59a26123c8
MINOR-1 (spherical_functional.hpp:426)
Wrong comment said "second derivative < 0 for a convex functional".
The spherical energy is *concave* (NSD Hessian); the monotone-f argument
applies to both convex and concave functionals equally. Comment rewritten
to explain the actual physics: increasing scale increases all angles and
thus reduces Σ G_v.
MINOR-2 (spherical_functional.hpp:494-495)
Forward finite difference O(ε) → central finite difference O(ε²):
old: dft = (sum_Gv(t + fd_eps) - ft) / fd_eps
new: dft = (sum_Gv(t + fd_eps) - sum_Gv(t - fd_eps)) / (2*fd_eps)
Same cost when the extra sum_Gv(t - fd_eps) replaces the cached ft.
MINOR-3 (euclidean_functional.hpp, spherical_functional.hpp,
inversive_distance_functional.hpp)
New header gauss_legendre.hpp centralises the 10-point Gauss-Legendre
nodes and weights (gl10_nodes() / gl10_weights()). The three energy
functions now use the shared accessors instead of duplicated local
static arrays.
MINOR-4 (euclidean_functional.hpp, spherical_functional.hpp,
hyper_ideal_functional.hpp, inversive_distance_functional.hpp)
halfedge_to_index() centralised in conformal_mesh.hpp. All four local
aliases (eucl_hidx, spher_hidx, hidx, id_detail::hidx) now delegate to
it as one-line wrappers; the aliases are kept for now to avoid a larger
call-site churn, clearly documented as thin wrappers.
MINOR-5 (clausen.hpp:33-38)
Added a comment above inits() explaining the intentional off-by-one
return value and how it interacts with csevl() — matching the Java
Clausen.inits() / csevl() contract.
277/277 CGAL + 26/26 pure-math tests pass, 0 failed.
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
131 lines
6.4 KiB
C++
131 lines
6.4 KiB
C++
#pragma once
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// Copyright (c) 2024-2026 Tarik Moussa.
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// SPDX-License-Identifier: MIT
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// conformal_mesh.hpp
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//
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// Central mesh type for the discrete conformal mapping algorithms.
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// Replaces the Java CoHDS (de.varylab.discreteconformal.heds.CoHDS)
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// and its associated vertex/edge/face types (CoVertex, CoEdge, CoFace).
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//
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// Design
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// ------
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// Java │ C++ (this file)
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// ─────────────────────────────┼──────────────────────────────────────────
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// CoHDS │ ConformalMesh (CGAL::Surface_mesh)
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// CoVertex / CoEdge / CoFace │ Vertex_index / Edge_index / Face_index
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// HyperIdealRadiusAdapter │ property_map<Vertex_index, double>
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// HalfedgeInterface adapters │ named property maps ("v:lambda", …)
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//
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// Property-map naming convention
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// ───────────────────────────────
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// "v:lambda" per-vertex log scale factor (conformal variable u_i)
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// "v:theta" per-vertex target cone angle
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// "v:idx" per-vertex solver DOF index (-1 = pinned / boundary)
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// "e:alpha" per-edge intersection angle (α_ij, hyperbolic geometry)
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// "f:type" per-face geometry type (0=Euclidean, 1=Hyperbolic, 2=Spherical)
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//
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// All property maps are optional; add only what a given algorithm needs.
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//
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// Note on descriptor types (CGAL 6.x)
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// ────────────────────────────────────
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// CGAL::Surface_mesh exposes its index types as nested types:
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// Surface_mesh::Vertex_index, ::Halfedge_index, ::Edge_index, ::Face_index
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// The BGL graph_traits aliases expose the same types as vertex_descriptor etc.,
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// but those live in boost::graph_traits<Surface_mesh>, not in Surface_mesh itself.
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// We use the Surface_mesh member names throughout for clarity.
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#include <CGAL/Simple_cartesian.h>
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#include <CGAL/Surface_mesh.h>
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#include <cstdint>
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#include <string>
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namespace conformallab {
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// ── Kernel ──────────────────────────────────────────────────────────────────
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// Simple double-precision Cartesian. Conformal mapping algorithms never
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// need exact arithmetic — they operate on floating-point lengths and angles.
