关键词: 等距曲线, 三角网格, 测地B样条, 自交

Abstract: To represent the base curve and offset curve in triangle meshes with explicit mathematical form,a method was proposed for calculating offset curves on manifold mesh.The curve on the mesh surface was represented by geodesic B-spline,which had the explicit mathematical representation.The progenitor curve was decomposed into piecewise Bezier curves by using knot insertion algorithm,and linearized approximation was made,and its error was controlled in given tolerance ε1 through the curve subdivision strategy.A discretization geodesic structure algorithm with given source and initial direction was proposed,and the initial offset curve of the progenitor curve were obtained on this basis.The G1 continuous piecewise Bezier curves which was satisfied for given tolerance ε2 was constructed as the offset curve of the progenitor curve by initial offset curve and some proper vertex.The integral approximation error of offset curve consisted of tolerance ε1 plus ε2 which could realize the global error control.Aiming at the massive calculation to get the intersection of curve on mesh surface,the strategy that the partial self-intersection area was first identified and the intersection point was computed was proposed to reduce the calculation of segment intersection point.Experimental results showed that the proposed method was robust and effective,and could meet the requirements of curve offset on mesh surfaces.

Key words: offset curves, triangular meshes, geodesic B-spline, self-intersections