# Tagged Questions

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

37 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 ...
127 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 ...
160 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: ...
91 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.
128 views

### Calculate area from RegionPlot directly

I have a region plot, and I would like to calculate the area: ...
494 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 ...
65 views

### How to change a point to circle in a Graphics expresion [closed]

Given the following line of code, ...
172 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: ...
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### 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: ...
351 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. ...
63 views

### MaxCellMeasure fails in 3D?

Question How come MaxCellMeasure works in 2D but fails in 3D? Indeed if I try ...
118 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: ...
208 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 ...
61 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. ...
201 views

### ToElementMesh problem on Ball defined by ImplicitRegion?

Bug introduced in 10.0 and fixed in 10.2 Could any one please confirm the following bug in mathematica 10.0.2 ? If I define this ball ...
175 views

### Implementing AnglePath in Mathematica 10.0

Does anyone have an implementation for AnglePath (see AnglePath Documentation and example usage) in Mathematica 10.0?
533 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 ...
198 views

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

I achieve a dynamic graphics by using Manipulate as follows: ...
295 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 ...
442 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 ...
64 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 ...
181 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 ...
215 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 ...
58 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 ...
245 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 ...
176 views

This code: ...
653 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 ...
63 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: ...
125 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 ...
96 views

### Contourplot gives inaccurate ellipses

I'm trying to draw a family of ellipses with pre-defined foci as follows: ...
91 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 ...
324 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 ...
119 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 ...
1k 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 ...
227 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 ...
347 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, ...
264 views

### Unable to compute the area of region

For a set of data: ...
188 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. ...
147 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 ...
51 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 ...
223 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. ...
254 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., ...
124 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: ...
387 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 ...
171 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 ...