Vertex Shader: Model-View-Projection Transform

Four Coordinate Spaces

A 3D vertex starts in model space (local to the object). Before rendering, it passes through several spaces, each with a transformation matrix:

Model space: object-local coordinates, e.g. cube corners at (-1,-1,-1) to (1,1,1)
World space: model matrix M places the object in the scene
View space: view matrix V moves the camera to origin, looking down -Z
Clip space: projection matrix P maps the frustum to a canonical volume

The combined transform is v_clip = P * V * M * v_model. Column vectors apply right-to-left: M first, then V, then P.

Perspective Division to NDC

Clip space coordinates have a homogeneous w component. The GPU divides by w to reach normalized device coordinates in [-1, 1]. Projection matrices encode field of view, aspect ratio, and near/far planes. Distant objects appear smaller because w grows with depth.

glsl
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For example, a vertex at model-space (1, 0, 0) transformed by translation +45 on X lands at world (46, 0, 0) before view and projection compress it into clip space.

For This Exercise

You will implement 4x4 matrix-vector multiplication and the full MVP chain for a single vertex. This task requires you to print coordinates at each space. Getting multiplication order wrong (PVM vs MVP) is the most common bug on graphics forums, and this exercise forces you to trace the correct sequence.

Write a C program that implements a vertex shader transformation pipeline.

Requirements:

Define a 4x4 matrix struct and a vec4 struct
Implement matrix-vector multiplication for a 4x4 matrix and a 4D vector
Define a vertex in model space: (1, 0, 0, 1)
Define matrices:
- Model: translation by (5, 0, 0) — moves the vertex to world space
- View: translation by (0, 0, -10) — camera at (0,0,10) looking at origin
- Projection: simple orthographic matrix that maps x,y to [-1,1] for a 10-unit range
Compute and print the vertex at each stage:
- Model space
- After model matrix (world space)
- After view matrix (view space)
- After projection matrix (clip space)
Multiply the matrices together (P * V * M) and apply the combined matrix to the original vertex
Verify that the combined matrix gives the same result as applying each matrix in sequence
Print all matrices and intermediate results with 2 decimal places
Explain why the w component starts at 1 and why perspective division is needed

Four Coordinate Spaces

A 3D vertex starts in model space (local to the object). Before rendering, it passes through several spaces, each with a transformation matrix:

Model space: object-local coordinates, e.g. cube corners at (-1,-1,-1) to (1,1,1)

World space: model matrix M places the object in the scene

View space: view matrix V moves the camera to origin, looking down -Z

Clip space: projection matrix P maps the frustum to a canonical volume

The combined transform is v_clip = P * V * M * v_model. Column vectors apply right-to-left: M first, then V, then P.

Perspective Division to NDC

glsl

Loading…

For example, a vertex at model-space (1, 0, 0) transformed by translation +45 on X lands at world (46, 0, 0) before view and projection compress it into clip space.

For This Exercise

Topic Overview

Four Coordinate Spaces

Perspective Division to NDC

For This Exercise

Implementation Task

Progressive Hints

Resources

Open Source

Vertex Shader: Model-View-Projection Transform

Topic Overview

Four Coordinate Spaces

Perspective Division to NDC

For This Exercise

Implementation Task

Progressive Hints

Resources

Open Source