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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3
votes
2answers
85 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
62 views

How to make equidistant or split ListPoint [duplicate]

How to split the curve with more equidistant points? ...
5
votes
3answers
281 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: ...
2
votes
1answer
71 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 ...
10
votes
2answers
258 views

Probable Bug in ConvexHullMesh

Consider points taken from the following parametric plot. See this question ...
2
votes
1answer
74 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
89 views

Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
1
vote
0answers
120 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
88 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: ...
6
votes
2answers
109 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: ...
0
votes
0answers
57 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: ...
6
votes
1answer
157 views

Finding corresponding vertex from 3d to 2d

I have this simple 3d data points: ...
5
votes
1answer
170 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 ...
2
votes
1answer
84 views

Find area of polygon on a sphere from a set of latitude-longitude points

Given a list of latitude and longitudes say ...
1
vote
1answer
72 views

how to find iso-cost contours on a 2d plot efficiently

Consider a 2D plot in which dimension 1 and 2 represent quantity 1 and 2 respectively ranging over 0 to 100. Each point in the space corresponding to (x,y) represent cost of choosing quantity 1 as x ...
6
votes
2answers
359 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: ...
3
votes
1answer
225 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: ...
5
votes
1answer
101 views

How to create bounded diagram plot?

I have set of points: ...
2
votes
0answers
38 views

Voronoi diagram for line segments in Mathematica [duplicate]

I know that mathematica has built in functions for creating triangulations and Voronoi diagrams. However I haven't found a function that would create a Voronoi diagram for line segments. Is there a ...
1
vote
0answers
69 views

Trying to study the three points theorem of the Mobius Transformation

I am trying to study the three points theorem of the Mobius transformation. This theorem says that the Mobius transformation $M$ maps three distinct points p, q, r to three distinct points p', q', r'. ...
3
votes
1answer
92 views

Problem with PlanarGraphPlot And ConvexHull

I'm getting a lot of strange errors when using PlanarGraphPlot with a simple list of 11 points. This is using Mma 9.0.1 64-bit Mac OS X. ...
2
votes
2answers
298 views

Image processing: extracting ordered contour

Continuing the question How to extract the edge from a set of points and its answer by Simon Woods, I would like to ask if there is a way to extract the boundary of obtained as ...
0
votes
1answer
141 views

Area of a convex polygon with a set of points [duplicate]

I have a set of points Pts[a_,b_,c_]:={{a, b}, {b, a}, {c, a}, {a, c}, {b, c}, {c, b}} which define a convex polygon and I would like to find its area. There is ...
4
votes
4answers
210 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 ...
2
votes
0answers
219 views

Visualising Special Relativity

Mathematica newbie learning by doing (or not so far, in this case). Problem: Special Relativity - consider two inertial frames $A$ & $A'$ in relative motion. At a time $t0$ as measured in $S$, ...
-6
votes
1answer
112 views

Poincaré section for 3BP

I try to plot the Poincaré section for the 3BP i use the following code that works very well: ...
1
vote
2answers
136 views

intersection between function and plane

I try to solve a ODE system of equations and i want to plot the intersection of the 3D solutions with a costant plane. To do this i use the follow code: ...
2
votes
0answers
137 views

4 circular arcs, how plot the minimal surface?

By using Sjoerd de Vries code for circular arcs: ...
27
votes
3answers
1k views

Create a torus with a hexagonal mesh for 3D-printing

I am new to Mathematica, and I'm looking for a way to create patterns on the surface of 3D objects. One thing I have not been able to do is create a hexagonal mesh on a torus. What I would like to ...
2
votes
1answer
233 views

Bounded Voronoi Diagram

I am trying to compute a Voronoi diagram bounded by a box. In some cases, the points used to compute the diagram form a diagram such that at least two boundary points are within the same polygon. For ...
3
votes
6answers
397 views

How to find the vertices of a regular tetrahedron? a dodecahedron?

My question is: how to find the coordinates of the vertices of regular tetrahedron and dodecahedron? I tried to find the coordinates of the vertices of a regular tetrahedron as the solutions of a ...
3
votes
0answers
152 views

How to get vertices of a polytope given by equalities and inequalities?

I have a polytope given by some equalities and inequalities, how can I get all the vertices of the polytope? If there's a way to deal with the one given by inequalities only, how can I reduce the ...
3
votes
1answer
89 views

BoundedDiagram Error

Although BoundedDiagram function worked well for a small data set, I got errors in a specific case that I cannot explain. I am sorry I am pasting here a large list ...
2
votes
2answers
119 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 ...
2
votes
1answer
209 views

Calculate scalar potential from electric field

Is it possible for Mathematica to solve an equation like $\nabla f(\mathbf{r}) = - \mathbf{E}(\mathbf{r})$ for $f(\mathbf{r})$? I tried ...
4
votes
1answer
216 views

ListPlot3D of a set of points in a non-convex region

I would like to plot a set of points in the same style as ListPlot3D does, but only in a non-convex region that I can specify (e.g. using a ...
3
votes
2answers
199 views

Selecting for 2D points that are within a threshold distance of an upper- and lower-bound number of points

I have a very large set of 2D points: numberOf2DPoints = 10^6; pointList = RandomReal[{0, 1000}, {numberOf2DPoints, 2}]; I'd like to find a way to quickly ...
5
votes
1answer
156 views

Finding an optimal overlay of two point clouds

Imagine I have two sets of points: ...
5
votes
1answer
262 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 ...
10
votes
3answers
487 views

Insphere for Irregular Tetrahedron

I am looking for existing Mathematica code to compute the unique sphere inscribed inside an irregular tetrahedron. I can write it myself, but I would love to find that someone already performed this ...
4
votes
1answer
74 views

Error from BoundedDiagram

I cannot understand the meaning of the error BoundedDiagram::notuniq: BoundedDiagram requires that boundary vertices lie in unique Voronoi polygons. >> BoundedDiagram::nobd: Bounded ...
5
votes
1answer
330 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, ...
15
votes
3answers
676 views

Generate a Random Polygon

Does some package exist with a function that takes a parameter $n$ and generates a random 2D $n$-sided simple polygon (convex or non-convex), possibly within a certain bounding box? It does not ...
5
votes
1answer
174 views

Behavior of Graphics`Mesh`InPolygonQ with self-intersecting polygons

Playing around with some of the answers in the question How to check if a 2D point is in a polygon? I noticed that: Graphics`Mesh`InPolygonQ[poly,pt] Displays ...
1
vote
1answer
139 views

Complex surface: Finding the perimeter of the union of multiple disc intersections

Consider a system of $N$ circles($N>40$) Each of radius $5$ and the center of these circles along a circle at origin of radius $3$ [as given in code]. Code for above description :- ...
7
votes
1answer
260 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: ...
3
votes
0answers
163 views

Generating an obstacle-avoiding closed-curve with a fixed perimeter and a target area

I was wondering if there was a neat way to solve the following problem in Mathematica v9 - Provided a binarized image (where we call black pixels "obstacles" or vice versa, whichever is most ...
4
votes
2answers
192 views

How to use a ConvexHull as RegionFunction?

I have a set of data supported over a region in 2D. I want to use RegionPlot and ContourPlot on interpolations of my data, but want to restrict the Plots to the region over which my data is supported. ...
0
votes
1answer
154 views
0
votes
0answers
25 views

Pruning a list of points to find the largest clique of points with a minimum threshold point-to-point Euclidean distance [duplicate]

I have a array of points (which we'll just create randomly here): pointList = Table[{RandomReal[{0, 5}], RandomReal[{0, 5}]}, {i, 1, 100}]; I'd like to find the ...