# Tagged Questions

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

172 views

### Implementing AnglePath in Mathematica 10.0

Does anyone have an implementation for AnglePath (see AnglePath Documentation and example usage) in Mathematica 10.0?
498 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 ...
1k 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 ...
192 views

### The envelope of a set of translated and rotated ellipses

I achieve a dynamic graphics by using Manipulate as follows: ...
250 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 ...
392 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 ...
59 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 ...
160 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 ...
170 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 ...
56 views

### Find volume of a translated and rotated ellipsoid below xy (horizontal) plane

I am trying to find the volume of the lower part (above horizontal plane) of an ellipsoid that is clipped by the horizontal (or x-y) plane. This ellipsoid is also translated (i.e. origin is not at ...
194 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 ...
156 views

This code: ...
612 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 ...
59 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: ...
74 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 ...
87 views

### Contourplot gives inaccurate ellipses

I'm trying to draw a family of ellipses with pre-defined foci as follows: ...
85 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 ...
299 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 ...
113 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 ...
900 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 ...
209 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 ...
59 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): ...
341 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, ...
250 views

### Unable to compute the area of region

For a set of data: ...
186 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: ...
41 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 ...
2k views

### Drawing a square root spiral

Here is a start. I'm looking for a nice way to draw it. ...
143 views

### Symbolic geometry not working?

Bug fixed in 10.0.0+2014080602 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 ...
45 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 ...
203 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. ...
241 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., ...
119 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: ...
346 views

### How to create a Poincaré disk type kaleidoscope in Mathematica?

Creating a kaleidoscope in Mathematica is not a new topic at all, examples can be found from the links like Wolfram reference and Wolfram demonstrations. My question is how to create Poincaré disk ...
167 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 ...
266 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 ...
148 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: ...
377 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 ...
163 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 ...
448 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. ...
188 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 ...
269 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 ...
674 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 ...
251 views

### Constructing a list of Cartesian coordinates of the Icosahedron

I’m learning Mathematica and I need the coordinates of the Icosahedron vertices. This is my attempt at writing a program for it. The vertex coordinates are simply all cyclic permutations and ...
151 views

### Controlling PointSize in a RegionPlot

I have a "named" point in Mathematica 10 and am plotting it like this using RegionPlot: ...
127 views

### Labeling named point in Mathematica 10 [closed]

I have a "named" point in Mathematica 10 defined like this: point["camp location"] = Point[{latitude, longitude}]; I assume there is some way to make the name of ...
211 views

### How to construct new geometrical shapes in Mathematica?

In this question of mine I asked for how to implement a 2D random walk within a bounded area. In the provided solution one can use Rectangle[{-10, -10}, {10, 10}] ...
2k views

### Fitting ellipse to 5 given points on the plane

Five points are required to define a unique ellipse. An ellipse has five degrees of freedom: the $x$ and $y$ coordinates of each focus, and the sum of the distance from each focus to a point on the ...
820 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 ...