Explain linear algebra for graphics transforms
Overview
This question evaluates mastery of linear algebra for graphics transforms, covering homogeneous coordinates, the model–view–projection (MVP) pipeline, clip-space to NDC mapping, viewport/screen-space conversion, and correct normal transformation via the inverse-transpose of the model (or model-view) matrix.
NVIDIA
Aug 9, 2025, 12:00 AM
Software Engineer
Take-home Project
Statistics & Math
0
0
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.
Solution
Login required
Show