A pair (V, G) is called geometric structure, where V is a vector space and G is a subgroup GL(V), which is a set of transmission matrices. In this thesis we classify structures, which are based on properties of quaternions. Geometric structures based on quaternions are called triple structures. Triple structures are four structures with similar properties as quaternions. Quaternions are generated from real numbers and three complex units. We write quaternions in this shape a+bi+cj+dk.

The goal of this work is to create an application, which will combine procedural and keyfram animations with subsequent visualization. Composition of this two different animations techniques is used to animate a virtual character. To combine this two techniques one starts with interpolations from keyframe animation and then enchance them by procedural animations to properly fit into the characters surroundings. This procedural part of animation is obtained by using forward and inverse kinematics. Whole application is written in C++, uses GLM math library for computations and OpenGL and GLUT for final visualization.