Cartologium ↔ Morphologium
Tissot Indicatrices ↔ Conformal UV Parameterization
Cartographic projection distortion tensors (Tissot) and 3D computer graphics texture parameterization (LSCM) are identical differential geometric formulations of the Gauss-Bonnet theorem.
SOURCE ANCHOR NODECartologium
Tissot's Indicatrix
Differential geometry metric projecting infinitesimal surface circles into distortion ellipses.
Explore Sovereign EntryTARGET ANCHOR NODEMorphologium
Conformal UV Parameterization
Least-Squares Conformal Mapping (LSCM) minimizing angle shearing from 3D surfaces to 2D texture planes.
Explore Sovereign EntryMATHEMATICAL & STRUCTURAL HOMOLOGY
Both calculate singular value decompositions (SVD) of the Jacobian matrix $J = \begin{bmatrix} \partial u/\partial x & \partial u/\partial y \\ \partial v/\partial x & \partial v/\partial y \end{bmatrix}$ to minimize the Dirichlet energy functional.
EPISTEMIC RESOLUTION:
A cartographer flattening the Earth and a technical artist unwrapping a character mesh for PBR texturing are solving the exact same Riemann surface parameterization problem.Filter Ologium: