包装OpenGL矩阵翻译

Question

Let's say i have an OpenGL 4x4 Matrix i use for some transformation, inside my call i use "translate" many times but then, at the end, i want to "wrap" that translation around a specific size, so, in 2D terms, let's say that i translate X by 210, then i want to wrap that translation into a "50 width" box, resulting in a translation of 10 (210 % 50).

Since i need to convert the coordinates into screen pixels i init my Matrix in this way:

private float[] mScreenMatrix = {
        2f / width, 0f, 0f, 0f,
        0f, -2f / height, 0f, 0f,
        0f, 0f, 0f, 0f,
        -1f, 1f, 0f, 1f
};

So, if width is "50" and i call Matrix.translateM(210,0,0) how can i then "wrap" this Matrix so the final translation on x is just 10?

Answer 1

You can't (without doing extra work) because that wrap introduces modulo arithmetic (or a toroidal topology) which doesn't match the way OpenGL's NDC space (which roughly translate to the volume you can see in the window) is laid out. When a primitive reaches out of NDC space it gets clipped so that what remains is within NDC space.

So in order to get a toroidal topology you have to duplicate primitives that get clipped by the NDC and reintroduce them to appear the opposite end of NDC. The only ways to do this is either by explicit submission of extra geometry or by using the geometry shader to create such geometry in-situ.

Answer 2

If you are using orthogonal projection then you can render to a texture and then wrap it as you wish in the second render pass. If you are using perspective projection, still you can use the same method, but the result will be unrealistic.