Question background:

I need to align two images with the same resolution and display the alignment on an OpenGL canvas. So I prepared the vertices like so:

    float vertices[] = {
            // positions
            0.0f,  0.0f,     // bottom left
            width,  0.0f,    // bottom right
            0.0f, height,    // top left
            width,  0.0f,    // bottom right
            0.0f, height,    // top left
            width, height,   // top right
    };

This way I can draw any number of images on top the other using the same shader, I just send the texture and a transformation matrix to the shader per each aligned image.

With the following vertex and fragment shader, the effect is working as expected:

Vertex shader:

#version 330 core
layout (location = 0) in vec3 vertex_in;

out vec2 TexCoord;

uniform mat3 cvAffine; // OpenCV affine transformation matrix

const vec2 texture_coord[] = {
  vec2( 0.0, 0.0),
  vec2( 1.0, 0.0),
  vec2( 0.0,  1.0),
  vec2( 1.0,  0.0),
  vec2( 0.0,  1.0),
  vec2( 1.0,  1.0)
};


void main(){
    vec3 cvCoord = vec3(vertex_in.xy,1.0f); //Create homogenous 2D vector for 3x3 mat mult.
    vec3 transformedCoord = cvAffine*cvCoord; //Transform the image
    gl_Position = vec4((transformedCoord.xy*0.0002), 0.0, transformedCoord.z); //Scale it down for us to see it
    TexCoord = texture_coord[gl_VertexID]; //Send a texture coordinate to the frag. shader
};

Fragment shader

#version 330 core
in vec2 TexCoord;
out vec4 FragColor;

uniform sampler2D texture;
void main(){
    FragColor = texture(texture, TexCoord);
}

The effect:

The actual question:

When I modify this line in the vertex shader:

    gl_Position = vec4((transformedCoord.xy*0.0002), 0.0, transformedCoord.z);

with supposedly equivalent line:

    gl_Position = vec4(((transformedCoord.xy/transformedCoord.z)*0.0002), 0.0, 1.0);

the alignment breaks:

And there is this common problem with many names:

• Affine Texture mapping
• Perspective correct Texture mapping
• Projective Texture mapping
• Trapezoid texture mapping

How is it possible that Vector(xW,yW,z*W,W) is not equal to Vector(x,y,z,1)? Or at least the fragment shader does not agree with that? I need to have 1 in gl_Position.w component as it allows me to further transform pictures around the canvas while preserving the alignment. I have touched the w component of the uv texture space and project it in some way but I was not successful. How to properly transform the texture coordinates so that the texture is sampled uniformly across the whole distorted two-triangle rectangle?

The geometry itself does not change between the modification, only the texture is drawn differently.