Notes

NDC is the box x, y, z ∈ [-1, 1] that the GPU maps onto the window. Because the window is not square, one NDC unit is a different number of pixels in x and y, so geometry must be pre-squashed.

NDC

(-1, 1) ──────── (1, 1)
   │      (0,0)     │      center is the origin
(-1,-1) ──────── (1,-1)

Anything outside is clipped. z also has to be in [-1, 1].

(cos θ, sin θ) lies on the unit circle and touches the edges; multiply by a radius (e.g. 0.5) for margin.

Aspect ratio correction

640×480 window: one NDC unit in x = 320 px, in y = 240 px.
Divide x by aspect = width / height so the GPU’s stretch cancels it out.

	vs_Pos	after x /= 1.333	on screen
right point	(0.5, 0)	(0.375, 0)	0.375 × 320 = 120 px
top point	(0, 0.5)	(0, 0.5)	0.5 × 240 = 120 px

Same distance on screen → a true circle.

Which space to do math in

The corrected position is deliberately distorted so the screen stretch cancels it. Only gl_Position gets that stretch.

Shader math like length for a ring pattern is not stretched by anything, so it must use a space where x and y units are equal: the original vs_Pos, or gl_FragCoord / screenSize with uv.x *= aspect. Using the corrected position turns circles into ellipses.

2D homogeneous coordinates

• Store 2D vertices as vec3(x, y, 1) so a mat3 can translate as well as rotate and scale.
• Shader order: u_Model * vs_Pos first, aspect correction second, output z = 0.
• Transforming after the correction would rotate in the squashed space and deform the shape.

Related

OpenGL Hub · Coordinate spaces (rendering pipeline) · Clipping · Matrix composition order (SRT)