Geometric functions in computer aided geometric design

This book intends to be a compromise between the aforementioned extremes. It recalls basic concepts on functions, relations, transformations, matrices and groups and makes evident their impact in the engineering properties of projections, rotations, translations, perspectives, and so on. The material is of interest for computer scientists and electrical, mechanical, production, mathematical and physics engineers. In particular, it gives valuable insight into robotics, computer vision, design, manufacturing, kinematics and dynamics from a practical point of view while keeping contact whit the underlying decisive mathematical properties of the objects and transformations handled.The exercises and examples discussed in this book were stated, solved, documented and illustrated under the supervision of professors Oscar Ruiz and Carlos Cadavid during the years 2004 to 2007. Scenarios for such a work were the courses introduction to CAD CAM Systems and Geometric Modeling and the activities in the CAD CAM CAE laboratory at EAFIT University.The exercises and examples discussed in this book were stated, solved, documented and illustrated under the supervision of professors Oscar Ruiz and Carlos Cadavid during the years 2004 to 2007. Scenarios for such a work were the courses introduction to CAD CAM Systems and Geometric Modeling and the activities in the CAD CAM CAE laboratory at EAFIT University.