BH-Bézier Curves And Applications

Design and modification of curves is a significant research subject in the field ofCAD/CAM and numerical control technology and has wide backgrounds of application.Based on the studies done before, this paper constructs a new extended curve------BH-Bézier curve with Bézier curve, H-Bézier curve and weight theory andpresents the properties of its basis function and BH-Bézier curve.Since it is difficult to meet the need of representing and designing complicated freecurves with a single BH-Bézier curve, the geometric continuity problem betweenBH-Bézier curve and other curves is studied mainly with cubic BH-Bézier curves asexamples, some smooth connection theorems between cubic BH-Bézier curves and acubic BH-Bézier curve and other curves are obtained, and some corollaries are deduced,thus the relationship between the smooth connection theorems and existing curvecontinuity conclusions is revealed. The main work can be as follows:In the first chapter, the research background and main contents of this paper areintroduced.In the second chapter, the definitions of BH-Bézier curves and its basis functionare put forward and their properties are given, so the theoretical basis for the followingwork is provided.In the third chapter, the cubic BH-Bézier curve is studied. The geometric continuityproblems between the cubic BH-Bézier curves and a cubic BH-Bézier curve with thecubic rational Bézier curves are studied, thus the corresponding theorems of theG0,G1,G2continuity and their corollaries are obtained, and some of their practicalapplications are given.In the fourth chapter, the geometric continuity problems between cubic BH-Béziercurves and cubic uniform B-spline curves, cubic non-uniform rational B-spline curvesand cubic uniform rational B-spline curves are studied, thus the corresponding theoremsof theG0,G1,G2continuity and some known results are deduced, and some of theirpractical applications are given.In the fifth chapter, the geometric continuity problems between cubic BH-Béziercurves and C-Bézier curves or T-Bézier curves are studied, thus the corresponding theorems of theG0,G1,G2continuity and their corollaries are obtained, and some oftheir practical applications are given.In the sixth chapter, the summary of the paper is given and the future researchwork is put forward.