Application and importance of Linear Algebra in Computer Graphics

Geometric Algebra and its Application to Computer Graphics

Early in the development of computer graphics it was realized that projective geometry is suited quite well to represent points and transformations. Now, maybe another change of paradigm is lying ahead of us based on Geometric Algebra. If you already use quaternions or Lie algebra in additon to the well-known vector algebra, then you may already be familiar with some of the algebraic ideas that...

Non-linear co-ordinates and their application in Computer Graphics

There are many applications that are not naturally based on the orthogonal co-ordinate systems, like ultrasound imaging, astronomy, mechanical computations etc. In those cases it is necessary to transform the problem formulation to the orthogonal co-ordinate system, where the problem is solved, transform the solution back and visualize the solution. The polar, spherical or cylindrical co-ordina...

Trigonometric Identities, Linear Algebra, and Computer Algebra

Applications of Conformal Geometric Algebra in Computer Vision and Graphics

This paper introduces the mathematical framework of conformal geometric algebra (CGA) as a language for computer graphics and computer vision. Specifically it discusses a new method for pose and position interpolation based on CGA which firstly allows for existing interpolation methods to be cleanly extended to pose and position interpolation, but also allows for this to be extended to higher-d...

Computer graphics, linear interpolation, and nonstandard intervals

This document is an assessment of the value of optimal linear interpolation enclosures and of nonstandard intervals, especially with respect to applications in computer graphics, and of the extent a future IEEE interval standard should support these. It turns out that essentially all present applications of nonstandard intervals to practical problems can be matched by similarly efficient approa...