Under Readings you'll find the sections and page numbers from the book to read (Geometric Modeling by Mortenson, Wiley Publishers); Papers refers to the fact that I'll be handing out papers from the literature to read on the topic.
NOTES:
| Week | Topics | Readings | Assignments |
|---|---|---|---|
| 1 | Introduction to geometric modeling and associated terms; overview of course topics; overview of labs |
1.0-1.4, pp. 1-18 | |
| Course software, Motif | Class software, handouts | ||
| Course software, Motif | Class software, handouts | ||
| 2 | Terms: constructive solid geomtery, solid modeling; Euler equation; review math, vector algebra basics; solids of revolution, extrusion | 11.1: Euler Formula, pp. 294-296; Appendix A, pp. 417-430; 10.5-10.6, pp. 260-275 (ignore the math for now) |
|
| Extrusion, sweep operations: generator curve & trajectory curve; lofting: registration of contours, handling bifurcation | Christiansen, Sederberg, Conversion of Complex Contour Line Definitions into Polygonal Element Mosaics, SIGGRAPH 78,pp. 187-192. | ||
| Lofting: acceptable surface as path through grid of vertex pairs, global optimizations, local optimization by fraction of traversal around contours | Ganapathy, Dennehy, A New General Triangulation Method for Planar Contours, SIGGRAPH 82, pp. 69-75; 9.2, pp. 384-395; 9.8-9.9, pp. 420-430; |
||
| 3 | Curves: intrinsic v. extrinsic properties; explicit v. implicit v. parametric equations, algebraic v. geometric form, basis functions, matrix form, tangent vectors, continuity, complexity, local v. global control | 2.0-2.6, pp. 19-38 | |
| Curves: Hermite curve,derivation of algebraic form from end point/tangent constraints, matrix form; briefly: reparameterization, truncating and subdividing, continuity, Catmull-Rom (cardinal) splines | 3.0-3.8, pp. 39-74 | ||
| Curves: composite Hermite by enforcing C2 continuity, blended parabolas | From Mathematical Elements for Computer Graphics by Rogers and Adams | ||
| 4 | Curves - Bezier: characteristic polygon, control points, convex hull property, Bernstein basis, binomial distribution, Bezier-Hermite conversion, affine transformation invariance, duplicating control points, open/closed curves, elevating degree, extracting a segment, recursive subdivision | 4.0-4.3, pp. 81-105 | Lab 1 due |
| Curves: review truncating Bezier, recusive subdivision of Bezier, test of colinearity, C1 v. G1 continuity, comosite Bezier enforcing G1 continuity, B-spline curves and recursive definition of basis functions | 4.4-4.5, pp. 105-112 5.0-5.5, pp. 113-137 |
||
| Curves: B-spline, knot vectors, rational B-spline, non-uniform rational B-splines | |||
| 5 | B-splines, NURBS | ||
| review homework; NURBS & DesignMentor | |||
| surfaces: linear, bilinear, ruled, bicubic Hermite, twist vectors | Chapter 6, especially 6.1 and the first part of 6.3; 7.0-7.4, 7.9 |
||
| 6 | midterm | ||
| surfaces: composite, 16-point form, reparameterization | 7.5-7.10 | ||
| NO CLASS: CIS Animation Day | |||
| 7 | review midterm; Composite bicubic Hermite, continuity | Lab 2 due | |
| Bezier surfaces, composite Bezier surfaces, B-spline surfaces, trimmed surfaces | |||
| Subdivision surfaces | T. DeRose, M. Kass, T. Truong, Subdivision Surfaces in Character Animation, SIGGRAPH 98, pp. 85-94 | ||
| 8 | Hierarchical B-spline refinement | D. Forsey, R. Bartels, Hierarchical B-Spline Refinement, SIGGRAPH 88, pp. 205-212. | |
| Analytic properties of a curve: moving trihedron (Frenet frame) along a curve, curvature, torsion, point of inflection; surface normal, curvature, Gaussian curvature, Geodesic curves; arc length. | From the first edition of the class text (Geometric Modeling by Mortenson) | ||
| closest point to a curve, closest curve-curve points, closest point to a plane and polygon, clostest point on a curve to a plane, closest point between two surfaces; intersection of ray and: plane, polygon, surface; scanline processing a surface | J. Lane, L. Carpenter, T. Whitted, J. Blinn, "Scan Line Methods for Displaying parametrically Defined Surfaces," CACM, Vol. 23, No. 1, January 1980, pp. 23-34. | ||
| 9 | fractals: self-similarity under scale, recursive, fractal dimension (D=log(N)/log(r) where N=number of replicants, r=1/scale of each replicant); internal consistency: invariant under tranformation, invariant under level of detail, reproducability; external consistency: tie random seed to parametric value and to geometric element so shared elements refine the same. | A. Fournier, D. Fussell, L. Carpenter, "Computer Rendering of Stochastic Models," CACM, Vol. 25, No. 6, June 1982, pp. 371-384. About Fractals Space filling curves The Fractal Microscope Generating Random Fractal Terrain |
|
| Review homework; continue fractals | homework 2 | ||
|
Implicit surfaces: density function, summed weighted functions, distance-based, offset surfaces, convolution surfaces, polygonization, sum & max hierarchical combining images: arm, face, skull, missle |
Jules Bloomenthal, Ed., Introduction to Implicit Surfaces, Morgan Kaufman Publ. Procedural Implicit Techniques for Modeling and Texturing Course #16, SIGGRAPH 98 Implicit Surfaces for Geometric Modeling and Computer Graphics Course #11, SIGGRAPH 96 |
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| 10 | NO CLASS | ||
| CSG and boolean operations; Winged Edge data structure | Lab 3 due | ||
| progressive meshes, optimization, simplification, multiresolution analysis | Hugues Hoppe, "Progressive Meshes," SIGGRAPH 96 pp. 99-108 Matthias Eck, Tony DeRose, Tom Duchamp, Hugues Hoppe, Michael Lounsbery, Wener Stuetzle, "Multiresolution Analysis of Arbitrary Meshes," SIGGRAPH 95, pp. 173-182. Hugues Hoppe, Tony DeRose, Tom Duchamp, John McDonald, Werner Stuetzle, "Mesh Optimization," SIGGRAPH 93, pp. 21-26. |
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| finals | Tuesday, June 8, 7:30 | ||
