Linked Questions

86
votes
17answers
4k views

Future enhancements for the finite element method

How should the finite element method (FEM) framework in the language be extended to be more useful? With the release of version 12.0 all fundamental FEM solvers (linear, nonlinear, stationary, ...
29
votes
4answers
2k views

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

I am trying to estimate curvatures on a triangulated surface/manifold using the algorithm of : Meyer, M., Desbrun, M., Schröder, P., & Barr, A. H. (2003). Discrete differential-geometry operators ...
18
votes
4answers
893 views

Draw circle on ellipsoid

Define a circle $\cal{C}(p,r)$ on the surface of an ellipsoid $E$ in $\mathbb{R}^3$ to be the set of points on $E$ whose shortest geodesic distance from centerpoint $p$ is $r$. Let me assume that $r$ ...
15
votes
2answers
702 views

Voronoi tessellations on meshed surfaces

Given a meshed surface, on which we can calculate geodesic distances between vertices, how can one calculate the Voronoi tessellation of a set of points located on this surface? This is somewhat ...
13
votes
2answers
1k views

How to interpret the FullForm of a SparseArray?

SparseArrays are atomic objects, but they do have a FullForm which reveals information about them. What is the meaning of the ...
19
votes
2answers
3k views

Estimating Principal Curvature Directions on Discrete Surfaces

I am continuing with working on implementing curvature estimations on triangulated surfaces (See: here), using the algorithm of : Meyer, M., Desbrun, M., Schröder, P., & Barr, A. H. (2003). ...
11
votes
2answers
2k views

Geodesics on a torus

Is it possible to draw geodesics between the points in a path on a torus - toroidal surface? geodesics: generalization of the notion of a "straight line" to "curved spaces" ...
8
votes
2answers
305 views

Contourplots on discrete surfaces

Does anyone know how one can plot contour lines on a meshed surface? For example I would like to be able to plot contour lines indicating lines of equal distance from a given point such as data coming ...
7
votes
3answers
302 views

Reduce quality of an imported MeshRegion

Importing STL files using Import results in a MeshRegion composed by the triangulation of the original file, and a similar ...
7
votes
1answer
423 views

Voronoi mesh from non-parametric surfaces for 3D printing

I am trying to make a Voronoi mesh from the Stanford Bunny surface for 3D printing, intended as a test case to make a Voronoi mesh from any arbitrary, non-parametric 3D surface. Related techniques ...
7
votes
1answer
364 views

Is it possible to use a function for EdgeWeight in a Graph?

Why I cannot calculate all edge weights beforehand: I have many large graphs for which I'd like to find the shortest path between two vertices (FindShortestPath ...
2
votes
0answers
54 views

Display minimum distance and minimum-distance path between two points on a polyhedron

Given a genus-zero polyhedron (e.g., PolyhedronData["Dodecahedron"]) and a point $P$ anywhere on its surface, color all points on the polyhedron by the length of ...