关于GLSL广告牌矩阵顶点转换失效问题的技术问询

Hey there, let's figure out why your matrix approach is acting up while the vector-based calculation works perfectly. The key issue here is a mix-up with how GLSL handles matrix structure and multiplication order—let's break it down step by step.

First, let's recap what your vector math is doing:

vertexModelSpace = axisX * vPosition.x + axisZ * vPosition.y + -axisY * vPosition.z;

This takes each component of your original vertex vPosition and scales the corresponding axis (x → axisX, y → axisZ, z → -axisY), then sums them up. This is equivalent to a standard linear transformation where your axes form the columns of a transformation matrix.

Now look at how you built your rotate matrix:

mat4x4 rotate = mat4x4(vec4(axisX, 0), vec4(axisZ, 0), vec4(-axisY, 0), vec4(0, 0, 0, 1));

In GLSL, matrices are constructed column-major—meaning each vec4 you pass becomes a column of the matrix. So this matrix already has exactly the columns you need for your transformation: column 0 is axisX, column 1 is axisZ, column 2 is -axisY.

The Problem with Transposing #

When you wrote:

//vec3 vertexModelSpace = (transpose(rotate) * vec4(vPosition, 1)).xyz; // 此处为我的困惑点

You're applying the transpose of your matrix, which flips rows and columns. This reverses the relationship between the vertex components and your axes. Instead of mapping vPosition.x to axisX, you're now mapping it to the first row of the original matrix (which is axisX.x, axisZ.x, -axisY.x, 0), which breaks the intended transformation for X and Z axes—only Y might coincidentally behave correctly if the axis alignment was lucky.

The Fix #

You don't need to transpose the matrix at all! Just multiply the original rotate matrix with your vertex vector (as a column vector, which is how GLSL handles vector-matrix multiplication by default):

vec3 vertexModelSpace = (rotate * vec4(vPosition, 1)).xyz;

This will produce exactly the same result as your vector-based calculation, because the matrix is already structured to map each vertex component to the correct axis.

To Confirm #

Let's expand both operations to see they're identical:

• Vector math:

  vertexModelSpace.x = axisX.x * vPosition.x + axisZ.x * vPosition.y + (-axisY.x) * vPosition.z;
  vertexModelSpace.y = axisX.y * vPosition.x + axisZ.y * vPosition.y + (-axisY.y) * vPosition.z;
  vertexModelSpace.z = axisX.z * vPosition.x + axisZ.z * vPosition.y + (-axisY.z) * vPosition.z;
  

• Matrix multiplication (rotate * vec4(vPosition, 1)):
  The x-component is calculated as rotate[0].x * vPosition.x + rotate[1].x * vPosition.y + rotate[2].x * vPosition.z + rotate[3].x * 1, which simplifies to the same as the vector math's x-component (since rotate[0].x is axisX.x, rotate[1].x is axisZ.x, rotate[2].x is -axisY.x, and rotate[3].x is 0). The same applies to y and z components.

That's why your vector approach worked perfectly—you were directly implementing the correct transformation—while the transposed matrix was flipping the axis mappings incorrectly.

内容的提问来源于stack exchange，提问作者HermitZHQ