# Tag Info

Accepted

### How to perform Loop subdivision on a triangle mesh with Mathematica?

We need quite a bit of preparation. In the first place we need methods to compute cell adjacency matrices from here. I copied the code for completeness. ...
Accepted

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

Here is a method that utilizes $H^1$-gradient flows. This is far quicker than the $L^2$-gradient flow (a.k.a. mean curvature flow) or using FindMinimum and friends, ...
Accepted

### How to exactly calculate the volume?

No numerics hacks here; this really computes the volume symbolically. It is a bit tedious and demands some tricks which may appear more obvious in this answer than they would really be on the first ...
• 19.1k

### How to estimate geodesics on discrete surfaces?

Geodesics in Heat Algorithm At the suggestion of @user21 I am splitting up my answers to help make the code(s) for calculating geodesics distances easier to find for other people interested in these ...
• 4,083
Accepted

### How to speed up estimation of Mean and Gaussian curvatures on triangular meshes?

Note added 1/29/2020: the routines here have a bug where the mean curvature is sometimes computed with the opposite sign. I still need to work on how to fix this. I guess I should not have been ...
Accepted

• 19.1k

### Find duplicates in list of InfiniteLine

DeleteDuplicates[lines, RegionWithin] {InfiniteLine[{{0, 0}, {1, 0}}], InfiniteLine[{{0, 1}, {1, 0}}]} Also ...
• 399k

### Converting a Sierpinski tetrahedron to a Graph

A natural and simple way to approach this problem, assuming that your SiPyramid function has been defined, is as follows: ...
• 32.5k
Accepted

### How to generate approximately equally spaced points efficiently

Annealing Found this to be an interesting question and immediately I thought it to be a good application for simulated annealing. Here's a little unoptimized annealing function I wrote. The idea is ...
• 531
Accepted

### How to get a specified number of points that are nearly equally spaced in a closed rectangle

There is a neat (and widely known) trick to produce n approximately evenly distributed points in a disk, or on any surface of revolution. Points are placed on a ...
• 236k

### How to exactly calculate the volume?

Surprisingly, the volume of this complicated shape can be computed analytically. Some steps exceed MA capabilities, however, using arbitrary precision (I check up to 200 digits) arithmetics one can ...
• 19.2k
Accepted

### Bridget Riley - Movement in Squares and Circles

Since I like the color image more than the black-and-white... ...
• 20k
Accepted

### How to draw a number of circles inscribed in a square so that the sum of the radii of the circle is greatest?

We only test n=5,n=6. We need three varaibles {x[i],y[i],r[i]} to determint a circle. Set ...
• 77.7k

### Determine whether points lie within a cow

One way is to compute the solid angle subtended by the cow viewed at the point by summing signed solid angles corresponding to the cow's polygonal faces. If the total is 4 pi, the point is inside the ...
• 421
Accepted

### How to construct a 3D 10-sided Die (Pentagonal trapezohedron) and Spin to a face?

Edit - forgot to add a necessary link Coincidentally I had a little personal project trying to make a good dice roller in Mathematica a while back. Here's some of my code (note: this was before I ...
• 2,412

### Voronoi tessellations on meshed surfaces

Using the Geodesics in Heat Algorithm implemented here, we can calculate the distances of all vertices on the surface to a given vertex. By repeating this algorithm on a selected subset of vertices on ...
• 4,083

### Catmull-Clark and Doo-Sabin Subdivision Implementations

Doo-Sabin Subdivision To my own surprise, Doo-Sabin subdivision is in many ways much easier to implement than Catmull-Clark subdivision. The only real problem I met was to compute the faces created at ...
Accepted

### GeometricTest doesn't work in ellipse

Yep, it's a simple mistake by WRI, that is, a bug. ...
• 239k
Accepted

### Efficiently Mowing Grass with Mathematica

This is just starting ideas for arbitrary regions. Perhaps you can improve it. Version 1 Define concave region with holes, which can be generalizable to arbitrary complexity: ...
• 73.4k