RorrKonn,

The linked page

Mathematical foundations

is an excellent summary of the common mathematics of n-dimensional vector arithmetic. In particular, 3D is 3-dimensional, and is thoroughly introduced (but not discussed in detail as a textbook would).

If you can follow that whole thing, then you're more than ready to do some very sophisticated stuff.

Section A.2 Rn as a real vector space is a must. If you're going to write any algorithms that interact with geometry, then you have to be able to understand coordinates in 3D, vectors in 3D and their normals, dot products and cross products of vectors to find how they relate to each other (angles and such).

Section A.3 The point set topology of Rn is crucial to being able to write a polygon reduction algorithm, since the primary aspect there is to know when you can safely collapse two points into one without fear of significantly altering the mesh.

Things get more complicated from there. You would want to understand how to generalize smooth functions in 3D (section A.6) to be able to do things like collision detection on subdivision surfaces and so on, where the recorded mesh points are not joined by simple flat faces.

Section A.7 Smooth curves in Rn would be really important for defining 3D splines for animation, as well as determining where a ray in ray-tracing might intersect various curved shapes expressed as mathematical relations.

Section A.9 Projection function is necessary to work with various kinds of cameras.

This is by no means a complete set. For example, nowhere in there is anything mentioned about rotation, translation, and scaling as it applies to manipulation of models in 3D space. That involves matrix arithmetic operations on the vectors.

If that leaves you hungry for more, OK then, have a look at this.

standards.iso.org/ittf/PubliclyAvailableStandards/C030811e_FILES/MAIN_C030811e/ISOIEC_18026E_TOC.HTM

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