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Results tagged with computational-geometry
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user 7462
Problems involving meshes and other geometry representations, and manipulating, transforming, or extracting information from them; algorithms for solving geometrical problems such as computing intersections, filling holes, triangulating a shape, etc.
3
votes
1
answer
294
views
Why is the valence of regular vertices 6?
So I recently learnt that supposedly for any mesh, and pretty much any scheme, the valence of regular vertices must be 6. It seems to be related to the Euler-Poincare formula but I have not been able …
- 1,831
0
votes
1
answer
777
views
What's a simple way to find connected components in a mesh?
As stated I have a triangle mesh I want to separate into connected components. One way I would assume would be to do a depth first search on a vertex and remove vertices, then repeat until the set is …
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0
votes
1
answer
151
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Is the laplacian operator for meshes just the sum of the differences of neighbouring vertices?
I am starting to learn about the laplacian operator $\Delta = \nabla \cdot \nabla\phi(p)$
Which can be described as the divergence of the gradient of a scalar function $\phi$. This is equivalent to th …
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1
vote
0
answers
43
views
Geodesic triangle strip algorithm
I think somewhere in the literature there is an algorithm that, given 2 points on a triangle mesh, finds the triangle strip through which the geodesic passes, but I cannot find it anywhere.
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2
votes
1
answer
167
views
How to create a mesh from a skeleton?
Say you have a topological skeleton, you want to fabricate a mesh out of it, what algorithms exist to accomplish this?
I know of at least one way, which is to represent each edge as an implicit capsul …
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1
vote
2
answers
454
views
Clever projection of point onto triangle?
I know of at leas tone way to project a point onto a triangle.
Project onto the plane, check barycentric coordinates, if outisde triangle, project onto the 3 segments, check distance, retain closest p …
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0
votes
2
answers
161
views
How do algorithmic botany algorithms generate their plant geometry from a skeleton?
I read the Algorithmic Beauty of plants.The resource goes in depth as to how to generate plant topology, but it does not talk about how to make the geometry except for the leaves.
I tried looking into …
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3
votes
1
answer
495
views
How to subdivide faces with a half edge DS?
Assume we have a mesh represented as a half edge datastructure.
We want to subdivide faces without introducing unnecessary vertices (i.e the new number of vertices must be exactly V + E where V is the …
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1
vote
2
answers
160
views
Heat Method (Crane et Al) How do we pick u?
The heat method is a very interesting paper for distance computation:
https://www.cs.cmu.edu/~kmcrane/Projects/HeatMethod/paperCACM.pdf
The idea behind the paper is that, heat travels along the surfac …
- 1,831
2
votes
2
answers
805
views
Discrete Gradient?
I am trying to understand how to get the discrete gradient of a mesh that is being used as the input of some function $f$. In other words for every vertex $v$ there is a scalar quantity $s$ associated …
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2
votes
0
answers
54
views
Stitching 2 boundaries together
Let us say we have 2 boundaries of 2 meshes that are roughly aligned, for example 2 generalized cylinders (sweeping surfaces) with a small gap in between. And let us say we want to connect them to eac …
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0
votes
2
answers
47
views
Finding vertices of a polytope?
Assume that in 3D we have a polytope defined by the intersection of halfspaces.
A half space is the set of all solutions of a linear inequality $P = N \cdot x + c \leq 0$ Where $N$ is the normal to th …
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0
votes
1
answer
85
views
Faring a region of a mesh connecting two curves
In the book Polygon Mesh Processing, there is a section dedicated to fairing. In particular page 59 has this lovely figure:
I am specially interested in the rightmost image. According to the text thi …
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0
votes
0
answers
38
views
How to smooth out normals on a boundary
I am stitching together parts of a mesh and using normal information to interpolate between the gaps.
I am finding that sometimes I get a difference in the normals due to numwrical impressions:
In th …
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0
votes
0
answers
5
views
Stitching two mesh borders with non-equal vertex counts?
Assume you have two meshes $M1$ and $M2$ and that each has a boundary $b1, b2$. You want to connect the two boundaries together.
If both boundaries had the exact same number of vertices, then you coul …
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