目前为止,我们仍然把三维顶点视为三元组(x,y,z)。现在引入一个新的分量w,得到向量(x,y,z,w)。请先记住以下两点(稍后我们会给出解释):
若w==1,则向量(x, y, z, 1)为空间中的点。 若w==0,则向量(x, y, z, 0)为方向。 (请务必将此牢记在心。)
二者有什么区别呢?对于旋转,这点区别倒无所谓。当您旋转点和方向时,结果是一样的。但对于平移(将点沿着某个方向移动)情况就不同了。”平移一个方向”是毫无意义的。
齐次坐标使得我们可以用同一个公式对点和方向作运算。
单位矩阵很特殊,它什么也不做。单位矩阵的身份和自然数”1”一样基础而重要,因此在这里要特别提及一下。
TransformedVector = TranslationMatrix * RotationMatrix * ScaleMatrix * OriginalVector;
注意这行代码首先执行缩放,接着旋转,最后才是平移。这就是矩阵乘法的工作方式。
- 第一步:创建模型观察投影(MVP)矩阵。任何要渲染的模型都要做这一步。
// Projection matrix : 45° Field of View, 4:3 ratio, display range : 0.1 unit <-> 100 units
glm::mat4 Projection = glm::perspective(glm::radians(45.0f), (float) width / (float)height, 0.1f, 100.0f);
// Or, for an ortho camera :
//glm::mat4 Projection = glm::ortho(-10.0f,10.0f,-10.0f,10.0f,0.0f,100.0f); // In world coordinates
// Camera matrix
glm::mat4 View = glm::lookAt(
glm::vec3(4,3,3), // Camera is at (4,3,3), in World Space
glm::vec3(0,0,0), // and looks at the origin
glm::vec3(0,1,0) // Head is up (set to 0,-1,0 to look upside-down)
);
// Model matrix : an identity matrix (model will be at the origin)
glm::mat4 Model = glm::mat4(1.0f);
// Our ModelViewProjection : multiplication of our 3 matrices
glm::mat4 mvp = Projection * View * Model; // Remember, matrix multiplication is the other way around
- 把MVP传给GLSL
// Get a handle for our "MVP" uniform
// Only during the initialisation
GLuint MatrixID = glGetUniformLocation(programID, "MVP");
// Send our transformation to the currently bound shader, in the "MVP" uniform
// This is done in the main loop since each model will have a different MVP matrix (At least for the M part)
glUniformMatrix4fv(MatrixID, 1, GL_FALSE, &mvp[0][0]);
- 第三步:在GLSL中用MVP变换顶点
// Input vertex data, different for all executions of this shader.
layout(location = 0) in vec3 vertexPosition_modelspace;
// Values that stay constant for the whole mesh.
uniform mat4 MVP;
void main(){
// Output position of the vertex, in clip space : MVP * position
gl_Position = MVP * vec4(vertexPosition_modelspace,1);
}