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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 ...

3
votes
1answer
86 views

Generate convex-hull of a 15 dimensional space

This question follows my last post. I have a function $ \vec{f}: S^6 \times S^6 \rightarrow \mathbb{R}^{13} $ defined on two 6-dim hyperspheres. We will denote the function $ \vec{f}(\vec{x},\vec{y}) ...
2
votes
2answers
53 views

Vertices of a Rotated Polyhedron

I am attempting to geometrically transform a polyhedron (namely rotate and translate the polyhedron in global coordinates) and than find the new vertices. Here is what I have so far, but I am stuck at ...
0
votes
0answers
38 views

How to write the code for a general B-spline function?

I write the code for B-spline basis and it works very nicely but now I need help to write code for general B-spline functions I would like the code to show the spline segment in this way:
6
votes
2answers
265 views

How do I verify a vector identity using Mathematica?

I am trying to verify well known Frenet–Serret formulas in general setting using Mathematica. I need to consider a general space curve $r(s)=(x(s),y(s),z(s))$ in $\mathbb{R}^3$ and define its unit ...
8
votes
2answers
98 views

Speeding up Nearest with multiple distance thresholds

Consider the following example of using Nearest: ...
4
votes
2answers
98 views

How to make a frustum of a cone

For finite element purposes I need a frustum of a cone with a finite wall thickness, i.e. a tapered pipe. To make a cone is easy ...
2
votes
1answer
60 views

Finding Intersections Between Arbitrary Surface and A Line

I have a self-intersecting surface H defined as follows: ...
0
votes
1answer
77 views

Why is RegionIntersection failing on my custom Region?

I load a custom region, specified as BoundaryMeshRegion R = Import["C:\\data\\Profile.stl", "BoundaryMeshRegion"] and I try ...
1
vote
1answer
57 views

ImplicitRegion evaluates the region incorrectly when it must be empty

Consider the following implicit region: ...
8
votes
2answers
119 views

Relative Neighbourhood Graph

Is there some way to efficiently compute the relative neighbourhood graph on $n$ Euclidean points in $\mathbb{R}^{d}$? Though one can simply define ...
3
votes
1answer
47 views

Extract Halfspace representation of a ConvexHullMesh

I have computed the convex hull of a set of points in $\mathbb{R}^{n}$ using ConvexHullMesh. This describes a convex polytope $\mathcal{P}$. I was wondering if there is any easy way of getting a ...
0
votes
0answers
85 views

How to evenly distribute points inside a sphere?

SpherePoints[] gives me a fairly even distribution of points on the surface of a sphere. However, following this, I can have a much better distribution (although ...
5
votes
3answers
112 views

How to get size of each polygon of a Voronoi diagram using Shoelace formula?

The following code gets all vertices of all polygons (mesh cells) of VoronoiMesh[pts]: ...
7
votes
3answers
181 views

Draw circles and compute <sum of circle areas>-<area of overlaps of the circles>

The following code draws the polygons of VoronoiMesh[pts]: ...
8
votes
2answers
129 views

Detect and fix invalid polygon

I have a polygon given by ...
6
votes
0answers
67 views

Higher order Laplacian flows

Given disjoint surfaces $q_i$ in 3D and their 1D boundary curves $\partial q_i = \gamma_i$, I seek a surface $p$ that joins the $q_i$, where $p \cup q_i$ forms a (piecewise) $C^k$ surface that ...
11
votes
5answers
480 views

Evenly spaced points on boundary of polygon

I have a polygon and I would like to generate $n$ evenly spaced points along the boundary.
5
votes
1answer
71 views

How do I plot a distance map in $R^2$ to a curve given in form $y=f(x)$?

As in the title, I'd like to display image using DensityPlot representing distance to a given curve, e.g., $y=x^2$. I find it difficult to derive distance ...
10
votes
3answers
196 views

RegionMember[ ] in polygon

I am seeing a difference in RegionMember[ ] testing a point inside a 3-vertex polygon and testing a point inside a more complex polygon: ...
0
votes
1answer
42 views

What are some good ideas on how to Map a Replace function over a list of equations?

I've been working on a rather simple implimination of parameterizing a 3D line in space, and now am trying to find a way to map different values of t over those ...
4
votes
3answers
134 views

How can I get the vertices of each polygon of a Voronoi diagram?

For the following image; How can I get the vertices (which are highlighted by orange dots) of each Voronoi polygon of the following Voronoi diagram? The picture is from the Internet. It is just for ...
13
votes
2answers
418 views

Project map to a particular shape

I want to project a map to a particular shape, like a circle or ellipse. For example, let's imagine we want to project a map of the continental United states so that its outline is that of a circle. ...
4
votes
3answers
320 views

Drawing the Pursuit curves

I was reading this post on Filling Space with Pursuit Polygons. I didn't really see where the filling was, but found it quite interesting. Then I saw these pursuit ...
3
votes
1answer
33 views

How to get the coordinates of the 4 vertexes of a GeoListPlot?

