Imported from Rah-Rah-Mitra/Geometry (Geometric-Tools-for-Computer-Graphics/AGENTS.md). Install upstream with npx skills add Rah-Rah-Mitra/Geometry --skill Geometric-Tools-for-Computer-Graphics. Copyright stays with the author.

Agent Instructions: Geometric Tools For Computer Graphics Notebook Course

This folder is a standalone notebook edition of Geometric Tools for Computer Graphics by Philip J. Schneider and David H. Eberly. Treat this folder as the project root for this course. The workspace root still owns the shared uv environment.

Repo-Local Skills

Use the repo-local skills under D:\Geometry\.codex\skills for course work:

• geometry-visualization-planner for chapter storyboards.
• geometry-chapter-notebook-author for authoring canonical notebooks.
• geometry-notebook-qc for standalone, artifact, and execution review.

Non-Negotiables

• Write original teaching prose, derivations, code, and visual explanations.
• Do not copy textbook passages, long exercise text, page screenshots, or page crops.
• The notebooks must stand alone without the PDF open.
• Visualization is part of the teaching argument, not decoration or a fixed quota.
• Keep helpers in utils/, generated outputs in artifacts/, and validation tools in scripts/.
• Every canonical notebook must execute cleanly with nbclient.
• Generated paths in notebooks must be relative or book-local.
• Preserve one canonical teaching notebook per chapter or appendix folder plus a local 00-index.ipynb.

Source Map

The PDF has 1056 physical pages. Printed body page 1 starts on PDF page 48, so body spans use pdf_page = printed_page + 47. The course uses inferred parts because the book table of contents does not define formal parts.

• Chapter 01: part-01-foundations/chapter-01-introduction/01-introduction.ipynb; printed pp. 1-8; PDF pp. 48-55; Floating-point failure modes, parameter-domain search, robust predicates, and the shared pattern behind geometric queries.
• Chapter 02: part-01-foundations/chapter-02-matrices-and-linear-systems/02-matrices-and-linear-systems.ipynb; printed pp. 9-62; PDF pp. 56-109; Linear maps, row reduction, rank, determinants, eigenspaces, Euclidean inner products, and least-squares fitting.
• Chapter 03: part-01-foundations/chapter-03-vector-algebra/03-vector-algebra.ipynb; printed pp. 63-108; PDF pp. 110-155; Affine and vector-space distinction, frames, orientation, barycentric coordinates, simplexes, and geometric operations.
• Chapter 04: part-01-foundations/chapter-04-matrices-vector-algebra-and-transformations/04-matrices-vector-algebra-and-transformations.ipynb; printed pp. 109-170; PDF pp. 156-217; Homogeneous point/vector representation, affine transformations, projections, change of basis, and normal-vector transforms.
• Chapter 05: part-02-2d-geometric-tools/chapter-05-geometric-primitives-in-2d/05-geometric-primitives-in-2d.ipynb; printed pp. 171-188; PDF pp. 218-235; Line, ray, segment, triangle, rectangle, polygon, conic, Bezier, B-spline, and NURBS representations.
• Chapter 06: part-02-2d-geometric-tools/chapter-06-distance-in-2d/06-distance-in-2d.ipynb; printed pp. 189-240; PDF pp. 236-287; Closest-point regions for points, linear components, polygons, quadratic curves, polynomial curves, and GJK distance.
• Chapter 07: part-02-2d-geometric-tools/chapter-07-intersection-in-2d/07-intersection-in-2d.ipynb; printed pp. 241-284; PDF pp. 288-331; Intersections among linear components, curves, convex polygons, moving objects, and the method of separating axes.
• Chapter 08: part-02-2d-geometric-tools/chapter-08-miscellaneous-2d-problems/08-miscellaneous-2d-problems.ipynb; printed pp. 285-324; PDF pp. 332-371; Circle and line constructions with tangency, prescribed radius, offsets, perpendicularity, and solution multiplicity.
• Chapter 09: part-03-3d-geometric-tools/chapter-09-geometric-primitives-in-3d/09-geometric-primitives-in-3d.ipynb; printed pp. 325-364; PDF pp. 372-411; Lines, rays, segments, planes, planar components, meshes, polyhedra, quadrics, torus, curves, and surfaces.
• Chapter 10: part-03-3d-geometric-tools/chapter-10-distance-in-3d/10-distance-in-3d.ipynb; printed pp. 365-480; PDF pp. 412-527; Point, line, ray, segment, triangle, rectangle, box, polyhedron, quadric, curve, surface, and geodesic distances.
• Chapter 11: part-03-3d-geometric-tools/chapter-11-intersection-in-3d/11-intersection-in-3d.ipynb; printed pp. 481-662; PDF pp. 528-709; Intersection tests for linear components, planes, triangles, polyhedra, quadrics, polynomial surfaces, bounding boxes, cylinders, and torus.
• Chapter 12: part-03-3d-geometric-tools/chapter-12-miscellaneous-3d-problems/12-miscellaneous-3d-problems.ipynb; printed pp. 663-672; PDF pp. 710-719; Projection of points and vectors onto planes, line-plane angles, plane-plane angles, and planes through geometric constraints.
• Chapter 13: part-04-computational-geometry/chapter-13-computational-geometry-topics/13-computational-geometry-topics.ipynb; printed pp. 673-826; PDF pp. 720-873; BSP trees, point containment, Boolean operations, convex hulls, Delaunay triangulation, polygon partitioning, minimum bounds, area, and volume.
• Appendix A: part-05-appendices/appendix-a-numerical-methods/appendix-a-numerical-methods.ipynb; printed pp. 827-922; PDF pp. 874-969; Linear solvers, polynomial systems, decompositions, rotations, root finding, minimization, least-squares fitting, subdivision, and calculus tools.
• Appendix B: part-05-appendices/appendix-b-trigonometry/appendix-b-trigonometry.ipynb; printed pp. 923-948; PDF pp. 970-995; Angles, trigonometric functions, identities, laws, inverse branches, derivatives, integrals, and conversion examples.
• Appendix C: part-05-appendices/appendix-c-basic-formulas-for-geometric-primitives/appendix-c-basic-formulas-for-geometric-primitives.ipynb; printed pp. 949-959; PDF pp. 996-1006; Formula atlas for triangles, quadrilaterals, circles, polyhedra, cylinders, cones, spheres, and torus primitives.

