Construction of G2 continuous curve on point-cloud surface

Abstract

PurposeThe curve construction on surfaces is becoming more and more important in computer-aided design (CAD), computer graphics (CG) and the other related fields. This problem is often encountered in NC machining, tool path generation, automated fiber placement and so on. However, designing curves on curved surfaces is quite different from constructing a curve in Euclidean space. Therefore, the traditional methods of curve design are not suitable for constructing a continuous curve on surface. The authors need to perform interpolation directly on surface so that the final target curve is embedded into the given surface and also meets the continuous conditions.Design/methodology/approachFirstly, adopting a series of Hermite blending functions, the authors design a space curve passing the given knots on the point-cloud surface. Then, the authors construct a class of directrixes that are adopted to determine vector fields for projection. Finally, a complete G2 continuous curve embedded in point-cloud surfaces is constructed by solving the first-order ordinary differential equations (ODEs).Findings The authors’ main contribution is to overcome the problem of constructing G1 and G2 continuous curves on point-cloud surfaces and the authors’ schemes are based on the projection moving least square (MLS) surfaces and traditional differential geometric.Originality/valueBased on the framework of projection MLS surfaces, a novel method to overcome the problem of constructing G2 continuous curves on point-cloud surfaces is proposed.