Manipulation Of Curves On Triangulation Surface

In recent years, the design and manipulation of curves on triangular meshsurfaces has become the focus point of studies home and abroad. This paper mainlystudies the key technology of manipulation of curves on triangular mesh surfaces,which mainly includes offset and pattern of geodesic B-spline curves on triangulationsurface, then implements those algorithms on the self-developed software.In allusion to deficiencies of the existing methods of offset of curve on surface,an offset method of geodesic B-spline curves on manifold triangulation surface isproposed. The problem that offset of curves on Manifold triangulation is converted tothe problem that offset of curves on plane in this method. As for a given geodesicB-spine curve on manifold triangulation surface, firstly, the region where geodesicB-spline curve is parameterized locally using discrete exponential maps; secondly, thecurve in the parameter domain is offset using the method of based on shifting controlpoints; finally, the offset curve is mapped to the manifold triangulation surface usingparameter matching, and finishing the work that offset of curve on surface. Accordingto the self-intersections that appeared in the offset curve on plane, a new approach thatdetecting and eliminating self-intersections is proposed, which eliminating effectivelyself-intersection. The results show that, the proposed method is not only robust,effective, and able to meet the interactive design requirements, but also the expressionof offset curve consistent with the source curve.For a given geodesic B-spine curve on manifold triangulation surface, patternpath, and pattern parameters, firstly, by using the method of transfer of curve, thepattern path is translating to area where the source curve is. And then,find the patterndatums along the translational pattern path, and the areas where pattern datums areparameterized using the method of discrete exponential mapping. Finally, find thecorresponding points of the control points of the source curve in the area wherepattern datum is by the method of parameter matching, and generate the pattern curveusing the method of geodesic B-spline curve on triangulation surface. The resultsshow that, the proposed method is not only robust, effective, and able to meet theinteractive design requirements, but also the expression of pattern curve consistentwith the source curve.With the research results of this thesis, the module of offset of geodesic B-spline on triangulation surface and the module of pattern of geodesic B-spline ontriangulation surface have been developed, implementing the offset and patternmanipulation of geodesic B-spline on triangulation surface, enriching the contents ofthe manipulation of curves on surface, forming the manipulating system of curve onsurface.