Questions on the application of Mathematica to geometric problems. You might also consider adding the [graphics] tag, if appropriate.

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3
votes
1answer
46 views

How to find points along the inner and outer edge of a ring along a specific direction

I have a set of random numbers distributed on a annular disk. I want to find points on the inner and outer edge along a particular angle. One possibility is to use ...
4
votes
2answers
150 views

Implementing AnglePath in Mathematica 10.0

Does anyone have an implementation for AnglePath (see AnglePath Documentation and example usage) in Mathematica 10.0?
40
votes
4answers
2k 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 to create a hexagonal mesh on a torus. What I would like to ...
10
votes
2answers
179 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 ...
4
votes
2answers
157 views
13
votes
1answer
700 views

Uniformly distributed n-dimensional probability vectors over a simplex

What's the right way to generate a random probability vector $p={p_1,\ldots,p_n} \in {(0,1)}^n$ where $\sum_i p_i=1$, uniformly distributed over the $(n-1)$-dimensional simplex? What I have is ...
36
votes
2answers
835 views

Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
17
votes
6answers
2k views

Find intersection of pairs of straight lines

I have a list of 24 points, in which two consecutive points (1st and 2nd, 3rd and 4th, …) are supposed to form a line: ...
3
votes
1answer
253 views

Visualization of Gaussian Curvature

I need to visualize Gaussian Curvature of a parametric surface. There is a solution in this math.SE post. However, I'm not sure its working because when I draw a sphere it's all white, but it should ...
6
votes
3answers
144 views

Easy way to bind rect to geometrical 2D line?

I got stuck with the following problem. For some calculation and visualization purposes I need to draw different shapes (like rectangle) with proper slope on custom line. The trivial example: ...
11
votes
2answers
488 views

Is there a triangle like this?

I want to find the numbers $a$, $b$, $c$, $d$ of the function $y = \dfrac{a x + b}{c x + d}$ so that the triangle $ABC$ with three points $A$, $B$, $C$ have integer coordinates and lies on the graph ...
6
votes
1answer
101 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 ...
15
votes
2answers
1k views

How do I split up a curve into chords of equal length?

I have a curve that is defined as f[x] and what I'm attempting to do is to divide the curve into equal straight lengths for a number of segments of my choosing that I've defined as nSeg. I've created ...
2
votes
0answers
213 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: ...
0
votes
0answers
34 views

Finding intersection of two infinitely long lines using points [duplicate]

EDITED In the Find intersection of pairs of straight lines problem, it is assumed that line are intersected by default and the purpose is to find the intersection points. In the present problem, two ...
13
votes
6answers
11k views

How to determine the center and radius of a circle given some points in 3D?

I was wondering if anyone could give me a hand with this problem I have. I have six points on a plane, and I am trying to determine if they form a circle or not. I know that any three points in 2D ...
1
vote
1answer
89 views

Calculate area from `RegionPlot` directly

I have a region plot, and I would like to calculate the area: ...
0
votes
2answers
61 views

Draw a vector with mathematica [closed]

at the risk of being trivial I would like to draw the vector $\vec{AB}$ where $A$ an d $B$ have the coordinates $(1,1,1)$ and (1,-1,2) respectively.
14
votes
3answers
396 views

Solve a trig equation system

Background of the problem In the same plane, P is a fixed point, A,B,C are moving point, PA=a, PB=b, PC=c, find the maximize perimeter of △ABC. let ∠BPC=A, ∠CPA=B, ∠APB=2*Pi-A-B, then the ...
2
votes
1answer
160 views

Confusion with SplineFit (Angle calculation)

This question is continuation to this other one I am creating polymers (where each monomer is of equal length) using this method: ...
12
votes
1answer
280 views

How do I create a triangulated surface from points?

I have a set of points in a nx3 matrix and I would like to convert them into a surface, so that I may calculate its surface area. The function ListSurfacePlot3D creates the surface how I want it. ...
2
votes
1answer
64 views

Why are these methods giving me different results? (Trying to test SplineFit)

I am creating a polymer(where each monomer is of equal length) using this method: ...
33
votes
6answers
2k views

How to plot ternary density plots?

How can I get a ternary density plot just like the plots from OriginLab? ContourPlot and DensityPlot seemingly can accept the ...
0
votes
0answers
37 views

MaxCellMeasure fails in 3D?

Question How come MaxCellMeasure works in 2D but fails in 3D? Indeed if I try ...
4
votes
3answers
597 views

Computing Gaussian curvature

Can Gaussian curvature $K$ be computed from WolframAlpha or any other available Mathematica program? Please indicate the program or its reference. If input ...
2
votes
1answer
172 views

Distinguishing left from right adjacent triangles in triangle mesh [closed]

What I'm trying to do: I'm trying to create a path-drawing function which will produce a path like the one I-P in the diagram below. The way this path was generated requires me to swap between the ...
2
votes
1answer
90 views

ToElementMesh fails on DodecahedronIcosahedronCompound

Context I would like to compute the eigenmodes of a DodecahedronIcosahedronCompound. Why? Because it is cool! and I wonder how it rings… Starting with: ...
0
votes
1answer
40 views

Is there a package that can calculate the Ricci tensor from a numerically given metric?

