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

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0
votes
2answers
46 views

Draw a vector with mathematica [on hold]

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.
1
vote
1answer
78 views

Calculate area from `RegionPlot` directly

I have a region plot, and I would like to calculate the area: ...
14
votes
3answers
373 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 ...
1
vote
1answer
55 views
2
votes
1answer
156 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: ...
2
votes
1answer
63 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: ...
10
votes
1answer
211 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. ...
0
votes
0answers
34 views

MaxCellMeasure fails in 3D?

Question How come MaxCellMeasure works in 2D but fails in 3D? Indeed if I try ...
2
votes
1answer
74 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: ...
9
votes
1answer
138 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 ...
0
votes
1answer
33 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
111 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 ...
4
votes
1answer
98 views

Implementing AnglePath in Mathematica 10.0

Does anyone have an implementation for AnglePath (see AnglePath Documentation and example usage) in Mathematica 10.0?
6
votes
5answers
382 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 ...
35
votes
2answers
763 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 ...
9
votes
2answers
171 views

The envelope of a set of translated and rotated ellipses

I achieve a dynamic graphics by using Manipulate as follows: ...
0
votes
2answers
151 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 ...
4
votes
3answers
254 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 ...
2
votes
1answer
114 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 ...
0
votes
1answer
96 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 ...
3
votes
0answers
121 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 ...
2
votes
2answers
117 views
18
votes
5answers
501 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 ...
1
vote
1answer
43 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
56 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
0answers
65 views

Implementation of Lubaehevsky-Stillinger Algorithm to pack hard spheres

To generate a model of a polycrystalline material with specified grain size distribution (e.g coming from a Monte Carlo Grain Growth simulation) the Paper "Effects of grain size distribution and ...
5
votes
2answers
249 views

Calculate area under a polyline

Consider the following code: tmp = {{0, 0}, {1, 1}, {2, 1}, {3, 2}, {1, 0.5}}; ListLinePlot[tmp, Filling -> Axis] Is there any easy way to compute filled ...
1
vote
1answer
100 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
715 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 ...
2
votes
1answer
160 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 ...
0
votes
0answers
58 views

How to plot a ternary plot? [duplicate]

Does anybody know how to plot a ternary plot (equilateral triangle)? Suppose, I have a list of lists like this (triplets): ...
24
votes
2answers
321 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, ...
7
votes
3answers
229 views

Unable to compute the area of region

For a set of data: ...
1
vote
2answers
168 views

Only show part of a cube below an intersecting plane

I plot a cube and a plane. I just want to show the part below the plane. The code: ...
0
votes
1answer
39 views

Computing $V(p_1, p_2)$ and determining whether $V(p_1) \subset V(p_2)$

Say I have two homogeneous polynomials $p_1, p_2 \in \mathbb{C}[x_0, \dots, x_n]$. In other words, they cut out co-dimension 1 varieties in $\mathbb{P}^n$. I would like to know how to compute two ...
4
votes
1answer
116 views

Symbolic geometry not working?

I have Mathematica 10 on the Raspberry Pi. (wolfram-engine version 10.0.0+2013112003) According to the "What's New in Mathematica 10" page ...
1
vote
0answers
41 views

Coding the Gibbons-Hawking metric

I am studying the Gibbons-Hawking metric, which is $ g= U^{-1}(d\tau + \omega.dx)^2 + U.dx.dx$ where $U = \sum_{s=1}^n \frac{1}{|x-P_n|}$. It is a family of metrics defined on a four-dimensional ...
6
votes
2answers
173 views

Building bounded polygon around heatmap (or points)

I have a set of data for world marine piracy. I'd like to build polygons encircling areas of active piracy. So to start with I get piracy data and make a heatmap from it. ...
6
votes
1answer
190 views

Obtain polygons describing all intersections of many polygons

I have 6894 polygons describing zones in a state plane (i.e., cartesian) coordinate system. Most are not very complex, and I believe none have holes. A random example is Polygon[{{351633., ...
1
vote
2answers
104 views

Draw Multiple Polygons Given Their Vertices

Hi I have a very simple question but I haven't been able to find a set answer. How would I draw a bunch of polygons on one graph. The following does not work: ...
4
votes
2answers
158 views

Compute the average distance from the base of a rectangular pyramid to its apex

How can I compute the average distance from the base of a rectangular pyramid to its apex? For example, if the base of the pyramid is 30 feet by 8 feet, and the height of the pyramid is 12 feet, then ...
4
votes
2answers
220 views

Equation of a transformed (roatted) ellipsoid

Given an ellipsoid with semi-axis {a,b,c} and cantered at {a,0,0}, how do I use ...
2
votes
1answer
133 views

Mean curvature of Sphere

I am trying to calculate mean curvature of a parametric surface(like sphere), and I wrote this code based on this discussion. Here is my code: ...
4
votes
2answers
312 views

Plane Geometry Diagrams With Labels

I can make some basic diagrams in Mathematica (stolen from their pages, for example see the below: LaminaData["FilledIsoscelesTriangle", "Diagram"] However, I'm ...
2
votes
2answers
132 views

Finding the area bounded by a logspiral curve and two straight lines

I'm facing some trouble with finding the area of a region which is described by x-y coordinates (or line equations) and a curved line represented by logspiral. I tried my best in coming up with the ...
5
votes
3answers
381 views

Finding volume of a segment

I'm still pretty new to Mathematica, so I would like to seek advice regarding a geometrical problem. I am currently trying to define that as an extra condition in the Mathematica code below. ...
7
votes
1answer
158 views

Getting the coordinates of GeoDisk[] and similar Mathematica 10 GeoObjects

I'm a big fan of the new Mathematica 10 geographic capabilities and functions such as GeoDisk[], GeoCircle[] and others. One limitation of these functions, however, is the transformation of the actual ...
0
votes
1answer
218 views

Order contour points in clockwise

I want to describe shape of an object using contour points descriptor. Given a silhouette (image black white of an object), I extrait the contour points using EdgeDetect[] fonction. After that, I need ...
4
votes
3answers
586 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 ...