How to keep Opengl Scatter Instances size unchanged?

Question

Here is my question, i will list them to make it clear:

1. I am writing a program drawing squares in 2D using instancing.
2. My camera direction is (0,0,-1), camera up is (0,1,0), camera position is (0,0,3), and the camera position changes when i press some keys.
3. What I want is that, when I zoom in (the camera moves closer to the square), the square's size(in the screen) won't change. So in my shader:

#version 330 core
layout(location = 0) in vec2 squareVertices;
layout(location = 1) in vec4 xysc; 
out vec4 particlecolor;
uniform mat4 VP; 

void main()
{
    float particleSize = xysc.z;
    float color = xysc.w;
    
    gl_Position = VP* vec4(xysc.x, xysc.y, 2.0, 1.0) + vec4(squareVertices.x*particleSize,squareVertices.y*particleSize,0,0);
    particlecolor = vec4(1.0f * color , 1.0f * (1-color), 0.0f, 0.5f);
}

Please notice that, inorder to keep the squares' size unchanged, what I do is:

1. transform the center of the square first
VP * vec4(xysc.x, xysc.y, 2.0, 1.0) 

2. then compute one of the four corners (x,y,z,1) of the square 
+ vec4(squareVertices.x*particleSize,squareVertices.y*particleSize,0,0);

instead of:

   gl_Position = VP* (vec4(xysc.x, xysc.y, 2.0, 1.0) + vec4(squareVertices.x*particleSize,squareVertices.y*particleSize,0,0));

However when I move the camera closer to z=0 plane. The squares' size grows unexpectedly. Where is the problem? I can provide a demo code if necessary.

Answer 1

Sounds like you use a perspective projection, and the formula you use in steps 1 and 2 won't work because VP * vec4 will in the general case result in a vec4(x,y,z,w) with the w value != 1, and adding a vec4(a,b,0,0) to that will just get you vec3( (x+a)/w, (y+b)/w, z) after the perspective divide, while you seem to want vec3(x/w + a, y/w +b, z). So the correct approach is to scale a and b by w and add that before the divde: vec4(x+a*w, y+b*w, z, w).

Note that when you move your camera closer to the geometry, the effective w value will approach towards zero, so (x+a)/w will be a greater than x/w + a, resulting in your geometry getting bigger.