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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13
votes
1answer
629 views

rule-based implementation of an algorithm

When I first started learning about rule-based programming with Mathematica, I tried to translate this algorithm for computing the convex hull of a set of 2-D points in $O(n \log(n))$ time, to use ...
13
votes
1answer
469 views

Cropping a Voronoi diagram

Someone know how can I get the correct crop of this Voronoi image using RegionFunction? As you can see, there is a lot of undesired white regions inside the left ...
13
votes
1answer
465 views

Has anyone implemented cohomology for complex manifolds?

I'm investigating the cohomology of complex manifolds, and need to construct chain complexes, Mayer-Vietoris sequences etc. I use Mathematica for numerically tracing manifolds with geodesics, but ...
12
votes
4answers
362 views

Arranging connector lines

Heike gave an absolutely wonderful answer to my question about arranging subplots around a main plot and including connector lines. This is the result: Starting from Heike's answer, what is the ...
12
votes
2answers
3k views

Graphics3D: Finding intersection of 3d objects and lines

I found these two nice links 1) intersecting graphics 2) Implementation of Balaban's Line intersection algorithm in Mathematica which works for 2d. However, I need to find whether a ray(line) ...
12
votes
2answers
267 views

Possible Bug in DiscretizeRegion with Option MaxCellMeasure

Bug introduced in 10.0.0 and fixed in 10.0.2 Consider the following ImplicitRegion: ...
12
votes
1answer
1k views

Proving inequalities with Mathematica

Question summary: I would like to learn some tips and tricks on how to prove inequalities with Mathematica. I'm studying various inequalities in triangle that have the form $R+ar + bs\geq 0$, where ...
11
votes
3answers
854 views

Finding the surface area of a 3D convex hull

I have noted several instances here and here where ConvexHullMesh, introduced in v10 has been used to greatly simplify some geometry problems. Determining the ...
11
votes
1answer
241 views

Can I get the curvature at any point of a random curve?

Random curve like the above, for example. The data source is an image file. I don't have an expression. I want to start by curve fitting and then compute curvature. Is it possible?
11
votes
2answers
225 views

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

Bug introduced in 10.0 and fixed in 10.2 One nice way to view the new and exciting Mesh objects introduced in Version 10 is by utilizing the function ...
11
votes
2answers
739 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?
11
votes
2answers
425 views

Probable Bug in ConvexHullMesh

Bug introduced in 10.0 and persisting through 10.2 or later Consider points taken from the following parametric plot. See this question ...
11
votes
1answer
376 views

Finding minimal region with padding and linear map to circle

Suppose I have n ordered points. I would like to find a simple region that contains all the points and is close to the smallest region that contains the points except it is smooth and has some ...
11
votes
2answers
304 views

How to make geometric intersection faster for geographic borders?

I have developed a solution to identify geographic regions bordering a region in this post (94723). Can this functionality be made to execute any faster? Find which entities in a set border other ...
10
votes
6answers
3k views

How do I draw a hemisphere?

I want to draw a solid or partially transparent hemisphere above a partially transparent cuboid object in Graphics3D. However, I do not know how to do this s.t. only half the sphere is drawn. Here's ...
10
votes
3answers
419 views

How to find the outline of a country given the imperfect outlines of its administrative subdivisions?

I have a larger outline divided into several regions. While my data represents something else, let us think of this as the provinces/counties of a country, for the sake of simplicity. This is, for ...
10
votes
3answers
3k views

Randomly packing spheres of fixed radius within a cube

How can I have Mathematica randomly place spheres in a cube so they won't overlap? The cube is $20 \times 20 \times 20$, and the spheres have a radius of $0.7$.
10
votes
2answers
181 views

VoronoiMesh without edges

How can I remove the edges of a VoronoiMesh? I would like to display only the closed cells not touching the border of the image. This is my binarized source image (imgbw): I am doing this: ...
10
votes
2answers
209 views

How to convert a surface into a solid

Context I am interested in converting surfaces into solids (so I can make a 3D mesh out of them using ToElementMesh) Say I have the following cool surface ...
10
votes
1answer
178 views

Is DiscretizeRegion not yet ready ro discretize 3D-solids?

In the DiscretizeRegion documentation: "The region reg can be anything that is ConstantRegionQ and RegionEmbeddingDimension less than or equal to 3." With DiscretizeRegion there could be an easy way ...
10
votes
2answers
284 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 ...
10
votes
2answers
137 views

Possible Bug in Computing Surface Area of Certain Geometric Regions

Mathematica 10.2 introduced some new geometric regions. Two of the new regions include SphericalShell and CapsuleShape. ...
9
votes
3answers
2k 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? ...
9
votes
3answers
447 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 ...
9
votes
3answers
662 views

How to ensure that Polygon[list] plots a simple polygon?