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/// CGAL kernel used by all conformallab algorithms (double precision).
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using Kernel = CGAL::Simple_cartesian<double>;
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/// 3-D point type (vertex coordinates).
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using Point3 = Kernel::Point_3;
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/// 2-D point type (UV-domain layout coordinates).
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using Point2 = Kernel::Point_2;
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// ── Mesh type ────────────────────────────────────────────────────────────────
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/// Triangle mesh carrying all conformal-map data as property maps.
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using ConformalMesh = CGAL::Surface_mesh<Point3>;
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// ── Index/descriptor aliases (CGAL 6.x naming) ───────────────────────────────
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/// Vertex descriptor of `ConformalMesh`.
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using Vertex_index = ConformalMesh::Vertex_index;
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/// Half-edge descriptor of `ConformalMesh`.
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using Halfedge_index = ConformalMesh::Halfedge_index;
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/// Edge descriptor of `ConformalMesh`.
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using Edge_index = ConformalMesh::Edge_index;
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/// Face descriptor of `ConformalMesh`.
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using Face_index = ConformalMesh::Face_index;
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// ── Geometry type constant (replaces Java CoFace.type enum) ─────────────────
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/// Discrete geometry type that a face/mesh is interpreted in.
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/// Replaces the original Java `CoFace.type` enum.
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enum class GeometryType : int {
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Euclidean = 0, ///< Flat metric (ℝ²).
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Hyperbolic = 1, ///< Hyperbolic metric (ℍ²).
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Spherical = 2 ///< Spherical metric (S²).
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};
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// ── Standard property-map bundles ────────────────────────────────────────────
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/// Register and return the vertex-side property maps used by all five
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/// DCE functionals: `v:lambda` (log conformal factor), `v:theta` (target
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/// cone angle), `v:idx` (contiguous integer index).
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inline auto add_vertex_properties(ConformalMesh& mesh)
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{
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auto [lambda, ok1] = mesh.add_property_map<Vertex_index, double>("v:lambda", 0.0);
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auto [theta, ok2] = mesh.add_property_map<Vertex_index, double>("v:theta", 0.0);
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auto [idx, ok3] = mesh.add_property_map<Vertex_index, int> ("v:idx", -1);
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(void)ok1; (void)ok2; (void)ok3;
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return std::make_tuple(lambda, theta, idx);
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}
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/// Register and return the edge intersection-angle property `e:alpha`
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/// (used by the hyper-ideal functional).
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inline auto add_edge_properties(ConformalMesh& mesh)
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{
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auto [alpha, ok] = mesh.add_property_map<Edge_index, double>("e:alpha", 0.0);
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(void)ok;
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return alpha;
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}
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/// Register and return the per-face geometry-type property `f:type`.
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inline auto add_face_properties(ConformalMesh& mesh)
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{
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auto [ftype, ok] = mesh.add_property_map<Face_index, int>(
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"f:type", static_cast<int>(GeometryType::Euclidean));
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(void)ok;
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return ftype;
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}
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// ── Half-edge index helper ────────────────────────────────────────────────────
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//
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// Convert a Halfedge_index to std::size_t for use as a vector subscript.
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// Each functional previously duplicated this one-liner under a name like
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// eucl_hidx / spher_hidx / hidx. Centralised here (MINOR-4 fix).
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//
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// Implementation: the double-cast uint32_t → size_t is intentional. CGAL 6.x
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// Surface_mesh stores half-edge indices internally as 32-bit unsigned integers.
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// Casting directly to size_t on a 64-bit system would produce the same result
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// because CGAL index types use non-negative values, but the explicit intermediate
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// cast documents the assumption and silences spurious sign-conversion warnings.
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/// Convert a `Halfedge_index` to `std::size_t` for vector subscript use.
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/// Replaces the duplicated `eucl_hidx`, `spher_hidx`, `hidx` helpers.
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inline std::size_t halfedge_to_index(Halfedge_index h) noexcept
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{
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return static_cast<std::size_t>(static_cast<std::uint32_t>(h));
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}
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} // namespace conformallab
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