# Questions tagged [subdivision]

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### How do I evenly subdivide the projection of a circle in 3D?

I want to draw a circle in 3D from line segments. There are plenty of examples how to do this with an even number of subdivisions in 3D space, but I want the minimum number of subdivisions to produce ...
• 121
47 views

### How would you represent a mesh with tris and quads?

My understanding is that, while subdivision algorithms like Catmull-Clark can work for any polygonal mesh (including triangles) it's preferable to start with a quad mesh. Currently my rendering engine ...
• 195
1 vote
84 views

### Can surface subdivision results be predicted?

I just took a online computer graphics course and studied surface subdivision. I knew that surface subdivision could update a coarse surface into a fine one, but can we predict the updated surface ...
116 views

### Catmull–Clark issue with plane corners

I implemented catmul clark based on this Wikipedia article. And it seems to work fine for meshes where the edge point count is equal to the face point count, but not for planes where the corners have ...
• 123
1 vote
54 views

### Subdivision scheme where the faces and edges have weights (not necessarily scalar weights)

Subdivision schemes work by considering the vertices and their connectivity information to calculate averaging weights. However, other than specifying which vertices are connected, and perhaps which ...
• 1,656
108 views

### Rounding a 3D corner with Subdivisions

Following the instructions from this post on Stack Overflow, I have been able to find points A, B, and C from points V1, V2, and V3 and a radius value (code below). I would like to be able to find a ...
1 vote
95 views

### Approximating Geodesics in a half edge DS, how can I refine my mesh to get good approximations

I implemented Djikstra's shortest path algorithm to approximate Geodesics on arbitrary meshes. Djikstra's works, but I noticed a problem inherent to the discretization of my meshes. Consider the ...
• 1,656
105 views

### Loop subdivision, certain areas converging towards degenerate geometry

I coded loop subdivision and ran it on a cube with triangle faces. I noticed this: I am using doubles to represent my vertex positions, I am not 100% sure these are caused by floating point ...
• 1,656
191 views

### How do people come up with subdivision schemes?

Be it chaikin subdivision, loop subdivision, catmull-clark subdivision... How do people come up with the coefficients for an arbitrary subdivision scheme?
• 1,656
244 views

### If you can use subdivision surfaces for 2D curves

I've seen how subdivision surfaces are good for 3D curves/modeling, but haven't seen anything on if it's good, or even usable, in 2D. My question is just that, if (a) you can even use subdivision ...
• 123
518 views

### Problems with Subdivision Surfaces

It sounds like Subdivision Surfaces are better than NURBS but not as good as T-splines. I would like to know some of the disadvantages of Subdivision Surfaces, what they can't do or what they do ...
• 123
1 vote
49 views

### Ray tracing and mesh extraction

I have been reading this paper : 3D Surface Extraction using Incremental Tetrahedra Carving .pdf I have already generated a tetrahedra for my mesh and I would like to create a surface mesh. I can't ...
497 views

### How to smooth out a voxel grid?

So I am facing the following issue. Say I have a minecraft like mesh (i.e I have a bunch of cubes on top of one another). I wish to smooth out this mesh in such a way that only the regions where ...
• 1,656
753 views

### Visualizing the Lane-Riesenfeld Algorithm

Ok so, I keep reading papers about this and non of them have pictures. The lane Riesenfeld algorithm provides a way to subdivide set of points with B-spline conversion. The quesiton is simple HOW? If ...
• 1,656
310 views

### Where do the coefficients in the Catmull-Clark subdivision algorithm come from?

I'm learning about subdivision surface algorithms. The "Catmull-Clark" algorithm seems to be one of the most widely-used classical algorithms. The introduction of new face points and edges is ...
• 191
495 views

### B-Spline patches on the tessellation shader. How to get the control points

I have a polygonal mesh with ngons in it. I want to make a tessellation shader to which I send only the regular quads in such a way that it can construct a B-Spline surfaces across it. I came across ...
• 201
197 views

### What is this triangle sub-division scheme called?

I have thought of a triangle sub-division for the purpose of smooth triangulation (no popping) over time on the fly. I think it is very likely the scheme is already invented and has a name but I can´t ...
• 359
33 views

### Constructing base mesh for required subdivision surface

Given a triangle mesh, does there exist any algorithm to compute a base mesh (smaller in size than the triangle mesh) that could be subdivided multiple times to get back the original mesh (or an ...
• 31
330 views

### An introduction to Lane-Riesenfeld algorithms [closed]

I am looking for a good introduction to Lane-Riesenfeld algorithms, which are a family of subdivision methods for generating uniform B-splines. Any suggestions? Note. This is a copy of the question I ...
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