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For others who might have this question, here a perhaps more straight forward numeric answer (I'm now working myself on this book as well). Consider that: We are given object space coordinates that need to be transformed into upright and subsequently world space coordinates. We know that a vector $\vec{v}$ can be represented as a linear transformation of ...


The space at which you transform your vertices is completely up to you, because it depends on what algorithms and kind of effects that you are trying to achieve. As of my personal experience, I usually shoot rays in world space because eventually we all need some sort of "world-space" acceleration data structure, such as a space-partition tree, that gathers ...

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