# OpenGL 3D rendering of bilinear surface patch

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This may be the incorrect thread, and the subject may not describe my issue very well, but I ask that you bear with me. I'm currently working on a renderer for bilinear surface patches just as a fun little side project and I've currently got my algorithm spitting out a list of ordered vertices as the patch is sampled. I'm having a problem figuring out how best to reorder the vertices in to a vertex array for rendering as a 3D mesh. I know it's basically the same process as polygonizing a height map, however instead of one value for each point, I've got three and I'm not exactly sure the best way to render the data. When thrown straight in to an array and rendered as points using GL_POINT in OpenGL I get the desired shape of the surface patch (This would mostly likely work in DirectX as well so it's not an API dependent question), however it's not really 3D and it's a very bad way to render a vertex array and nothing can really be done with the data as there aren't any polygons. I've been thinking that reordering all the vertices in order to create triangle strips would be expensive so perhaps an index array would work, however I'm not sure how best to calculate the indices. Any help would be appreciated as this has been bugging me for days and I can't seem to see the answer or come up with a clean algorithm for reordering the vertices into triangle strips. For clarification in case it's necessary:
current vertex array:
x1, y1, z3, x2, y2, z3, x4, y4, z4, etc..

Need to reorder or index so that triangle strip looks something like:

(x1,y1,z1)--------(x2,y2,z2)-----------(x3,y3,z3)
|                  /|                     /
|                /  |                  /
|              /    |               /
|            /      |             /
|           /       |           /
(x4,y4,z4)/         (x5,y5,z5)/


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Indexed tri strips. see this for an example. The ParametricSurface.cpp file contains the code to do what you are after.

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Hi,

You should go with indexed triangle lists, using indexed triangle strips will just give you some extra head ache (need of degenerated triangles to join strips together).

You don't need to re-order any vertices, assuming that they are in a grid shape.

Here's a little example for the indexed tri-list:

The vertex layout:

0-1-2
|/|/|
3-4-5
|/|/|
6-7-8

The index buffer (put on different lines to show different triangles)

0,1,3,
1,3,4,
1,2,4,
2,4,5,
3,4,6,
4,7,6,
4,5,7,
5,8,7

I think that you should study the matter on the paper to find out the rule used here.

Good luck!

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RobTheBloke: Thanks for the source. I looked at it briefly and I'm not entirely sure it really helps as the vertices appear to already be assumed to be in the correct order unless I'm mistaken.

kauna:I have figured that an indexed array would probably be the best way to do what I'm after, however I'm not 100% sure how they work anymore as I tend to avoid them because they make normal calculations a bit less straightforward. From your example I would be doing something like this?:

vertexArray = {x1,y1,z1, x2,y2,z2, x3,y3,z3, x4,y4,z4}indexArray = {0,0,0, 1,1,1, 2,2,2, 1,1,1, 3,3,3, 2,2,2}Where the polygon looks like:P0-P1| / |P2-P3and is wound clockwise.

[Edited by - DerUnterMensch on January 30, 2008 1:57:58 PM]

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Quote:
 I have figured that an indexed array would probably be the best way to do what I'm after, but I can't really remember how to do indexed arrays and can't seem to find any of my books on either DirectX or OpenGL.

DirectX SDK (for example) should have examples about using indexed primitives.

Quote:
 When provided with an array of vertices the API looks for a single index for every three vertices in the vertex array? Or is it more complicated?

When using triangle list, the API reads 3 indices at a time from the index buffer and makes one triangle out of them (by using the vertices defined in the vertex buffer).

So, when defining triangle list the index buffer has three times as many indices as there is triangle primitives.

Quote:
 Regrettably even if I can find my books and refresh on index arrays, I've no idea how to calculate the indexes algorithmically as I want to be able to control the resolution of the patch on runtime so I can't simply work out the indexes and expect them not to change.

I am not sure what you are talking about. Are you trying to implement some sort of LOD algorithm?

If I am not totally mistaken about your question, the following code would do the work for you.

//Something like thisfor(int y = 0; y < NumVerticesY-1; ++y){for(int x = 0; x < NumVerticesX-1; ++x){    int Index = y * NumVerticesX;    *indices++ = Index;    *indices++ = Index+1;    *indices++ = Index+NumVerticesX;    *indices++ = Index+1;    *indices++ = Index+NumVerticesX;    *indices++ = Index+NumVerticesX+1;}}

Regards!

