Computer Aided Engineering Design

1. Computer Aided Engineering Design AnupamSaxena Associate Professor Indian Institute of Technology KANPUR 208016

3. Lecture # 36Design of Surface Patches

4. Design of Surface patches A closed, connected composite surface represents the shape of a solid. This surface, in turn, is composed of surface patches, aesthetics, aerodynamics, fluid flow etc. may influence surface design Surfaces of aircraft wings and fuselage, car body and its doors, seats, and windshields are all designed by combining surface patches at their boundaries. Surface patches can be modeled mathematically in parametric form as scalar polynomials in parameters (u, v)

5. Types of Surface patches Tensor product surface patches Boundary interpolating patches Sweep surfaces Quadric (Analytic) surface patches

6. Tensor Product Surface patch Let  and  be univariate functions such that uU and vV Cij3 is called a tensor product surfacewith domainUV e.g. The surface is bi-quadratic for m = n = 2 and bi-cubic for m = n = 3

7. Tensor Product Surface patch… u = constant v = constant

8. Tensor Product Surface patch… Generalization m and n are user-chosen degrees in parameters u and v For a bi-cubic surface patch, one needs to specify 16 sets of data as control points and/or slopes One for each Dij patches with degrees in u and v greater than 3 can be modeled one can as well choose the degrees unequal in parameters for most applications, use of bi-cubic surface patches seems adequate

9. Ferguson’s Bicubic Patch In matrix form Hermite functions

10. Ferguson’s Bicubic Patch … (v =1) (u =0) (u =1) (v =0)

11. Ferguson’s Bicubic Patch … Ferguson’s patch = UMGMTVT Geometric matrix Ferguson coefficient matrix

12. Example A simple Ferguson Bicubic Patch Specifying twist vectors is not easy; we assign them 0 values r(u, v) = UMGMTVT=

13. Example A simple Ferguson Bicubic Patch