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

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11
votes
2answers
155 views
11
votes
2answers
342 views

Implementing an algorithm for finding the largest circle that contains a single point in a set (and no other point)

This question concerns the implementation of an algorithm proposed by Rahul Narain on a former question of mine that was migrated to math.stackexchange: ...
18
votes
2answers
288 views

Object separation from a 2.5D surface

I'm trying to identify the shape and the boundaries of objects. The data was generated with a laser scanner and represent the surface of an area in which many boulders lay on the ground and making up ...
3
votes
5answers
195 views

Ordering the Boundary points of a Polygon

I feel like this should be simple, but I keep running into walls. Say someone gives you the coordinates of the vertices of a pentagon and the center point of the hexagon. Is there any way to get an ...
4
votes
3answers
436 views

How to create a planar graph from a set of random points

Question Given a set of points in the plane, how can you create a planar graph in the standard graph representation of Mathematica (version 9 or higher), from these points? Background A planar ...
8
votes
2answers
252 views

Torus triangulation

I'd like to plot something similar to this but with a triangle instead of a pentagon. Also, I'd like to triangulate the faces, that is, to insert the diagonals for each face of the 3 prisms used. In ...
5
votes
1answer
89 views

Numerical Functions Compatible with Regions Fail with MeshRegions and BoundaryMeshRegions

Given a MeshRegion: region = DelaunayMesh[RandomReal[1, {50, 3}]] We can numerically ...
7
votes
3answers
1k views

How to check if a 3D point is in a planar polygon?

Following up on ndroock1's question, I naively tried to apply the solutions to a 3D point and polygon and they didn't work. For example, functions involving ArcTan ...
14
votes
3answers
1k views

Checking if a point is in a convex 3D polyhedron

Extending from these questions How to check if a 3D point is in a planar polygon? and How to check if a 2D point is in a polygon?. I'm trying to do this to render specific shapes made up of spheres. ...
0
votes
2answers
234 views

Integrating polynomial functions over polytopes with an add-on package

There is a Mathematica package to evaluate integrals over polytopes: http://library.wolfram.com/infocenter/Books/3652/ In the documentation (Functions.nb file) I ...
3
votes
0answers
90 views

Convex hull of a large data set of 3D points

I recently needed to deal with a large data set of 600.000 points in three dimensions. My task was to find a convex hull for this data. I have Mathematica 10, so I could use the function ...
5
votes
2answers
707 views

Extracting polygons from 3D contour plot surface

Edit: This question turned out to be two parts so I am going to make this question about only the first part a kguler provided an excellent answer. Here is a better representation. My actual data ...
5
votes
6answers
280 views

Choosing $n$ equidistant points on a circle with given radius and center

I would like to have a function circle which takes two inputs: a tuple {x,y} and a real number ...
16
votes
4answers
706 views

How to determine the convex hull of some text?

How can I get the co-ordinates of the convex hull of a piece of Text?
16
votes
4answers
1k views

How to get actual triangles from DelaunayTriangulation[]?

The ComputationalGeometry package has a DelaunayTriangulation[] function. It returns a list of points connected to each point, ...
5
votes
2answers
470 views

Voronoi Diagram: Displaying site specific color in a voronoi diagram

I am using Voronoi Poligonization as a support form simulating island erosion; my data are the output of VoronoiDiagram, ...
2
votes
1answer
109 views

RegionPlot3D run forever when plotting 3D ParametricRegion

when working with 2D, RegionPlot works fine with ParametricRegion as can be seen in this example: ...
10
votes
3answers
1k views

Create triangular mesh from random list of points

I have a list of points. I would like to take these points and create a mesh of triangles from them, making sure triangles don't overlap. So here's a list of points: ...
1
vote
1answer
120 views

Is it necessary to introduce ImplicitRegion and ParametricRegion in version 10?

In version 10.0, Mathematica introduced a new function about region plotting: ImplicitRegion. But I'm wondered that haven't this function been already existed in the older version? That is, ...
10
votes
2answers
193 views

How can I decide whether a closed surface is intersected by a triangle?

A closed surface consisted of Polygons or GraphicsComplex and a triangle made by 3 points are in a 3D space. How can I decide ...
4
votes
1answer
96 views

Problem with clipping of tick labels

Please look at Show[DiscretizeGraphics[Graphics3D[{Cone[]}]], Axes -> True, Boxed -> True] Well, there are some ...
11
votes
2answers
435 views

Finding the perimeter, area and number of sides of a Voronoi cell

Does anyone have any suggestions how to determine the perimeter, area and number of sides of each Voronoi cell in Voronoi diagram?
15
votes
1answer
920 views

Faster way to compute the distance from a point to a surface in 3D

I am trying to compute the shortest distance between a point and a triangle in 3D ...
6
votes
2answers
2k views

Delaunay Triangulation for 3D Surface Data

I want to do a Delaunay triangulation on scattered 3D surface data. Mathematica itself does it only for 2D through the command DelaunayTriangulation[], which gives ...
10
votes
1answer
100 views

Possible Bug in DiscretizeRegion with Option MaxCellMeasure

Consider the following ImplicitRegion: reg = ImplicitRegion[x^2 + y^2 + z^2 == 16, {x, y, z}]; We can discretize it using ...
0
votes
0answers
6 views

Term For Rotating 3d Vectors About a Pivot Point [migrated]

