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Everything about Geodesic
Straight path on a curved surface or a Riemannian manifold
In geometry, a geodesic is a curve representing in some sense the locally shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line". Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: GeodesicA 5-minute orientation
- Skim a recent paper: Interactive medical image annotation using improved Attention U-net with compound geodesic distanceInfluential work since 2022
- Pick up a classic book: Sphere cells & surfacesThe most-reprinted book on the subject
- Read the landmark paper: Geodesic Active ContoursCited 4,154 times
- Go sideways: Parallel transportA closely related topic
- Go sideways: Affine connectionA closely related topic
📖 Definitions
Noun The shortest curve between two points on a specific surface.
Noun A segment of a great circle.
Noun A course allowing the parallel-transport of vectors along a course that causes tangent vectors to remain tangent vectors throughout that course (a straight curve, a line that is straight).
Adjective Of or relating to geodesy.
🏆 Landmark papers (most cited)
Geodesic Active Contours
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
Geodesic stability, Lyapunov exponents, and quasinormal modes
Computing geodesic paths on manifolds
Geodesic active contours and level sets for the detection and tracking of moving objects
Geodesic Polyarenes by Flash Vacuum Pyrolysis
Geodesic Acoustic Waves in Hydromagnetic Systems
Spatial sampling of head electrical fields: the geodesic sensor net
🆕 Influential since 2022
Interactive medical image annotation using improved Attention U-net with compound geodesic distance
Semisupervised Feature Extraction of Hyperspectral Image Using Nonlinear Geodesic Sparse Hypergraphs
Geodesic Lens Antennas for 5G and Beyond
Geodesic incompleteness of some popular regular black holes
Geodesic motion in Euclidean Schwarzschild geometry
📚 Books worth reading
- 📕Sphere cells & surfacesEssential Structures Research Association. · 1975
Sub-Riemannian geometryOvidiu Calin · 2009
PolyhedraAnthony Pugh · 1976
Spherical modelsMagnus J. Wenninger · 1979
Geodesic math and how to use itHugh Kenner · 1976
An introduction to tensegrityAnthony Pugh · 1976
How to design and build your dome homeGene Hopster · 1981- 📕What I am trying to doR. Buckminster Fuller · 1968
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Parallel transport In differential geometry, parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold. If…
- Affine connection In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector…
- Finsler manifold In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold M where a (possibly asymmetric) Minkowski norm F(x…
- Riemannian manifold In differential geometry, a Riemann space (or Riemannian manifold) is a geometric space on which many geometric notions such as distance, angles, length…
- Exponential map (Riemannian geometry) In Riemannian geometry, an exponential map is a map from a subset of a tangent space T p M {\displaystyle T_{p}M} of a Riemannian manifold (or pseudo-Riemannian…
- Glossary of Riemannian and metric geometry This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following…
- Affine differential geometry In differential geometry, affine differential geometry is the study of differential invariants of curves, surfaces, and higher-dimensional submanifolds…
- Differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It…