Triangular Interpolation Spline Curves And Surfaces Modelling Via Blending

This thesis discusses triangular interpolation spline curve and surface modeling by means of blending method, and the shape controlling parameters are introduced in the blending mesh to control on the shape of the surface. The main work of this thesis are:A kind of Bezier-like interpolation curve is constructed using the singular hybrid idea. G1 and G2 Hermite-type and Lagrange-type triangular interpolation spline curves are constructed using the blending method, furthermore, the proposed meshes are generalized to the surface case, sub-curve. These triangular interpolation spline curves and surfaces constructed by the proposed method have some good properties, that is they are interpolation, smoothing, local adjustable and so on. This thesis is structured as follows:First, In triangular function space, we construct a kind of curve that is similar to the Bezier curve, then some shape parameters are introduced to improve the curve modeling controllability. A kind of Bezier-like interpolation curve is constructed using the singular hybrid idea.Then, three blending mesh are proposed to construct G1 and G2 Hermite-type and Lagrange-type triangular interpolation spline curves. Compared with other blending method, this blending can approximate some quadratic curves more efficiently.Further,we extended the blending triangular interpolation spline method to three-dimension case, and some shape controlling parameters are introduced to adjust the surfaces. Next, the continuity of trigonometric blending surfaces are discussed, and it shows that surface connecting condition do not need to think about.