What is the term for Rotating a 3d Vector about another 3d Vector (Pivot Point)? For example; if I want to move X distance from one point towards another point - the mathematical term for this ...
5
votes
1answer
198 views

Difference (or intersection) of two convex polyhedra

I have two convex polyhedra stored in the following form: a set of vertices vertices = {{x1,y1,z1},...}, a set of faces, where each face is a convex polygon ...
4
votes
1answer
112 views

How do I get a MeshRegion from an obj file, or from Geometry3D

How do I read in an obj file as a MeshRegion so I can e.g. compute its area? If I just import the object and try Area[O] it ...
7
votes
4answers
421 views

Distances between points in periodic cube

How can one implement more efficiently/elegantly/memory savvily the following function which returns a matrix of all Euclidian distances between points in 3D within a cube of width ...
4
votes
1answer
123 views

How can one compute a 3D Periodic Delaunay Triangulation using DelaunayMesh?

Given a non-periodic point set, one can easily tetrahedralize it using the new (in V10) DelaunayMesh function. e.g.: ...
6
votes
1answer
97 views

User-defined DistanceFunction for RegionNearest

In the function Nearest , I can define my custom function using the DistanceFunction option. e.g: ...
7
votes
2answers
121 views

Probable Bug in HighlightMesh with 2D Convex Hulls created via ConvexHullMesh

One nice way to view the new and exciting Mesh objects introduced in Version 10 is by utilizing the function HighlightMesh, so ...
0
votes
0answers
66 views

How to make equidistant or split ListPoint [duplicate]

How to split the curve with more equidistant points? ...
5
votes
3answers
327 views

How to measure cross sectional area of Tube

I have modified my question to a simple version. I have vertex clusters, polygons and a list of center points. Attached pts and polygons of 3d tube are: ...
3
votes
3answers
603 views

How to integrate a function over a 3D planar polygon?

I am trying to integrate a function over a planar polygon in 3D. In 2D, this is fairly straightforward, using either answer from this question (I use the second answer). If we use an equilateral ...
3
votes
1answer
228 views

How to map vertex points from the surface of a straight pipe onto 2D plane

How to map vertex points from the surface of a straight pipe onto 2D plane. The 3D surface points of the straight pipe can be found here: data Working code: ...
6
votes
2answers
399 views

How to get UV mapping of 3D tube

Here is cylinder data: file We can mesh the surface, thanks to lalmei, Belisarius and Simon (link) How to achieve uv mapping from a 3d straight and curved tube? Working code: ...
6
votes
2answers
139 views

“The function DiscretizeGraphics is not implemented for GraphicsComplex” confusion

Why does DiscretizeGraphics seems to work on one GraphicsComplex and not the other? Here is an example that works: ...
18
votes
4answers
807 views

How to calculate the volume of a convex hull?

Given a spatial curve represented by a parametric equation, is it possible in Mathematica 9 to calculate symbolically (or at least numerically) the volume of its convex hull?
2
votes
1answer
82 views

How to draw a 3D convex hull of a set of points with styling

I´m trying to obtain the convex hull (with transparent faces) of a small number of points. I would like the Plot to have the points shown with small spheres numbers 1, 2, 3, ... along the axes ...
11
votes
2answers
288 views

Probable Bug in ConvexHullMesh

Consider points taken from the following parametric plot. See this question ...
2
votes
1answer
82 views

About TetGenTetrahedralize Mesh Size

I have used TetGenTetrahedralize to generated a cubic mesh. I want that the edge size of the triangle to be 0.2, how can realized this? And What does the word "pq1.414a1" mean? inst1 = ...
6
votes
1answer
108 views

Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
2
votes
2answers
134 views

Are there built-in functions for testing if a point lies within Graphics3D primitives?

I noticed in this question, Behavior of Graphics`Mesh`InPolygonQ with self-intersecting polygons, that Mathematica has some "psuedo-hidden" functionality for allowing one to quickly perform a winding ...
8
votes
3answers
953 views

Convex hull of a 3D object?

I am trying to find a convex hull command for a Graphics3D object. Does it exist in Mathematica? ...
21
votes
4answers
2k views

Efficiently determining if 3D points are within a surface composed of polygons

This is the 2nd part of a previous question which I edited to make into 2 separate questions: Extracting polygons from 3D contour plot surface As an extension of my earlier question involving simple ...
1
vote
0answers
123 views

How to define two polyhedron intersect or not?

Recently I have used Mathematica to simulate the concrete structure. The most important point is generate random concrete aggregate. As you know, concrete aggregate can be looked as a polyhedron. We ...
3
votes
1answer
99 views

What kind of object results from RegionIntersection function?

I'm trying to use RegionIntersection in a couple of Polygons. The polygons are the following: ...
1
vote
0answers
67 views

Death of parallel sub-kernels

EDIT : Finally, the new Mathematica 10.0 seems to fix it. I have a little parallelization problem. I wrote a code to generate a quasicrystal by dynamical generation. Here the code: ...
21
votes
5answers
952 views

How can I define a 3D version of the built-in VoronoiDiagram (VoronoiMesh in V10) function?

Can anybody point me in a direction that will guide me to extend the VoronoiDiagram function in Mathematica to handle 3D (three dimensional) situations (i.e. points in 3D)? Any help will be greatly ...