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Listing "all the maths" is a big task!
The creation of a CAD system requires a broad mix of mathematical knowledge. The line between math and computer science knowledge is blurry. For example, the design of a CAD’s data structure is key to fast display and computation. Is this a “math” skill or would you place it in another category? If you plan to have a 3D system capable of modeling complex sculptured surfaces then I would include numerical analysis and the math of non-uniform rational B-splines (NURBS) to those topics already listed.
Looking at the courses available at a university with a good graduate level computer graphics degree program and a history in computer graphics will give you a feel for the breadth of mathematical topics needed to create a CAD system. For example, examine this list of courses in Computer Science at the University of Utah and search for those that address visualization or geometry. In particular read the course descriptions for:
CS4600 - Introduction to Computer Graphics
CS5610 - Interactive Computer Graphics
CS6160 - Computational Geometry
CS6600 - Mathematical Foundations of Computer Graphics and Visualization
CS6670 - Computer-Aided Geometric Design I
Here’s a portion of the course description for Computer-Aided Geometric Design I:
Introduction to current concepts and issues in CAGD systems with emphasis on free-form surface design; mathematics of free-form curve and surface representations, including Coons patches, Bezier method, B-splines, triangular interpolants, and their geometric consequences; classical surface geometry…
As you can see, there's a lot of math and other skills required to create a sophisticated CAD program.