Understanding the Geometric Foundations of Tangent Space and Normal Mapping in Computer Graphics
By
betamark
Hand-rolled, kettle-boiled, baked to perfection. Worth every minute at the bakery.
Summary
This article provides a deep dive into the geometric foundations of tangent space and normal mapping in computer graphics. It explains how tangent vectors emerge from UV mapping to bridge 2D and 3D space, moving beyond the typical shader code snippets to explore the underlying mathematical and geometric principles that make normal mapping work. The author shares their journey from simply using normal maps to understanding the fundamental geometry behind them, addressing the common confusion around tangent space that's often presented as opaque mathematical formulas without clear geometric intuition.
Key quotes
· 4 pulledI first ran into tangent space while learning about normal mapping. It was described as this in-between space that connects surfaces and UVs, something you need to make lighting work. Nobody really explained what it was.
Tutorials showed math and shader code snippets, but none of them answered the real question: what is tangent space and why does it exist at all?
When I first learned about normal mapping I didn't care as long as the normals looked right. But while working on mesh processing for VGLX that answer stopped being enough.
This is a deep dive into what tangent vectors actually mean, how they emerge from UVs to bridge 2D and 3D space, and the geometry that makes normal mapping possible.
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