Free Curve Interpolation With Normal Constrains

In Computer Aided Geometric Design, the interpolation of free curve is one of the key research problems. The main research of curve interpolation is to study the way of constructing appropriate smooth curves which pass through the given points. The problem of free curve interpolation almost permeates all areas like in engineering designs and computer science, such as military research and life practice and so on, and it has the advantages of intuitive and easy to construct, so we can often see the use of free curves. With the development of science and the research of free curve, the use of free curves shows more and more strong vitality, and with the same time, more and more researchers show interests in the study of curve interpolation. The research of free curve has become a relatively mature technology. To make the interpolation curves more fairing, adding the normal constrains on the given points is a new direction in the research of free curve interpolation.This thesis is focused on several types of free curves interpolation algorithms with normal constraints. The research background and research status of the free curve interpolation with normal constraints is introduced in the first chapter. Preparatory knowledge of several types of the free curve including B-spline curve and algebra curve is introduced in the second chapter. The interpolation algorithm of cubic uniform B-spline curve with normal vector constraints is proposed in the third chapter. The interpolation algorithm of algebraic curves including cubic algebraic curve and fourth algebra curve with normal constraints are proposed in the fourth chapter. The research prospect of free curve interpolation algorithm and its future directions are discussed in the fifth chapter.