Inverting Matrices
If you multiply 5 by 4, you get 20. If you later decide to undo that operation, you can multiply 20 by the inverse of 4 (or 1/4) and get 5 again.
That’s pretty much the idea for matrices, too. If you multiply some matrix A by another matrix B, producing C, you can multiply C by the inverse of B to get A again. You’ll use this approach a lot, starting in Chapter 5, Ray-Sphere Intersections, because inverting matrices is the key to transforming and deforming shapes in a ray tracer.
Inverting matrices is a bit more complicated than inverting numbers, though. You’ll employ a method known as cofactor expansion. If that sounds intimidating, take heart! We’ll approach it nice and slow, one step at a time. Starting with routines ...
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