshCellStyle -> {{1, All} -> {Thick, Red}}] ...
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1answer
113 views

Drawing a “realistic” VoronoiMesh

Consider a set of points generated via Lloyd's relaxation algorithm ...
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0answers
39 views

An apparent bug in Geometry`ConvexHull2

I was replacing some usages of Geometry`ConvexHull2 with ConvexHullMesh and found one of my tests failing. It turned out the ...
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1answer
50 views

Generating points inside convexhullmesh

How could I generate these points hexagon={{0, Sqrt[3]/2}, {1/2, Sqrt[3]}, {3/2, Sqrt[3]}, {2, Sqrt[3]/2}, {3/2, 0}, {1/2, 0}} following this rule ...
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2answers
70 views

How to Parallel submit nested do loop

This is the first time I'm trying to parallel compute something on Mathematica. So this question might be silly. I have a nested Do loop of the form: ...
3
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1answer
75 views

Hyper Tetrahedron in terms of inequalities

The command Tetrahedron[] seems to work fine for the 3-d case. But how can we get hyper-tetrahedron for 4-d case in terms of inequality? Take for example the points: ...
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1answer
70 views

Region bounded by planes in terms of inequalities

Suppose I have 5 planes that intersect to give a bounded region in 4D. For example, the planes are x1==0; x2==0; x3==0; x4==0; x1+x2+x3+x4==1; ...
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1answer
46 views

Convert ConvexHull in a array to Inequality

This question is in continuation with the previous post Convert ConvexHull to Inequality There are two problems that I faced. Suppose we have two or more convex hull defined using an array R[i], like ...
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1answer
187 views

Convert ConvexHull to Inequality

I have the following convex hull. P0={0,0,0}; P1={1,0,0}; P2={0,1,0}; P3={0,0,1}; ConvexHullMesh[{P0,P1,P2,P3}] Now I want the region algebraically as equality ...
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0answers
39 views

Image Size change with changing ViewPoint

I have the following code to show the intersection of two convex hulls. The plot has no problem when ViewPoint->Default. But when I try to change the viewpoint manually by holding and dragging the ...
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1answer
43 views

How to label vertex of a 3D convex hull?

I have the following code to plot a 3d convex hull with 4 corners only. ...
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3answers
70 views

A DistanceFunction for use with a mouse in a DynamicModule

I need to have a mouse cursor that identifies points that are close to the mouse position on a graphics plot. The difficulty is that the scaling of the plot makes this difficult. I think I am missing ...
7
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1answer
121 views

RandomPoint inside mesh for walk-on-spheres Monte Carlo PDE solver

I'm trying to understand a Monte-Carlo Laplace/Poisson PDE solver: http://www.cs.cmu.edu/~kmcrane/Projects/MonteCarloGeometryProcessing/paper.pdf This method inspired by random-walks and ray-tracing ...
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0answers
37 views

DelauneyMesh in 4d and higher

Is there any way to find the DelauneyMesh in 4D (or higher)? Its documentation implies that it should be possible "A Delaunay mesh consists of intervals (in 1D), ...
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0answers
82 views

Periodic Voronoi Mesh in a box

Is it possible to generate a periodic Voronoi Mesh inside a rectangular domain? I would also like to obtain the coordinates of each cell separately so that I can perform further operations on each ...
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2answers
400 views

How to add 'border' to Voronoi diagram

Suppose I have a set of points pts, from which I generate a Voronoi diagram VD: ...
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2answers
322 views

Finding shadow area of a 3D object

Given a 3D object, how could one find the area of the shadow? In effect, this is a measure of optical cross section. The ultimate goal would be a table showing latitude, longitude, and, optical cross ...
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2answers
70 views

How to speed up finding region centroid and plot3d

I have the following code to make 3D of 9 regions. ...
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0answers
36 views

How to find intersection of higher dimensional convex hull?

I have often used ConvexHullMesh to obtain a convex hull for 2-d and 3-d points. But when I try to find it for 4-D points I encounter error even for simple cases. <...
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1answer
65 views

Represent a Concave Mesh Volume

I programmatically generate a shape, where the top surface is defined by a series of polygons. I generate all the points of the polygon. ...
2
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1answer
129 views

Periodic boundaries for a 3D walk in a Bravais lattice?

I'm using a Bravais lattice, 'face-centered', which is implemented in Mathematica in LatticeData[]. I want to simulate a random walk over neighboring points using ...
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0answers
14 views

How to concatenate multiple `CapsuleShape[]` while changing their size?

I am trying to create a 'chain' of capsules so that they are concatenated at certain points. Then, I want to change the size (radius, etc) of a given capsule, while preserving the relative orientation ...
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0answers
76 views

Projecting a 3D mesh region to 2D

How do I project a 3D MeshRegion to a 2D MeshRegion (or equivalent for a BoundaryMeshRegion). This question is similar to ...
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2answers
338 views

Shading Intersection Region

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1answer
31 views
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0answers
40 views

Boxed Convex Hull

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0answers
47 views

Convex Hull Mess Axis Label

P0={0,0}; P1={1,0}; P2={-1,0}; R[1]=ConvexHullMesh[{P0,P1,P3},Axes->True ] I use this code to draw the convex hull but I want to also label the ...
2
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1answer
64 views

How can I calculate volume of such a MeshRegion Object

The Data is here: meshData === PolygonData is here ...
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0answers
94 views

How to use Mathematica to find the coordinates of 7 points?

Could anyone please help me with using Mathematica to find the coordinates of 7 equally spaced points on the unit sphere $S^3$ in $\mathbb{R}^4$? Thanks a lot!
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0answers
34 views

Torus Hex Mesh - Need Unique Hex Dimensions

I'm looking to laser cut a bunch of hexagons and assemble them into a torus (using hot glue or tape). How do I get the dimensions of the individual unique hexagons? I've seen Create a torus with a ...
6
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2answers
110 views

Penalty function on discrete mesh using Laplace-Beltrami operator?

Context I am interested in extending to the ill-condionned regime the inversion of linear equations arising from inverting differential equations which have been solved via 0-splines over a mesh ...
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1answer
47 views

Finding an instance of a parametric equation that intersects given points

So I have this equation for a circle centered at the origin that has some orientation in 3D space. ...

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