There are many packages about general relativity or differential geometry, and they can calculate the Ricci tensor from a symbolically given metric, for example, $g_{tt}=-f(r)$, $g_{rr}=h(r)$, etc. ...
4
votes
2answers
125 views

ToElementMesh problem on Ball defined by ImplicitRegion?

Could any one please confirm the following bug in mathematica 10.0.2 ? If I define this ball Ω = ImplicitRegion[0 <= x^2 + y^2 + z^2 <= 1, {x, y, z}]; and ...
23
votes
4answers
8k views

How to calculate scalar curvature Ricci tensor and Christoffel symbols in Mathematica?

I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. ...
6
votes
5answers
394 views

How to draw a dodecahedron with each face modified to a pentagram?

I'd like to draw a dodecahedron with each face carved on the sides so it becomes a pentagram. I wonder how to start to do this kind of task in Wolfram language? Edit: The result should still be a ...
5
votes
4answers
644 views

Distance between two line segments in 3-space

I need to compute the distance between two line segments in a project. After googling, I found this algorithm and used it to implement a Mathematica version: ...
29
votes
1answer
723 views

Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
36
votes
6answers
2k views

Generating evenly spaced points on a curve

In the KnotData package a simple command such as points = Table[KnotData[{3, 1}, "SpaceCurve"][t], {t, 0, 2 Pi, 0.1}]; will ...
0
votes
2answers
165 views

Projection of triangles onto a sphere

I am trying to find the solid angle taken up by a large set of triangles around a central point. I have normalized the vertices of the triangles to a unit sphere around the central point, But the ...
9
votes
2answers
180 views

The envelope of a set of translated and rotated ellipses

I achieve a dynamic graphics by using Manipulate as follows: ...
2
votes
1answer
123 views

Calculate the total length of line segments within polygon

So we have a polygon with N vertices located on grid. All vertices are located at the intersection of cells (so their coordinates are integers). The objective is to calculate the total length of line ...
4
votes
2answers
614 views

Triangle mapped on a sphere in $\mathbb R^3$?

How can I map a triangle on a sphere? I want to visualize (plot or animate) it for my student in Non-Euclidean geometry. I have no restrictions on the triangle's kind or on the sphere in $\mathbb ...
3
votes
0answers
149 views

Minimalistic code challenge on Apollonian gaskets

I've been recently fascinated by the beauty, symmetry and mathematical richness of the Apollonian gaskets. So I felt myself challenged to see if it was possible to generate one in Mathematica with ...
4
votes
3answers
273 views

How to find a length of a curve constructed using Spline?

By fitting the data using spline, I have created a curve. sp = SplineFit[data1, Cubic] I am trying to divide this curve into small segments of equal length. To ...
2
votes
1answer
49 views

Application of Maximize: The cuboid constrained to the ellipsoid in $\mathbb{R}^3$

Since I am a student of Mathematics I enjoy to apply MMA to problems that I have a solid understanding in. The following would be such a problem: Maximize $f: \mathbb{R}^3 \to \mathbb{R}$ given by ...
0
votes
1answer
106 views

Arbitrary hollow cylinders in mathematica 9

I'm having trouble displaying a hollow cylinder in Mathematica 9. A hollow cylinder looks like this: I tried to use RevolutionPlot3D with a step function. It ...
18
votes
5answers
527 views

Plot a partition of the sphere given vertices of polygons

I saw in this question that Mathematica can draw spherical triangles. I guess something similar can be done to plot a spherical polygon. I am interested in something similar: I have a set of ...
25
votes
2answers
325 views

Bug in ArcLength?

fixed in 10.1 (windows) With Mathematica 10.0.2: ArcLength[Line[{{0, 0}, {1, 0}, {2, 0}}]] ArcLength[Line[{{0}, {1}, {2}}]] (* 2 *) (* 2 *) However, ...
1
vote
1answer
46 views

Implicit region is not “valid” in ParamatricNDSolveValue function?

I am trying to solve a geometric problem with relation to my Schrodinger equation and its boundaries. Here is my code: ...
2
votes
0answers
58 views

Surface Plot 3D of a strongly concave shape

I have a list of {x,y,z} points that all lie on the surface of an object (model output from COMSOL). I would like to generate a graphics object that reproduces the surface. Ideally, I would like ...
1
vote
1answer
104 views

Implicit region misses subset?

Context I am interested in integrating a 2D function over lines defined implicitely Attempt Let me just start by integrating the identify on such sets of lines which a defined using ...
28
votes
3answers
750 views

Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?

Given a closed curve $\mathcal C$ in three dimensions, is it possible to use Mathematica's built-in functionality to compute a minimal surface whose boundary is $\mathcal C$? For simplicity, let us ...