I have a GeoListPlot as below. How can I get the latitude/longitude coordinates of the 4 vertexes of the GeoListPlot? I need the ...
2
votes
1answer
42 views

How to retrieve updated point coordinates that have been scaled or translated?

I'm sort of building off my previous question but the conditions of the points I'm trying to recover are different and therefore that solution is no longer applicable. Given said data, I'm trying to ...
10
votes
2answers
157 views

How to return the coordinates of the respective 3 vertexes of a DelaunayMesh's face?

I have a set of points pts1 and a point redPts as below:- ...
14
votes
3answers
526 views

Crop a Voronoi diagram and get a proper MeshRegion

How can I crop a VoronoiMesh (or any similar MeshRegion) to a non-rectangular region and receive the output as a ...
6
votes
1answer
95 views

Steiner Trees for Unit Polygons?

I know this is a longshot, and it's a rather broad question, but hopefully someone can help. Is there a simple or fast way to find Steiner Trees for unit polygons using Mathematica? By unit polygon, I ...
2
votes
1answer
64 views

Dashed hidden lines & Line-only Graphics3D

Consider the following lists: ...
0
votes
0answers
49 views

How to write a nonlinear polynomial system in matrix form

I have a nonlinear system like the following example ...
3
votes
1answer
119 views

Including periodic boundary conditions when drawing box of particles

This is essentially a follow-up question to this older post. Given a configuration of tubes (or for simplicity cylinders), we draw them in a box using Graphics3D, ...
3
votes
0answers
55 views

Is BooleanRegion limited to only the most trivial cases?

Consider these four regions: regions = Disk[#, 1] & /@ Tuples[{0, 4/5}, {2}] Graphics[{FaceForm[Opacity[0.2]], EdgeForm[Black], regions}] I was looking to ...
0
votes
2answers
88 views

Calculate area of a triangle

I have another problem that I can't figure out. A triangle har 2 of its summits in points (7.788,0,1.95), (0,7.788,1.95), and the last one on the curve with all the points (7.788,7.788,a^2+1.95), a ...
5
votes
2answers
379 views

How to decompose a self intersecting polygon into simple polygons?

I want to divide a self intersecting polygon into simple polygons with winding number. For example ...
7
votes
3answers
126 views

Creating MeshRegions of various 2D lattices

This is a soft question about the best approach to design a function that creates MeshRegion objects of various 2D lattices, e.g. kagome or hexagonal, all through ...
14
votes
4answers
1k views

Better way to calculate angle between lines?

I wrote anglecalc to calculate the clockwise angle from line a to b. Initially I thought <...
3
votes
2answers
98 views

How to obtain the neighboring lists of triangles for a given triangulation [duplicate]

I have asked this question before in my previous post, but I'm still unable to generate the coding. I'm new to Mathematica and I am currently still having some troubles generating the code for finding ...
1
vote
1answer
63 views

Converting a mesh surface discretized region to a solid region

What is the best way to convert a mesh surface region into a solid region? For example, we can obtain a mesh region of the surface of the left femur as follows. ...
4
votes
1answer
97 views

How to create a neighboring list for a given triangulation and find the triangle and construct the tile?

I am new to Mathematica and I am currently in need of some help with creating a neighboring list of triangles for a given triangulation and finding the path to the triangle containing the random point ...
7
votes
3answers
159 views

Test if line segments are part of a triangle

This looks simple, but I can't figure it out. I want an algorithm that will determine if three line segments are part of a triangle. If the line segments form a triangle the answer should be ...
0
votes
1answer
73 views
4
votes
1answer
85 views

ConvexHull peculiar behaviour - bug? (Definitely not a feature)

I ran in the last few days into a problem which I was afraid I couldn't solve: I use a set of 12 points in 3D to define a region and test whether and if how many other points lie inside this region. I ...
9
votes
2answers
248 views

Computing volume from node coordinates on the surface of a non-convex solid

I have a question regarding computation of volume of an irregular shape. I have looked around Mathematica -StackExchange but I could not find a solution which suits me the best. Problem Description: I ...
0
votes
0answers
57 views

Test varying number of inequalities

I want to test a varying number of inequalities ...
3
votes
0answers
60 views

ElementMesh from Tetrahedron subdivision

I would like to create a nice "structured" ElementMesh made of TetrahedronElement by dividing one larger ...
1
vote
0answers
63 views

How to find the boundary points of a list of points in a plot [duplicate]

If I plot a group of points like the one below, how do I differentiate and extract say the points on the bottom boundary? What about 3 dimensions?
3
votes
1answer
183 views

How to find non-overlapping triangles?

There are at least a few non-overlapping triangles made by the lines in the following graphic, how would I isolate them? ...
2
votes
0answers
40 views

Minimal “triangulation”

I have a list of 9 points in $\mathbb{R}^4,$ and I'd like to know the "minimal triangulation" of the convex hull of these points, i.e. the minimal number of 4-dim simplices such that their union gives ...
1
vote
0answers
36 views

Can't find RegionIntersection of DelaunayMesh

I want to find the RegionIntersection of two DelaunayMesh (given below), but the evaluation never ends. Though when I plot them, their regions are valid and shown to intersect. Why is this? ...