Surface Design by Ming-Jun Lai

Example 1. Given a set of scattered data which were sampled from a side panel of a car

Example 2. Given a set of scattered data which were sampled from a nose cone of an airplane,

Polygonal Hole Filling

Example 3. Given a surface which has a polygonal hole in the middle shaped in H. We used a C^1 cubic spline surface to mend the hole.

Ming-Jun Lai's Papers on Computer-Aided Geometric Design [14] L1 Spline Methods for Scattered Data Interpolation and Approximation (with P. Wenston) , to appear in Advances in Computational Mathematics, 2002. [13] Error bounds for minimal energy bivariate polynomial splines, (with Manfred von Golitschek, Larry L. Schumaker), Numer. Math., 2002. [12]Convex preserving scattered data interpolation using bivariate $C^1$ cubic splines, J. Comput. Applied Math., 119(2000), pp. 249--258. [11]Filling polygonal holes using C^1 cubic triangular spline patches , (with C. K. Chui), CAGD, 17(2000), 297--307. [10] Effective algorithms for joining NURBS surfaces in smooth fashion, to appear in Numer. Algorithm. [9] Removal of gaps among compound C^1 bi-cubic B-spline surface patches , 1998. [8] Geometric interpretation of smoothness conditions of triangular polynomial patches, Comput. Aided Geom. Design, 14(1997), pp. 191--199. [7] Scattered data interpolation and approximation by C^1 piecewise cubic polynomials, Comput. Aided Geom. Design, 13(1996), 81--88. [6] Approximation order from bivariate C^1 cubics on a four--directional mesh is full, Comput. Aided Geometric Design, 11(1994), pp. 215--223. [5] Some sufficient conditions for convexity of multivariate Bernstein-B\'ezier polynomials and box spline surfaces, Studia Scientiarum Math. Hungarica, 28(1993), pp. 363--374. [4] A characteristic theorem of multivariate splines in blossom form, Comput. Aided Geometric Design, 8(1992), pp. 513--521. [3] Algorithms for generating B-nets and graphically displaying box spline surfaces, (with C.K. Chui), Compt. Aided Geometric Design, 8(1992), pp. 479--493. [2] Fortran subroutines for B-nets of box splines on three and four directional meshes, Numerical Algorithm, 2(1992), pp. 33--38. [1] Computation of box splines and B-splines on triangulations of nonuniform rectangular partitions, (with C.K. Chui), J.Approx. Applic., 3-4(1987), pp. 37-62.