重庆大学机自实验班 计算机辅助设计及制造总复习.ppt

B-spline Surface Patch Model Consider a 4 ? 4 array of control vertices {Vij}. r (u, v) = = U N B NTVT for 0 ? u, v ? 1 N = Surface Construction Methods It is desired to use low degree (usually cubic) polynomial patch model to form a composite surface. Three methods to be introduced: The FMILL method Ferguson fitting method B-spline fitting method B-Spline Surface Fitting Comparison between Ferguson fitting and B-spline fitting Same composite surface resulted When making further changes, local change for B-spline surface, global change for Ferguson surface. Question: When one control point is changed, how many patches are affected? Curved Boundary Interpolating Surface Patches Methods of constructing a surface patch interpolating to a set of boundary curves: Ruled surfaces Lofted surfaces Coons surfaces Two types of sweep surface patches: Translational sweep patches Rotational sweep patches Ruled Surfaces Consider two parametric curves, r0 (u) and r1 (u) with 0 ? u ? 1 (see figure). A linear blending of the 2 curves defines a surface patch called a ruled surface r (u, v) = r0 (u) + v (r1 (u) - r0 (u)) ; 0 ? u, v ? 1 A vector in the direction of r1 (u) - r0 (u) is called a ruling vector t(u). Translational Sweep Surface Patches Input Summary Two parametric space curves, g (u) and d (v). A translational sweep surface is defined by the trajectory of the curve g (u) swept along the second curve d (v). The moving curve g (u) is called a generator curve The guiding curve d (v) is called a director curve r (u, v) = g (u) + d (v) - d (0) 0 ? u, v ? 1 r(u,v) g(u) Rotational Sweep Surface Patches Also known as surface of revolution Consider a section curve s(u) on the x-z plane s(u) = x(u)i + z(u)k = (x(u), 0, z(u)) Rotate the section curve s(u) about the z-axis, the resulting sweep surface can be expressed as an parametric equation as: