# OpenGL Quick confirmation on Triangle Strips / Degenerate Triangles

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In order to squeeze some increased performance out of iOS devices, I'm working on converting my geometry into indexed triangle strips. I found a program (htgen) that works with wavefront obj files and produces a list of indices to produce triangle strips. Brilliant I thought! But then when I tried rendering the newly generated data, the end result looked worse than this:

Now, initially I knew that I had to connect strips with degenerate triangles, however I had no idea that the number of degenerate triangles between strips were not constant.

After spending hours reading up on triangle strips, I finally discovered the winding of a proceeding strip can be altered if the incorrect number of degenerate triangles were inserted in between two strips. I spent a few more hours writing out some basic triangle strips over pages and pages of paper and figured out (or so I thought?) exactly how many degenerate triangles were needed depending upon the previous triangle's number.

So please correct me if I'm wrong, but:
1) If I have 4 triangles, defined as the indices 0 1 2 3 4 5, OpenGL will draw 4 triangles in the following order: 0 1 2, 2 1 3, 2 3 4, 4 3 5 (which let's assume is CCW for this example).

2)
When joining two strips, normally only 2 extra indices need to be inserted, generating 4 degenerate triangles. So building on the previous strip, if I were to want to join a new strip consisting of 3 new triangles defined as a strip of 6 7 8 9 10 (triangles 6 7 8, 8 7 9, 8 9 10), the final joined list of indices would look like 0 1 2 3 4 5 5 6 6 7 8 9 10 where the bolded numbers are the extra inserted vertices creating 4 new degenerate triangles.

3)
If joining two strips, and the first triangle of the new strip is odd (as in, the first strip had 3 triangles, numbered 0, 1 and 2, and now the starting triangle of the 2nd strip is numbered 3) three additional indices must be inserted in between the two strips generating a total 5 degenerate triangles in order for the winding of the 2nd strip to remain CCW.

Now based on what I just outline above, I fixed up my code to insert the correct number of degenerate triangles between strips and got the above image which while is an improvement over the original, it's still in no way correct (the object should look like Canada and the US). So now I'm stuck and I have to assume that if my above understandings are correct, that the htgen program is not generating strips with consistent winding orders (the objects render perfectly fine if I turn off culling).

If that's the case, it looks like I'll have try generating strips myself because I literally cannot find another suitable application that will generate triangle strips. So in the interest of saving myself even more headache and time spent on writing my own application to generate triangle strips, I wanted to confirm that my understanding of the subject is indeed correct.

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If you're using indexes you don't need degenerate triangles. Just draw with GL_TRIANGLES instead and arrange your indexes so that your strips are concatenated.

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If you're using indexes you don't need degenerate triangles. Just draw with GL_TRIANGLES instead and arrange your indexes so that your strips are concatenated.

Do you have something I can reference that describes what you're talking about? I've only ever read of concatenating strips using degenerate triangles. I'm not sure how I'd go about doing so in such a way that rendering the data as GL_TRIANGLES would work.

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Say you've got 2 strips, strip 1 has vertexes 0, 1, 2, 3 and strip 2 has vertexes 4, 5, 6, 7. To render them with GL_TRIANGLES you use indexes 0, 1, 2, 1, 3, 2, 4, 5, 6, 5, 7, 6 for your glDrawElements call. No need to make any changes to the vertexes. That'll do it.

The number of indexes you need for each strip is always (numverts - 2) * 3 and just remember to follow the winding order rules, reversing the order for alternate tris that make up the strip. Code for writing out indexes might look something like this:

 for (int i = 2; i < stripverts; i++) { indexes[totalindexes++] = totalverts + i - 2; indexes[totalindexes++] = (i & 1) ? (totalverts + i) : (totalverts + i - 1); indexes[totalindexes++] = (i & 1) ? (totalverts + i - 1) : (totalverts + i); } totalverts += stripverts;

Then just ensure that all of your vertexes for all strips are in a single big array (or single VBO, as appropriate) and your draw call is:

glDrawElements (GL_TRIANGLES, totalindexes, GL_UNSIGNED_WHATEVER, indexes); // _WHATEVER is _SHORT or _INT, replace indexes with 0 for a VBO

OK, it's more indexes, but indexes are much smaller than full vertexes, the duplicate vertexes will be in your cache and so won't need to be retransformed, and you'll find that the overall submission is lighter than with degenerate triangles.

