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# FUNDAMENTAL PROBLEMS IN GEOMETRY in Computer Graphics

## FUNDAMENTAL PROBLEMS IN GEOMETRY

Geometry, especially analytic geometry, offers an effective tool to model graphics objects. The coordinate systems in analytic geometry facilitate numerical representations of geometric models. This modeling scheme is fundamental in a computer graphics system, because geometric entities, properties, and transformations are directly related to the central problems in computer graphics.

Complex numbers and quaternions are highly structured algebraic systems. They have direct geometric interpretations, which make them valuable tools for solving certain problems in geometry and graphics.

Linear algebra is an algebraic subject that further extends the systems of real numbers, complex numbers, and quaternions to arbitrary dimensional vector spaces and systematically studies the properties and relationships on vectors. Matrices provide concrete representations for linear transformations and vectors. They can be directly implemented in computers to represent geometric transforms relevant to computer graphics.

Calculus may be applied to solve problems such as tangent lines and surface normal. These topics are related to certain modeling and rendering problems in graphics. Graph theory studies a discrete structure called a graph that has a wide range of applications in computer science and graphics.