Consider the following code which plots a triangle. p = {{0, 0}, {.2, 0}, {0, .2}}; {Cyan, Polygon[Dynamic[p]]} // Graphics Then adding (for example) ...
9
votes
1answer
721 views

Imposing a Periodic Boundary Condition in Nearest Neighbour Search

I am trying to find first nearest neighbour distributions of randomly dispersed point-like objects in an infinite system. To do this I make a finite sized box unit cell with a chosen concentration of ...
9
votes
2answers
360 views

How can I only draw outer common tangent to two circles?

I have code worked for drawing common tangent lines to two circles(http://en.wikipedia.org/wiki/Tangent_lines_to_circles), now I want to delete the inner common tangent lines, how? ...
8
votes
4answers
558 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 ...
8
votes
2answers
730 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: ...
8
votes
1answer
201 views

Decomposition of a semialgebraic set into connected components

Is there any built-in function for doing decomposition of a semialgebraic set into connected components? The only way I now can think of is to use ...
7
votes
5answers
1k views

How to check if a line segment intersects with a polygon?

The naive method is to bisect the line segment iteratively as asked here, and then check the bisection points using How to check if a 2D point is in a polygon?. Would there be an other way? I'm ...
7
votes
3answers
1k views

Generating a non-convex polyhedron from a list of vertex coordinates

I want to include a figure in a paper I am writing on Combinatorial Geometry which features a non-convex polyhedron given by the following vertices, EDIT: I was unaware that Mathematica could convert ...
7
votes
3answers
505 views

I can't understand FindShortest Tour

I can't understand the function FindShortestTour because of the result: FindShortestTour[{ {0, 1}, {5, 1}, {2, 1}, {10, 1}}] ...
7
votes
2answers
3k 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 ...
7
votes
3answers
2k 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 ...
7
votes
2answers
873 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, ...
7
votes
2answers
664 views

Finding concave hull for separated small clusters

Data : data3D = Import[file, "VertexData"]; Graphics3D[Point[data3D]] How to find concave polygon for separated small clusters.
7
votes
2answers
246 views

A question regarding “DiscretizeGraphics”

I want to find the volume of a torus torus = RevolutionPlot3D[{2 + Cos[t], Sin[t]}, {t, 0, 2 Pi}] ...
7
votes
2answers
141 views

How do I get ConvexHullMesh to return polygons instead of triangle as surface mesh?

I would need to identify the types of regular polygons forming the surface of a convex hull of 3D points. If I e.g. take the following example of a regular polyhedron ...
7
votes
1answer
151 views

User-defined DistanceFunction for RegionNearest

In the function Nearest , I can define my custom function using the DistanceFunction option. e.g: ...
7
votes
1answer
184 views

DiscretizeGraphics and BoundaryDiscretizeGraphics Fail on CapsuleShape and SphericalShell

It seems the new Graphics3D primitives have some incomplete features. Earlier, I uncovered a problem with computing their exact surface area see here. Now, I ...
7
votes
1answer
127 views

Why is RegionMeasure so slow when calculating intersection area of a 2D and a 3D object?

If you think this description is too long, you can read the problem directly I know normally when one wants to calculate an region, this guide is useful. However, when it comes to calculating an ...
7
votes
1answer
242 views

Finding corresponding vertex from 3d to 2d

I have this simple 3d data points: ...
7
votes
1answer
250 views

Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
7
votes
2answers
172 views

A method to discretize a three-dimensional solid

Consider the following region: ...
7
votes
1answer
451 views

How to draw quantum circuit with mathematica?

How to draw quantum circuit as the following one with mathematica? I only find the quantum package which is designed for MMA 7.0 as the author said. But the version of my Mathematica is 9.0 and when ...
6
votes
7answers
958 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 ...
6
votes
3answers
4k views

Mathematica function intersection points with 3D grid

I need to produce a 3-dimensional equispaced grid over a given function in a way, that I can calculate intersection points of the function with the grids edges. So my first question is how to produce ...
6
votes
3answers
243 views

Speed of ConvexHullMesh

Pick $N$ random points on the surface of the sphere, then use ConvexHullMesh[] to compute their convex hull. Empirically, this takes time quadratic time in $N,$ ...
6
votes
2answers
220 views

Discretizing regions with pointy boundaries

I'm trying to discretize a region with "pointy" boundaries to study dielectric breaking on electrodes with pointy surfaces. So far I've tried 3 types of boundaries, but the meshing functions stall ...