Problem 1935. Spherical surface triangulation
Create a triangulation of a spherical surface with approximatelyuniform coverage
http://www.alfnie.com/software/print_sphere01.jpg
Description:
A rather crude way to obtain a triangulation of the spherical surface would be:
[x,y,z] = sphere(64); fvc = surf2patch(x,y,z,'triangles');
The function sphere creates a uniform grid in spherical coordinates, so the resulting triangulation produces very small triangles/faces at the poles and considerably larger triangles/faces at the equator (see the sphere at the right in the examples above).
In general (with a few exceptions) it is not possible to construct a tessellation of the spherical surface made of triangles of exactly the same size. But we can try...
Your function should return a tessellation of the unitsphere surface formed by triangles with side lengths as similar as possible (as close to identical equilateral triangles as possible). An example of a somewhat reasonable solution would be the sphere at the left in the examples above.
Details:
Given a number N your function should return an approximately uniform triangulation of the spherical surface with at least N vertices.
Uniformity is measured as the ratio between the longest and the shortest edge across your entire triangulation (lower numbers are better). This ratio should be lower or equal to 2 in order to pass this problem (in other words, the longest edge should be at most twice the size of the shortest edge). Your solution will receive a score 1000*(ratio1). A score of 0 would correspond to identical equilateral triangles.
The function output should be a valid PATCH format: a structure with fields vertices (with size Nx3; each row of vertices defining the 3d coordinates of each vertex) and faces (with size Mx3; each row of faces defining the three vertices in each face/triangle as indices into the rows of the matrix vertices).
Solution Stats
Problem Comments

1 Comment
The tip here is averages. Catmull & Clark used them to smooth polyhedra for instance.
Solution Comments
Show commentsProblem Recent Solvers17
Suggested Problems

2214 Solvers

441 Solvers

Project Euler: Problem 2, Sum of even Fibonacci
2186 Solvers

274 Solvers

166 Solvers
More from this Author38
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!