Notebook Shape

Each canonical notebook should include:

1. Title and source span.
2. Translation guide from book concepts into computational language.
3. Route through the chapter.
4. Setup cell that discovers BOOK_ROOT.
5. Original concept sections with equations and diagrams.
6. Executable examples using book-local utilities.
7. Visual artifacts saved under artifacts/ and displayed inline.
8. Applied lab or design exercise.
9. Sanity checks asserting core identities and artifact existence.
10. Takeaways.

Geometry Stack

Use the shared uv environment at D:\Geometry. Prefer installed packages before adding dependencies: numpy, scipy, matplotlib, plotly, ipywidgets, sympy, networkx, shapely, pyvista, trimesh, PIL, and the other packages listed in the repo-local geometry library catalog. Document external-only tools rather than importing them.

Worker Boundaries

Assign one worker to one canonical notebook or one shared helper/script task. Chapter workers should read their assigned source span, consume or create a visualization storyboard, and edit only the assigned chapter folder, its artifact subtree, and any explicitly assigned helper.

Commands

Run from D:\Geometry:

uv run python "Geometric Tools for Computer Graphics/scripts/build_gtcg_course_indexes.py"
uv run python -m compileall -q "Geometric Tools for Computer Graphics/utils" "Geometric Tools for Computer Graphics/scripts"
uv run python "Geometric Tools for Computer Graphics/scripts/audit_gtcg_notebooks.py" --min-words 1200 --min-code-cells 5
uv run python "Geometric Tools for Computer Graphics/scripts/audit_gtcg_visuals.py"
uv run python "Geometric Tools for Computer Graphics/scripts/validate_gtcg_course.py" --limit 8 --timeout 300
uv run python "Geometric Tools for Computer Graphics/scripts/validate_gtcg_course.py" --all --timeout 300
git diff --check

Geometry visualization library policy

Use the installed geometry stack intentionally. Do not default to generic Matplotlib-only notebooks when the chapter’s geometry calls for richer representations.

Library routing

• Use Matplotlib for durable 2D diagrams, proof sketches, constructions, incidence, orientation, area, angle, curves, and labeled static figures.
• Use Plotly for interactive 2D/3D parameter exploration, transformations, surfaces, and standalone HTML artifacts.
• Use ipywidgets/ipympl when parameter variation is central to understanding the concept.
• Use PyVista, VTK, Trimesh, and MeshIO for 3D surfaces, meshes, normals, curvature, polyhedra, frames, slicing, and spatial inspection.
• Use gpytoolbox, potpourri3d, robust_laplacian, manifold3d, and xatlas for mesh Laplacians, geodesics, parameterization, remeshing, and surface diagnostics.
• Use SymPy for exact symbolic checks, coordinate transformations, polynomial identities, and derivations.
• Use Galgebra, Clifford, Kingdon, and PyGanja for exterior algebra, geometric algebra, rotors, bivectors, conformal/projective models, and algebraic proof experiments.
• Use Gudhi, Ripser, and Persim for topology, filtrations, simplicial complexes, persistent homology, and persistence diagrams.
• Use Geomstats and PyRiemann for manifolds, geodesics, metrics, curvature intuition, SPD geometry, and statistical geometry.
• Use Shapely, scipy.spatial, and NetworkX for computational geometry, intersections, Voronoi/Delaunay, arrangements, graph structures, and proof dependency diagrams.
• Use OpenCV, Kornia, Torch, Torchvision, scikit-image, and Pillow for projective geometry, homographies, epipolar geometry, image geometry, camera models, and transformation experiments.
• Use POT and GeomLoss for optimal transport, Wasserstein geometry, barycenters, and metric geometry of distributions.
• Use GIS libraries only when geographic geometry clarifies the chapter.

Visual justification rule

Every major visualization must have:

1. the concept it teaches,
2. the reason this representation was chosen,
3. an inspection target for the learner,
4. a nearby prose explanation,
5. a check, invariant, or sanity test where practical.

Decorative visuals are not acceptable.

Notebook-first rule

A chapter notebook is a teaching document, not the output of a generic course generator. Scripts may support indexing, auditing, validation, and reproducible artifact creation, but they must not mass-populate chapter notebooks with generic teaching cells.