Background on Smooth Surfaces
E. Catmul and J. Clark: "Recursively generated B-spline surfaces on arbitrary topological meshes,"
CAD, Nov. 1978, pp 350-355.
D. Doo and M. Sabin "Behaviour of recursive division surfaces near extraordinary points,"
CAD, Nov. 1978, pp 356-360.
J. Bloomenthal and B. Wyvill "Interactive Techniques for Implicit Modeling,"
Proc.1990 Symp. on Interactive 3D Graphics, pp109-116.
H. P. Moreton and C. H. Sequin: "Functional Optimization for Fair Surface Design,"
H. Hoppe: "Progressive Meshes" SIGGRAPH'96.
M. Garland and P. Heckbert: "Surface Simplification Using Quadratic Error Metrics"
Tony DeRose et.al. "Subdivision Surfaces in Character Animation" SIGGRAPH'98.
3D Model Acquisition
H. Hoppe, T. DeRose, T. Duchamp, and M. Halstead: "Piecewise Smooth Surface Reconstruction," SIGGRAPH'94 pp 295-302.
B. Curless and M. Levoy: "A Volumetric Method for Building Complex Models from Range Images,"
SIGGRAPH'96 pp 303-312.
W. Lorensen and H. Cline: "Marching Cubes: A High Resolution 3D Surface Construction Algorithm,"
SIGGRAPH'87 pp 163-
L. Kobbelt, M. Botsch, U. Schwanecke, H.-P. Seidel: "Feature Sensitive Surface Extraction from Volume Data,"
SIGGRAPH'01, pp 57-66.
M. Segal: "Using Tolerances to Guarantee Valid Polyhedral Modeling Results,"
SIGGRAPH'90, pp 105-114.
M. Desbrun and M.-P. Gascuel, "Animating Soft Substances with Implicit Surfaces,"
T. Murali and T. Funkhouser "Consistent Solid and Boundary Representations from Arbitrary Polygonal Data"
Symp. on Interactive 3D Graphics, 1997, p. 155-162.
A. Rappaport and S. Spitz: "Interactive Boolean Operations for Conceptual Design of 3-D Solids,"
SIGGRAPH'97, pp 269-278.
S. F. Frisken, R. N. Perry, A.P. Rockwood, and T. R. Jones, "Adaptively Sampled Distance Fields: A General
Representation of Shape for Computer Graphics," SIGGRAPH'00, pp 249-254.
S.J. Gortler and M.F. Cohen: "Hierarchical and Variational Geometric Modeling with Wavelets,"
SIGGRAPH'95, pp 35-
Deforming and Sculpting
T. W. Sederberg and S.Parry: "Free-Form Deformation of Solid Geometry Models," SIGGRAPH'86, pp 151-160.
C. Gonzalez-Ochoa and J. Peters: "Localized-hierarchy surface splines (LeSS),"
Proc. 1999 Symposium on Interactive 3D Graphics, Atlanta, pp 7-15.
J. Dorman and A. Rockwood: "Surface design using hand motion with smoothing,"
CAD 33, pp 389-402, (2001)
K. T. McDonnell, H. Qin, R. A. Wlodarczyk; "Virtual Clay: A Real-time Sculpting System with Haptic Toolkits,"
Proc. 2001 Symposium on Interactive 3D Graphics, pp 179-190.
R. N. Perry, and S. F. Frisken: "Kizamu A System For Sculpting Digital Characters,"
SIGGRAPH'01, pp 47-56.
Evolutionary and Genetic Techniques
Alvy Ray Smith: "Plants, Fractal, and Formal Languages," SIGGRAPH'84 pp 1-7.
K. Sims: "Evolving Virtual Creatures" SIGGRAPH'94, pp 15-22,
P. Prusinkiewicz, L.Muendermann, R. Karwowski, Brendan Lane: "The use of positional information
in the modeling of plants," SIGGRAPH'01, pp 289-300.
J. Yen and C. H. Sequin, Escher Sphere Construction Kit,"
Proc. 2001 Symposium on Interactive 3D Graphics, pp 95-98, 252.
Y. I. H. Parish and P. Mueller: "Procedural Modeling of Cities,"
SIGGRAPH'01, pp 301-308.
J. Legakis, J.Dorsey, S. Gortler, "Feature-Based Cellular Texturing for Architectural Models,"
SIGGRAPH'01, pp 309-316.
M. Walter, A. Fournier, D. Menevaux, "Integrating Shape and Pattern in Mammalian Models,
SIGGRAPH'01, pp 317-326.
L.-Y. Weiand M. Levoi: "Texture Synthesis over Arbitrary Manifold Surfaces,"
SIGGRAPH'01, pp 355-360.
Some of these papers we may read in this course ...
Books on CAD/CAM, Geometry, Visualization
This is a rather informal and incomplete collection of
book titles which I found to be stimulating and helpful
in my research in the area of advanced geometric modeling.
Contributions of additional titles and suggestions for improving
the synoptic description of these works are welcome.
E.R. Tufte, Envisioning Information, Graphics Press,
Cheshire, Conn., 1990.
-- Effective display of complex data using just two dimensions.
I.D.Faux and M.J.Pratt, Computational Geometry for
Design and Manufacture, Halsted Press, Wiley, New York, 1979.
-- A solid book on the geometry of curves and surfaces.
Preparata & Shamos, Computational Geometry, Springer Verlag, Berlin, 1985.
-- Thorough treatment of the subject matter.
M.E. Mortensen, Geometric Modeling, Wiley & Sons, New
-- Very comprehensive text on the subject.
Adobe Systems Inc., PostScript Tutorial and Cookbook,
Addison Wesley, Reading, Mass., 1985..
-- Good introduction to the language and its use.