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Thanks a lot mhagain for your detailed explanation. In the end it's essentially functions like indexed triangles correct? If so I'm not sure it'll provide any performance improvements over what I'm doing already. It's recommended that on the iPhone that actual triangle strips are to be used for optimal performance.

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This site has source code that works and an explanation of all the little gotchas related to creating triangle strips.
For example, yes you need to add a vertex when joining strips, but only one vertex if the first vertex of the second strip has already been duplicated.
Some strips need to be reversed under certain circumstances.

Following his article and code I implemented my own triangle stripper that does work 100% of the time.
However as you can see by my results here, adding triangle strips actually decreased my performance. The reason was that they thrashed my cache.
For me, ordering the vertices for best use of the cache has proved the most helpful. My site is specifically for these kinds of discoveries, so that you can see what types of things have what impact on performance.

However there is no difference between graphics RAM and CPU RAM on iPhone devices, and caching will work a bit differently. You could continue your quest and see what happens, but don’t be surprised if nothing is gained.
I am waiting for my Macintosh computer so I can test this myself too, and I will post my results when I have done so.

L. Spiro

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I love it when a plan comes together! After writing my Triangle Stripper program over the course of a few hours, I tested it today and it worked completely in the first try! It runs amazingly quick (about 1 second to strip a model composed of 2400+ vertices) and produces some very large strips. Unfortunately it produces quite a few short strips as well. But most importantly is, the strips that it does generate render 100% perfectly.

Compared to the htgen program I was using before, it produces roughly 17% more strips .

Now that it works, I can tinker with it and try and eliminating those rogue strips of 1 or 2 faces.

edit:
And just an additional small update. My game's performance has now jumped over 26% from using indexed triangles in VBOs. Now I just need to perform some basic frustum culling and I should be set!

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Be warned: the code he provides, while very helpful for getting a result and understanding all the gotchas, is not particularly fast (and there is a leak of memory when it fails in some cases).
My rewrite of his code is over 4 times faster, so if you did use his as a reference, be aware that there is tons of room for improvement. Your 1 second would go below to 0.25 seconds.

Suggestions for improving upon his code: Use a faster sort (I use a bottom-up merge sort) and make fewer allocations. Pass buffers down to be reused when you are searching the 3 directions of the triangle strips.

L. Spiro

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Be warned: the code he provides, while very helpful for getting a result and understanding all the gotchas, is not particularly fast (and there is a leak of memory when it fails in some cases).
My rewrite of his code is over 4 times faster, so if you did use his as a reference, be aware that there is tons of room for improvement. Your 1 second would go below to 0.25 seconds.

Suggestions for improving upon his code: Use a faster sort (I use a bottom-up merge sort) and make fewer allocations. Pass buffers down to be reused when you are searching the 3 directions of the triangle strips.

L. Spiro

I read over the article before in the past, and re-read it again but wrote my stripper on my own. I'm not doing much sorting and the results are written as binary data to files which are loaded at the appropriate time when the game is running. So the actual performance of the code is not a huge importance since the binary files are loaded extremely quickly.

The actual logic for the stripper is rather simple. It essentially just generates all possible strips for a given mesh and selects the longest strip and keeps repeating until no more free faces are left.

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any one have sample code for triangle strip

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I literally can't find what is wrong. If you need more code, ask me to post it. I will also attach all the source files.
Brain.cpp
Error.cpp
IndexBuffer.cpp
Input.cpp
Renderer.cpp
Scene.cpp
Sprite.cpp
Texture.cpp
VertexArray.cpp
VertexBuffer.cpp
VertexBufferLayout.cpp
Window.cpp
Brain.h
Error.h
IndexBuffer.h
Input.h
Renderer.h
Scene.h
SpaceShooterEngine.h
Sprite.h
Texture.h
VertexArray.h
VertexBuffer.h
VertexBufferLayout.h
Window.h

• Hello fellow programmers,
For a couple of days now i've decided to build my own planet renderer just to see how floating point precision issues
can be tackled. As you probably imagine, i've quickly faced FPP issues when trying to render absurdly large planets.

