If glPosition is (ProjectionMat * ViewMat * WorldMat * vertexPosition). How to convert from gl_Position to Screen Coordinates

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Gotanod said:

Hi @bogdan7

I'm curious about what you are trying to do with that transformation, could you share more details?

Anyway, glPosition will be in NDC (non-device coordinates) [-1,1] with center in the middle of the screen.
You just need to escalate and translate to get Screen coordinates (pixel in the screen)

From [-1,1] to [0, screenWidth]
From [-1,1] to [0, screenHeight]

X - width
screen.x = (1 + glPosition.x) * screenWidth/2 ===> 0 will be the left side of the screen

Y-Height
screen.y = (1 + glPosition.y) * screenHeight/2 ===> 0 will be the bottom of the screen
screen.y = (1 - glPosition.y) * screenHeight/2 ===> 0 will be the top of the screen

Regards.

I started experimenting with GPU related things and I tried to make a 3D scene without using any API like OpenGL or DirectX or Vulkan. I used java and I created a simple JFrame and added a BufferedImage to the JFrame where I change every frame the BufferedImage. I created a simple graphics math library with the definition of matrices, vector3, vector4, transformation matrix, lookat, perspective, orthographic matrices and I am trying to display a simple triangle like this:

vec3[] vertices = new vec3[]{
	new vec3(-1f, -1f, 0),
	new vec3(0, 1f, 0),
	new vec3(1f, -1f, 0)
};
vec2[] screenPositions = new vec3[vertices.length];
mat4 transformation = new mat4(); //idendity
mat4 view = mat4.lookat(new vec3(0, 0, -2), vec3.zero, vec3.up);
mat4 projection = mat4.perspective(45.0f, 3f/4f, 0.03f, 1000f);

mat4 matrix = mat4.multiply(mat4.multiply(projection, view), tranformation);
for(int i=0;i<vertices.length;i++){
	vec4 vertex_clip_position = mat4.multiplyMatWithVector(matrix, new vec4(vertices[i], 1))
	vec2 vertex_screen_position = ? //That's what I asked, how to get the screen_verte_position using clip position
	screenPositions[i]=vertex_screen_position;
}
/*(BufferedImage)*/renderBuffer = Screen.Interpolation(renderBuffer, screenPositions, DrawMode.Solid);//A method created by me to fill all pixels between the 3 vertices

It is just a test and with no purpose.

I know I should divide somewhere by the w component of the vector

@Gotanod The screen is 800x600. I want to know what corresponds from the vertex positions in object space to the screen coordinate for example vec2(300, 200) is what I mean by screen coordinate. After that the Screen.Interpolation has the role of the finding all the pixels that the triangle occupies on the screen by passing the array of 2D screen coordinates and filling it with color.
I've done this already with OpenGL and Direct3D11 and there I pass to the vertex shader the vector4 after multiplying the 3 matrices with the vector representing the 3D coordinates in object space and then the pixel(HLSL)/fragment(GLSL) shader takes care of drawing. Now I need to understand what this shader does with the coordinates supplied by the matrix calculation:
For example:
1. vertexPositionObjectSpace * Transformation Matrix = vertexPositionWorldSpace
2. vertexPositionWorldSpace * View Matrix = vertexPositionCameraSpace
3. vertexPositionCameraSpace * Projection Matrix = vertexPositionClipSpace //I don't understand what clip space means, is it synonime with NDC?
4. vertePositionClipSpace * ? = vertexPositionScreenSpace
5. Interpolation to fill the pixels with material

The 1, 2, 3 points is what I am used to. 4 and 5 is what the shader did in my other projects.

The screen interpolation method takes the vertices in screen coordinates(Represented by A B C) and aproximates which pixels(represented by blue dots) should be filled with the material to draw the triangle:

To create the method I followed this tutorial: https://www.scratchapixel.com/lessons/3d-basic-rendering/rasterization-practical-implementation/rasterization-stage

Gotanod said:
Anyway, try to multiply the vertex_clip_position with this matrix, where sW = frame width in pixels, sH= frame Height in pixels.

Where is the part where I divide the x, y by the w? That's what I know I should do in order to project the 3D to 2D