Books on Polygons, Patterns, Symmetry
E.A. Lord and C.B.Wilson, The Mathematical Description of Shape and Form,
Halsted Press / Wiley, New York, 1984. Evans Hall Library: QA501 L86
-- Interesting sections on Surface Generators, Symmetry, Point Lattices.
R.S. Beard, Patterns in Space, Creative Publications, Inc., Palo Alto , 1973.
-- Intriguing geometrical constructions in 2D and 3D:
Tilings, polygons, hexaflexagons, conic drawings, cycloids, cardioid.
P.S. Stevens, Patterns in Nature, Atlantic Monthly
Press, Little, Brown & Co., Boston, 1974.
-- Geometric patterns formed by the natural world: Regular polygons,
spirals, tilings, close packings, fractals.
D.W. Brisson, Hypergraphics, AAAS Selected Symposia
Series, Westview Press, Boulder, Colo., 1978. Doe
Library: QA491 H97
-- Visualization of the commplex
relationships in art, science and technology.
R. Williams, The Geometrical Foundation of Natural
Structure, Dover Publications, Inc., New York, N.Y., 1979.
Subtitled: "A source book of design".
-- It indeed contains a rich set of ideas about the
interrelationships of the various Platonic and Archimedean solids
and transformations leading from one to the other.
Particularly strong in the issues of subdivision of
3-D space with these solids.
E.A. Lord, The Mathematical Description of Shape and
Form, Halsted Press, New York, 1984. UCB Math/Stat
Lib. QA501 .L86
-- Descriptive Geometry.
A.L. Loeb, Space Structures, Addison-Wesley Co., Reading,
Mass., 1976. Evans Hall Library: QA491 L631
-- Nice coverage of 2-D tesselations and space-filling
polyhedra. Intuitive treatment of vertex and edge truncations.
M.J. Wenninger, Polyhedron Models, Cambridge University
Press, Cambridge, England, 1971. Evans Hall Library: QA491 W391
-- Contains 119 photos of paper models of all
the Platonic and Archimedean solids and of many of their stellations.
Contains explicit instructions and nets for building the models.
M.J. Wenninger, Spherical Models, Cambridge University
Press, Cambridge, England, 1979. Evans Hall Library: QA 491 W43
-- Contains 47 photos of paper models of all
the sperical frame projections of the Platonic and
Archimedean Solids and of many of their stellations.
Contains explicit instructions and nets for building the models.
H.S.M. Coxeter, Regular Polytopes, MacMillan Co., New
York, 2nd edition, 1963. Evans Hall Library: QA691 C68
-- Detailed discussion of regular and semiregular
polyhedrons in all dimensions.
H.S.M. Coxeter, Regular Complex Polytopes, Cambridge
University Press, Cambridge, Great Britain, 1974.
Evans Hall Library: QA691 C661
-- Profound geometric, algebraic, and group theoretic treatment
of regular solids and lattices in all dimensions.
L. Fejes Toth, Regulare Figuren, Ungarische Akademie
der Wissenschaften, Budapest , 1965. Evans Hall
Library: QA601 F3815
-- Good construction for the 4D regular polytopes.
Interesting 3D stereograms of 3D semiregular solids.
A. Pugh, Polyhedra, A Visual Approach, University of
California Press, Berkeley, CA , 1976. Evans Hall
Library: QA491 P831
-- A concise, simple and very
attractive introduction to the regular and semi-regular
solids and their relationships.
B.M. Stewart, Adventure Among the TOROIDS, B.M. Stewart,
Okemos, Mich., 1970. Evans Hall Library: QA491 S75
-- A mind-boggling book, full of crazy constructions of
toroidal solids bounded by equilateral polygons.
A. Holden, Orderly Tangles, Columbia University Press,
New York, 1983. Evans Hall Library: QA491 H626
-- Nice pictures and construction hints for cloverleafs,
gordian knots, and regular polylinks.
B.B. Mandelbrot, The Fractal Geometry of Nature, W.H.
Freeman & Co., San Francisco, 1977.
-- THE book on the mathematics of fractals.
H.O. Peitgen and P.H. Richter, The Beauty of Fractals,
Springer Verlag, Berlin, 1986.
-- An easy introduction with many beautiful pictures.
Prusinkiewicz and A. Lindenmayer, The Algorithmic
Beauty of Plants, Springer Verlag, Berlin, 1990.
-- Algorithmic fractal descriptions of plants with neat pictures.
M. McGuire, An Eye for Fractals, Addison Wesley, Redwood City, 1991.
-- Beautiful photographs of fractal structures in nature.
This is a random collection of interesting articles that
relate to the material in the course on advanced geometric
N.J.A. Sloane, "The Packing of Spheres," Scientific
American, vol. 250, no. 1, Jan. 1984.
-- Dense packing of spheres in N dimensions, kissing number,
relation to optimal codes.
B. Hayes, "The cellular automaton offers a model of the
world and a world uto itslf," Scientific American, vol.
250, no. 3, pp. 12-21, Mar. 1984.
-- Game of life, one and two dimensional cell colonies.
L. Neuwirth, "The Theory of Knots," Scientific American,
vol. 240, no. 6 , pp. 110-124 , June 1979.
-- Equivalence, knot groups, homotopy class, torus knots, genus of a knot.
M. Gardner, "Extraordinary nonperiodic tiling that
enrich the theory of tiles.," Scientific American, vol. 236, no. 1, pp. 110-121, Jan. 1977.
-- Escher drawings, spiral tiling, dart and kite tiles, Penrose rhombuses.
T. Lance and E. Thomas, "Arcs with Positive Measure and
a Space-Filling Curve," The American Mathematical
Monthly, vol. 98, no. 2, p. 124 127, 1991.