COURSE NOTES · 2013Crane, de Goes, Desbrun & Schröder
Digital Geometry Processing with Discrete Exterior Calculus
The canonical computational path from cochains and incidence matrices through metric Hodge stars and geometry-processing algorithms.
PAPER ↔ OPERATOR ↔ EXPERIMENT
Follow the idea
back to its source.
This is a selective reading path, not an exhaustive bibliography. Each work earns its place by defining an operator used in the lab, comparing a representation choice, or showing where the student experiment can grow.
Discrete exterior calculus and Hodge decomposition
Read these when an incidence matrix, Hodge star, adjoint, boundary condition, or harmonic component feels like a convention rather than a mathematical choice.
COURSE NOTES · 2016de Goes, Desbrun & Tong
Vector Field Processing on Triangle Meshes
A representation-aware account of face-, edge-, and vertex-based fields, with their differential operators and Hodge decompositions.
Representations, connections, and field design
These works separate where a field is stored from how vectors in different tangent planes are compared.
CGF · 2010Crane, Desbrun & Schröder
Trivial Connections on Discrete Surfaces
Builds smooth discrete connections with controlled singularities—the intrinsic reference behind connection-based field comparison.
ACM TOG · 2013Knöppel, Crane, Pinkall & Schröder
Globally Optimal Direction Fields
Turns smooth direction-field design and singularity placement into a sparse global eigenproblem.
REFERENCE LIBRARYVaxman et al.
Directional tutorial
A practical taxonomy and C++ implementation of tangent bundles, symmetries, representations, matching, and field processing.
Integrability is not one operator
Closest exact fields, curl penalties, hard constraints, unit-length fields, and parameterization-aligned fields solve related but different problems.
ACM TOG · 2015Diamanti, Vaxman, Panozzo & Sorkine-Hornung
Integrable PolyVector Fields
Optimizes tangent fields that both respect design constraints and correspond exactly to local parameterization gradients.
ACM TOG · 2016Liu, Tong, de Goes & Desbrun
Discrete Connection and Covariant Derivative
Develops a principled discrete connection for analysis and design, clarifying what it means to differentiate vertex-based tangent vectors.
From direction fields to stripe patterns
The lab’s complex phase is a compact teaching model of this lineage. The important leap is from a local direction to a globally continuous periodic function.
ACM TOG · 2015Knöppel, Crane, Pinkall & Schröder
Stripe Patterns on Surfaces
Introduces globally continuous, equally spaced surface stripes as the smallest eigenvector of a sparse connection energy.
ACM TOG · 2019Vekhter, Zhuo, Gil Fandino, Huang & Vouga
Weaving Geodesic Foliations
Separates designing an approximately geodesic unit field from integrating it into a periodic foliation, including relaxed global integrability.
ACM TOG · 2023Montes Maestre et al.
Differentiable Stripe Patterns for Inverse Design
Extends stripe patterns into an end-to-end differentiable design space and addresses non-uniqueness in the original formulation.
Sparse derivatives without hand-written Hessians
The browser exposes the local-element idea; these systems show two routes into larger compiled research code.
CGF · 2022Schmidt, Born, Bommes, Campen & Kobbelt
TinyAD: Automatic Differentiation in Geometry Processing Made Simple
Differentiates small mesh elements through second order and assembles their sparse global gradient and Hessian.
COMPILER ADMoses, Churavy et al.
Enzyme
Differentiates optimized LLVM IR across several source languages—a complementary path when research code should remain ordinary compiled code.
Surface flow and explorable explanations
One branch supplies the physical destination; the other asks how a computational argument can remain inspectable and editable.
SCA · 2007Wang, Miller & Turk
Solving General Shallow Wave Equations on Surfaces
A canonical graphics treatment of shallow water directly on curved surfaces without requiring a global parameterization.
ESSAY · 2011/2024Bret Victor
Explorable Explanations
The design north star: claims backed by computational models whose assumptions and calculations remain visible and editable.
BROWSER COURSEGeometry Collective
Geometry Processing in JavaScript
Direct precedents for teaching DEC and direction-field design through focused interactive browser assignments.
FOR STUDENT REPORTS
Cite the method you actually use.
This page is an orientation map. Follow the project or DOI link for the authors’ preferred BibTeX and version of record, and distinguish an inspiration from an implemented method.