| Week# | Date | Notes |
Topics (high-level) |
Chapter | Topics (detail) |
Assignments Projects:: Projects.pdf |
Due Date |
|---|---|---|---|---|---|---|---|
1 |
J25 |
Notes1 | Polygons & Visib | 1 | Overview. Open Problems. Art Gallery Theorems. | A1.pdf (A1.tex) |
— |
1 |
J27 |
Notes2 | Polygons & Visib | 1 | Art Gallery Theorems. Polygon triangulation. | — | |
2 |
F1 |
Notes3 | Polygons & Visib | 1 | Polygon triangulation: Proof.
Ear clipping 3-coloring Orthogonal art gallery theorem |
A1 Feedback: A1_ans.pdf | Tue 1Feb |
2 |
F3 |
Notes4 | Polyhedra Triangulation | 1 | 3D: Surface meshing, Tetrahedralization
Review A1 |
A2.pdf (A2.zip) |
— |
3 |
F8 |
Notes5 | Polygon Triangulation | 1 | Big-Oh Triangulation Algorithms Projects Work |
— | |
3 |
F10 |
Notes6 | Convex Hulls | 2 | Naive algorithm
Incremental algorithm Gift-wrapping algorithm Graham Scan |
Thu 10Feb | |
4 |
F15 |
Notes7 | Convex Hulls | 2 | Review P1_all.
Divide and Conquer Lower bound |
— | |
4 |
F17 |
Notes8 | Convex Hulls | 2 | 3D hull
Euler's Polyhedral Formula Interdigitation Proof Implications: V, E, F all O( n ) |
— | |
5 |
F22 |
Notes9 | Triangulations | 3 | Incremental Algorithm
Triangle Splitting Number of Triangles Number of Triangulations |
A2 Feedback: A2_ans.pdf | Tue 22Feb |
5 |
F24 |
Notes10 | Triangulations | 3 | Review A2.
Flipping diagonals |
A3.pdf A3.zip |
— |
6 |
M1 |
Notes11 | Triangulations | 3 | Flip Graph
Flip Graph → Delaunay Triangulation |
— | |
6 |
M3 |
Notes12 | Triangulations | 3 | Delaunay Triangulation geometric properties
DelTri ↔ Empty Circle property |
Thu 3Mar | |
7 |
M8 |
Notes13 | Voronoi Diagrams | 4 | Review P2.
Voronoi Diagrams |
— | |
7 |
M10 |
Notes14 | Voronoi Diagrams | 4 | VorDiags ↔ DelTri ↔ 3D Hull | — | |
— |
M15 |
— |
Spring Break |
— |
— |
Spring Break |
— |
— |
M17 |
— |
Spring Break |
— |
— |
Spring Break |
— |
8 |
M22 |
Notes15 | Polyhedra | 6 |
Five Platonic Solids: Regular Polyhedra
Semi-Regular: Archimedean Polyhedra Gauss-Bonnet Thm Curvature Exactly 5 regular polyhedra Semi-regular polyhedra: Archimedean solids, Johnson solids |
— | |
8 |
M24 |
Notes16 | Polyhedra | 6 | Euler's Theorem with holes
Regular Polyhedra in higher dimensions The Hypercube Unfoldings of the hypercube Tiling space with unfoldings |
— | |
9 |
M29 |
Notes17 | Polyhedra | 6 | Cauchy Rigidity Thm
Flexing Polyhedra The Bellows Conjecture Alexandrov's Gluing Thm Perimeter-halving→ ∞ convex polyhedra D-forms D-forms: baseball stitches |
Assign3 | Tue 29Mar |
9 |
M31 |
Notes18 | Polyhedra | 6 | Review A3.
Latin cross re-foldings: 23 polyhedra Project work |
A3 Feedback: A3_ans.pdf | — |
10 |
A5 |
Notes19 | Polyhedra | 6 |
Foldings of a square Space of all foldings Maximum volume polyhedron from square Project work |
— | |
10 |
A7 |
Notes20 | Polyhedra | 6 | Dürer's Problem: Unfolding convex polyhedra→Nets Reshaping convex polyhedra Quasi-twisting Project work |
Thu 7Apr | |
11 |
A12 |
Notes21 | Origami | new | Review P3. Flat Vertex Folds Maekawa-Justin Thm: |M-V|=2 Kawasaki-Justin Thm: ±θi=0 Map Folding |
— | |
11 |
A14 |
Notes22 | Origami | new | New Projects
Fold & One-Cut Theorem Projects work |
— | |
12 |
A19 |
Notes23 | Origami/Pop-Ups | new | Rigid Origami Shopping Bag Theorem Flattening Polyhedra |
— | |
12 |
A21 |
Notes24 | Origami/Pop-Ups | new |
Curved Creases Projects work |
— | |
13 |
A26 |
Notes25 | Pop-Ups | new | Course Evals Pop-up cards Protein Folding Pop-Up Spinner Projects work |
— | |
13 |
A28 |
P4_all | Projects | new | Project presentations (5min each) | Thu 28Apr | |
