关于opengl：mat4x4与vec4的乘积顺序有什么区别？

What is the difference between the order in which a mat4x4 is multiplied with a vec4?

考虑两个GLSL顶点着色器：

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#version 450

in vec4 vertex;
uniform mat4 transformationMatrix;

void main() {
gl_Position = transformationMatrix * vertex;
}

和

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#version 450

in vec4 vertex;
uniform mat4 transformationMatrix;

void main() {
gl_Position = vertex * transformationMatrix;
}

根据我的测试，这两个文件都可以正确编译。

mat4与vec4的乘积顺序之间是否有区别？

如果是这样，到底有什么区别？

相关讨论

对于vec4 vertex和mat4 matrix，vertex * matrix等效于transpose(matrix) * vertex。

请参阅GLSL编程/向量和矩阵运算：

Furthermore, the *-operator can be used for matrix-vector products of the corresponding dimension, e.g.:

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vec2 v = vec2(10., 20.);
mat2 m = mat2(1., 2., 3., 4.);
vec2 w = m * v; // = vec2(1. * 10. + 3. * 20., 2. * 10. + 4. * 20.)

Note that the vector has to be multiplied to the matrix from the right.

If a vector is multiplied to a matrix from the left, the result corresponds to multiplying a row vector from the left to the matrix. This corresponds to multiplying a column vector to the transposed matrix from the right:
Thus, multiplying a vector from the left to a matrix corresponds to multiplying it from the right to the transposed matrix:

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vec2 v = vec2(10., 20.);
mat2 m = mat2(1., 2., 3., 4.);
vec2 w = v * m; // = vec2(1. * 10. + 2. * 20., 3. * 10. + 4. * 20.)