I have used the classical quadtree LOD approach;
I've generated my grids with 33 vertices, (x: -1 to 1, y: -1 to 1, z = 0).
Each grid is managed by a TerrainNode class that, depending on the side it represents (top, bottom, left right, front, back),
creates a special rotation-translation matrix that moves and rotates the grid away from the origin so that when i finally
normalize all the vertices on my vertex shader i can get a perfect sphere.
T = glm::translate(glm::dmat4(1.0), glm::dvec3(0.0, 0.0, 1.0)); R = glm::rotate(glm::dmat4(1.0), glm::radians(180.0), glm::dvec3(1.0, 0.0, 0.0)); sides[0] = new TerrainNode(1.0, radius, T * R, glm::dvec2(0.0, 0.0), new TerrainTile(1.0, SIDE_FRONT)); T = glm::translate(glm::dmat4(1.0), glm::dvec3(0.0, 0.0, -1.0)); R = glm::rotate(glm::dmat4(1.0), glm::radians(0.0), glm::dvec3(1.0, 0.0, 0.0)); sides[1] = new TerrainNode(1.0, radius, R * T, glm::dvec2(0.0, 0.0), new TerrainTile(1.0, SIDE_BACK)); // So on and so forth for the rest of the sides As you can see, for the front side grid, i rotate it 180 degrees to make it face the camera and push it towards the eye;
the back side is handled almost the same way only that i don't need to rotate it but simply push it away from the eye.
The same technique is applied for the rest of the faces (obviously, with the proper rotations / translations).
The matrix that result from the multiplication of R and T (in that particular order) is send to my vertex shader as r_Grid'.
// spherify vec3 V = normalize((r_Grid * vec4(r_Vertex, 1.0)).xyz); gl_Position = r_ModelViewProjection * vec4(V, 1.0); The r_ModelViewProjection' matrix is generated on the CPU in this manner.
// No the most efficient way, but it works. glm::dmat4 Camera::getMatrix() { // Create the view matrix // Roll, Yaw and Pitch are all quaternions. glm::dmat4 View = glm::toMat4(Roll) * glm::toMat4(Pitch) * glm::toMat4(Yaw); // The model matrix is generated by translating in the oposite direction of the camera. glm::dmat4 Model = glm::translate(glm::dmat4(1.0), -Position); // Projection = glm::perspective(fovY, aspect, zNear, zFar); // zNear = 0.1, zFar = 1.0995116e12 return Projection * View * Model; } I managed to get rid of z-fighting by using a technique called Logarithmic Depth Buffer described in this article; it works amazingly well, no z-fighting at all, at least not visible.
Each frame i'm rendering each node by sending the generated matrices this way.
// set the r_ModelViewProjection uniform // Sneak in the mRadiusMatrix which is a matrix that contains the radius of my planet. Shader::setUniform(0, Camera::getInstance()->getMatrix() * mRadiusMatrix); // set the r_Grid matrix uniform i created earlier. Shader::setUniform(1, r_Grid); grid->render(); My planet's radius is around 6400000.0 units, absurdly large, but that's what i really want to achieve;
Everything works well, the node's split and merge as you'd expect, however whenever i get close to the surface
of the planet the rounding errors start to kick in giving me that lovely stairs effect.
I've read that if i could render each grid relative to the camera i could get better precision on the surface, effectively
getting rid of those rounding errors.

My question is how can i achieve this relative to camera rendering in my scenario here?
I know that i have to do most of the work on the CPU with double, and that's exactly what i'm doing.
I only use double on the CPU side where i also do most of the matrix multiplications.
As you can see from my vertex shader i only do the usual r_ModelViewProjection * (some vertex coords).