阴影映射中的偏差矩阵 [英] bias matrix in shadow mapping

问题描述

我正在研究OpenGL中的阴影映射.

I'm looking at shadow mapping in OpenGL.

我看到如下代码:

// This is matrix transform every coordinate x,y,z
// x = x* 0.5 + 0.5 
// y = y* 0.5 + 0.5 
// z = z* 0.5 + 0.5 
// Moving from unit cube [-1,1] to [0,1]  
const GLdouble bias[16] = {
  0.5, 0.0, 0.0, 0.0,
  0.0, 0.5, 0.0, 0.0,
  0.0, 0.0, 0.5, 0.0,
  0.5, 0.5, 0.5, 1.0};

// Grab modelview and transformation matrices
glGetDoublev(GL_MODELVIEW_MATRIX, modelView);
glGetDoublev(GL_PROJECTION_MATRIX, projection);


glMatrixMode(GL_TEXTURE);
glActiveTextureARB(GL_TEXTURE7);

glLoadIdentity();
glLoadMatrixd(bias);

// concatating all matrice into one.
glMultMatrixd (projection);
glMultMatrixd (modelView);

// Go back to normal matrix mode
glMatrixMode(GL_MODELVIEW);

现在，如果我剔除偏见矩阵.该代码不起作用.搜索其他阴影映射代码，我看到了相同的偏差矩阵，没有任何解释.为什么要让这种偏见将x，y，z映射到0.5 * x + 0.5、0.5 * y + y，...?

Now, if I rip out the bias matrix. The code does not work. Searching other shadow mapping code, I see the same bias matrix, without any explaination. Why do I want this bias to map x, y, z to 0.5 * x + 0.5, 0.5 * y + y, ... ?

谢谢！

推荐答案

当您使用标准的modelview/projection矩阵在视锥内部转换顶点时，得到的结果是一个顶点，一旦完成w-divide，就可以[-1:1] x [-1:1] x [-1:1]立方体.您希望纹理坐标在[0:1] x [0:1]范围内，因此需要重新映射x和y.假设您的 DepthRange 是[0:1]，这是默认设置.

when you transform vertices inside the frustum with a standard modelview/projection matrix, the result you get is a vertex that, once w-divide is done, is in the [-1:1]x[-1:1]x[-1:1] cube. you want your texture coordinates to be in the [0:1]x[0:1] range, hence the remapping for x and y. It's the same kind of thing for Z, assuming your DepthRange is [0:1], which is the default.

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