Research On Key Technology In Interaction Design And Reuse Of Carves On Mesh Surface

In recent years, benefited from the advance of3D scanning and modeling, highcomplex surfaces can be described with triangles, and the research of curve design onmesh model has gradually become one important subject in the area of CAD&CG.The thesis focuses on a few key techniques on curve design on mesh surface, whichmainly includes interaction design and correlation of curve on surface between3D and2D, and reuse of curves on manifold triangulation, then implements thisalgorithm on the experimental platform.To implement the disadvantage of algorithm based on geometryflattening/mechanics revision principle, an improved algorithm is presented inthis paper. Because constrained triangle flattening can be used duringflattening the non-developable surface generates the2D pattern, there willlead to deformation error and even fail. This paper presents a self-adjustmentinitial flattening method, which could solve the problem and retain itstopological completeness. Oscillating divergent phenomenon may behappened when the flattening optimization algorithm based on thespring-mass model was used. In order to eliminate it, the computed result ofrelative error is used to judge whether it is convergent or not before releasingenergy and after. We use mapping relationships of established3D meshsurface and flattening surface and B-spline curve editing technique to achieveinteractive edit of curve on surface and correlation between3D and2D, It isshown by example results that the method proposed in the paper can meet theneed of real-time interactive design.By introducing exponential mapping parameterization into curve designon the surface, a reuse approach of Geodesic B-spline curve on mesh surfaceis proposed. The exponential map has the property of local differentiablehomeomorphism, which can guarantee the effectiveness of meshparameterization. As for the generated Geodesic B-spline curve, its controlpoints are parameterized using discrete exponential maps and its Nor mal Coordinates will be obtained, under the prerequisite condition that thoseNormal Coordinates remained unchanged, the Geodesic B-spline curve couldbe moved, rotated and scaled by changing parameterized region. Thegeneration of Geodesic B-spline curve and the parameterization of local meshdo not depend on the scale of overall mesh vertices, so it has wide adaptability.The results show that, the method is robust, effective, and able to meet therequirements of curve interaction design on surface.With the research results of this thesis, a interactive reuse module of curves onmanifold triangulation has been developed，which lays the foundation for the reuseand redesign of curves on surface.