The thesis presents Bézier curves and surfaces - their definitions, fundamental properties, and examples. It also provides precise conditions on the control points under which the join of two Bézier curves (or surfaces) is continuous or geometrically diferentiable. The central aim of the thesis is the study of diagonals on Bézier surfaces. It is first shown that the diagonals themselves are Bézier curves and how to determine their degree and control points. The thesis then derives the conditions under which two arbitrary curves can be diagonals of a Bézier surface. Finally, the class of surfaces with identical diagonals is characterized, and the way this class changes when additional boundary constraints are imposed.
|