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Quote:
 Original post by DerUnterMenschkauna:I have figured that an indexed array would probably be the best way to do what I'm after, however I'm not 100% sure how they work anymore as I tend to avoid them because they make normal calculations a bit less straightforward.

Having index array shouldn't really affect the way you calculate your normals.

Quote:
 vertexArray = {x1,y1,z1, x2,y2,z2, x3,y3,z3, x4,y4,z4}indexArray = {0,0,0, 1,1,1, 2,2,2, 1,1,1, 3,3,3, 2,2,2}Where the polygon looks like:P0-P1| / |P2-P3

Your index array should look like:

indexArray = {0,1,2,1,3,2}

and usually vertices have more components than just position (such as normal, texture coordinates etc).

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Quote:
 ...and usually vertices have more components than just position (such as normal, texture coordinates etc).

I tend to send vertices, normals, and texture coordinates to the GPU in separate arrays. When I know the mesh isn't going to be messed with I try to package everything together, but repacking an array constantly for a program that changes the normals or texture coordinates every frame and doesn't touch the rest is a pest.

Quote:
 I am not sure what you are talking about. Are you trying to implement some sort of LOD algorithm?

At the moment I'm sampling the patch in increments to give me a 10x10 grid of points, but if I were to make it to were the program could sample more or less often the number of points would change. This would break most of the ways I can think of calculating the indices so that the grid would render as triangle strips as I can't simply say a polygon is vertexArray[x], vertexArray[x+1], and vertexArray[x+1*gridWidth] or something like that as the vertices are in groups of three and x would be the x coord, x+1 would be the y coord (not the x coord of the next point), and x+1*gridWidth would be something completely wrong.

Quote:
 If I am not totally mistaken about your question, the following code would do the work for you.

Perhaps this is exactly what I'm trying to do but I don't think so. I guess I'm just going to have to leave this unsolved and go back to basics as I seem to have allowed myself to forget way to much after I wrote my engine to do all this stuff for me (though I never did finish a model loader so I don't have any code relevant to this sort of problem, though an imported mesh is usually ordered correctly from the start, so that probably wouldn't help anyways).

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Hi,

I think that you are trying to do things a bit in hard way.

Quote:
 ...but repacking an array constantly for a program that changes the normals or texture coordinates every frame and doesn't touch the rest is a pest.

It is quite the same to change normals or texture coordinates was the data in vertex structures or in separate arrays. So, constant repacking shouldn't be needed.

Quote:
 At the moment I'm sampling the patch in increments to give me a 10x10 grid of points, but if I were to make it to were the program could sample more or less often the number of points would change.

It is perfectly ok to resample or recreate your patch vertices/indices if you want to present it in a different sampling resolution. In the case you are doing it very often so that it creates some significant overhead, then (and only then) you might consider a more complicated solutions.

However, I'd first work out the simple and working version, then do the profiling to see if it requires some optimisations.

As a programmer you'll need to define yourself the rules how your system works. For example, for triangulating a grid I have made a rule which works. Although it works only for grids, thats enough because it is only used with grids.

If you have just a bunch of vertices, there is absolutely no way to figure out the correct triangulation.

Cheers!

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Quote:
 Original post by DerUnterMenschRobTheBloke: Thanks for the source. I looked at it briefly and I'm not entirely sure it really helps as the vertices appear to already be assumed to be in the correct order unless I'm mistaken.

they are ordered as such

idx=0;for(i=0;i<divsu;++i){  for(int j=0;j<divsv;++j)  {    verts[idx] = evalAt(i,j);    ++idx;  }}

The tri strips then get generated as...

0       1       2            divsv-1|   /   |   /   |   /divsv+0 divsv+0 divsv+2 .... divsv+divsv-1

or something along those lines anyway.

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I think I've got it now. Thanks to you both. Most of my trouble was that I was letting it bother me too much because I couldn't figure it out. Now I just have to see how complicated I can make this thing. I wonder if it's possible to create a high res planet mesh by tiling bilinear patches, though I suppose the terrain would be unrealistically smooth.

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