Explain linear algebra for graphics transforms

Q: Explain linear algebra for graphics transforms

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Question

MVP Pipeline, Homogeneous Coordinates, NDC, Screen Space, and Normal Transformation

Context

You are working in a standard real-time graphics pipeline. Use column vectors, right-handed camera space, and OpenGL-style conventions unless noted:

Clip-space to NDC uses perspective divide by w.
NDC ranges: x, y, z ∈ [−1, 1].
Viewport origin at the bottom-left.

Tasks

Explain the model–view–projection (MVP) pipeline using homogeneous coordinates.
Derive how a 3D point in world space transforms to normalized device coordinates (NDC), and then to screen (window) space.
Explain why surface normals are transformed by the inverse-transpose of the model (or model-view) matrix.
Provide a concrete numeric example that goes from world space to screen space and demonstrates correct normal transformation.

Explain linear algebra for graphics transforms

MVP Pipeline, Homogeneous Coordinates, NDC, Screen Space, and Normal Transformation

Context

Tasks

Solution (Locked)

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