Publication and Presentations
» Click here to access the publications after 1999.
Computing Moments of Objects Enclosed by Piecewise Polynomial Surfaces
ACM Transactions on Graphics (TOG)
17,
3,
143-157,
1998
The first moment divided by the volume yields the center of mass
in pieces:
p.1~p.5
,
p.6
,
p.7
,
p.8
,
p.9~p.10
,
p.6
,
p.7
,
p.8
,
p.9~p.10
Algorithm 783: Pcp2Nurb - Smooth Free-Form Surfacing with Linearly Trimmed Bicubic B-Splines
ACM Transactions on Mathematical Software (TOMS),
24,
3,
261-267,
1998
- sample output in ivview format: out1, out2
- sample output in Matlab format: nurbs.dat
- Matlab program to render the output (needs spline toolbox) matlab 4: surfsp4.m, matlab 6: surfsp.m,
- C code with ivview output
- C code with openGL output
The 42 Equivalence Classes of Quadratic Surfaces in Affine n-Space
Computer Aided Geometric Design (CAGD)
15,
5,
459-473,
May
1998
Analysis of Algorithms Generalizing B-Spline Subdivision
SIAM Journal on Numerical Analysis (SINUM),
35,
2,
728-748,
1998
Typo on p.16: left Bezier patch of the characteristic map has
a number of transposed entries associated with cn.
The patch should equal the of lower right patch with the sign of the 2nd coordinate flipped.
Computing Volumes of Solids Enclosed by Recursive Subdivision Surfaces
Eurographics,
Budapest, Hungary,
September 4 - 8,
1997
Correction for tetroid, D_2q, middle column should be [-10 4 -12]
Correction for hexoid, upper left figure, the entries should be (top left: [-3 0 3], top right [3 0 3] and lower right[3 3 0])
Correction for hexoid, upper left figure, the entries should be (top left: [-3 0 3], top right [3 0 3] and lower right[3 3 0])
Box-Spline Based CSG Blends
4th ACM Symposium on Solid and Physical Modeling,
Atlanta, Georgia, USA,
1997
in pieces:
p.1~p.3
,
p.4~p.6
,
p.7~p.11
,
p.4~p.6
,
p.7~p.11
Smooth Blending of Basic Surfaces using Trivariate Box Spline
7th IMA Conference on the Mathematics of Surfaces,
1996
The Simplest Subdivision Scheme for Smoothing Polyhedra
ACM Transactions on Graphics (TOG),
16,
4,
420-431,
Oct.
1997
Pieter Barendrecht noticed that in Fig 4:
entries 0 should be 1/2 (so the final value = (1/2)/4 = 1/8).
Interpolation Regions for Convex Cubic Curve Segments
Advances in Computational Mathematics,
6,
1,
87-96,
Dec.
1996
Spline Surfaces from Irregular Control Meshes
Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
(Journal of Applied Mathematics and Mechanics),
ICIAM/GAMM 95 Numerical Analysis, Scientific Computing, Computer Science.
Hamburg
July 3 - 7, 1995
76,
S1,
69-72,
1996
a summary, rational extensions
Biquartic C¹-Surface Splines over Irregular Meshes
Computer-Aided Design,
27,
12,
895-903,
Dec.
1995
» figures (version May 1994)
Geometric Constraints for CAGD
in
M. Dahlen, T. Lyche, and L. L. Schumaker (eds),
Mathematical Methods in Computer Aided Geometric Design III,
Vanderbilt Press,
Nashville, Tennessee,
1995
C² Surfaces Built from Zero Sets of the 7-Direction Box Spline
6th IMA Conference on the Mathematics of Surfaces,
Brunel University,
September
1994
A Characterization of Connecting Maps as Nonlinear Roots of the Identity
in
Curves and Surfaces in Geometric Design,
Pierre Jean Laurent, Alain Le Méhauté, Larry L. Schumaker (eds.),
International Conference on Curves and Surfaces in Geometric Design, Chamonix-Mont-Blanc, France, 1994
International Conference on Curves and Surfaces in Geometric Design, Chamonix-Mont-Blanc, France, 1994
Constructing C¹ Surfaces of Arbitrary Topology using
Biquadratic and Bicubic Splines
in
Designing Fair Curves and Surfaces,
Nickolas S. Sapidis (eds.),
1994
» Q&A
For general modeling I recommend C^1-surface splines. Surfaces...bicubics is older, uses more patches, uses more complicated formulas, does not prove the convex hull property. It is however the first of this type of construction.
Smooth Free-Form Surfaces over Irregular Meshes Generalizing Quadratic Splines
Computer Aided Geometric Design (CAGD),
10,
3-4,
347-361,
Aug.
1993