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89 lines
3.2 KiB
C++
89 lines
3.2 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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// Projective and hyperbolic geometry utilities.
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// Ported from de.jreality.math.Pn / Rn and
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// de.varylab.discreteconformal.uniformization.SurfaceCurveUtility (Java).
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#include <Eigen/Dense>
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#include <cmath>
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#include <algorithm>
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#include <array>
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#include <cassert>
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namespace conformallab {
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/// Dehomogenise: divide a homogeneous vector by its last component.
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/// Same as Java `Pn.dehomogenize()`.
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inline Eigen::VectorXd dehomogenize(const Eigen::VectorXd& p) {
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return p / p(p.size() - 1);
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}
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/// Hyperbolic distance `arcosh(⟨p̂, q̂⟩)` between two homogeneous
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/// vectors (last component = timelike coordinate; jReality convention).
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/// Same as Java `Pn.distanceBetween(p, q, Pn.HYPERBOLIC)`.
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inline double hyperbolicDistance(const Eigen::VectorXd& p,
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const Eigen::VectorXd& q) {
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int n = static_cast<int>(p.size());
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double normP = std::sqrt(p(n-1)*p(n-1) - p.head(n-1).squaredNorm());
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double normQ = std::sqrt(q(n-1)*q(n-1) - q.head(n-1).squaredNorm());
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double inner = (-p.head(n-1).dot(q.head(n-1)) + p(n-1)*q(n-1))
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/ (normP * normQ);
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// clamp to [1, inf) to guard against floating-point rounding below 1
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return std::acosh(std::max(1.0, inner));
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}
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/// `true` iff the homogeneous point `p_h` lies on the segment
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/// `[s0_h, s1_h]`. Same as Java `SurfaceCurveUtility.isOnSegment()`.
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inline bool isOnSegment(const Eigen::VectorXd& p_h,
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const Eigen::VectorXd& s0_h,
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const Eigen::VectorXd& s1_h) {
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// Dehomogenize all points.
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Eigen::VectorXd p = dehomogenize(p_h);
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Eigen::VectorXd s0 = dehomogenize(s0_h);
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Eigen::VectorXd s1 = dehomogenize(s1_h);
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// Vectors from p to each endpoint.
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Eigen::VectorXd ps0 = s0 - p;
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Eigen::VectorXd ps1 = s1 - p;
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// Collinearity check: 3D cross product of first 3 spatial components
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// (after dehomogenize the w-component differences cancel to 0).
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// head<3>() gives compile-time size needed by Eigen's cross().
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Eigen::Vector3d cross = ps0.head<3>().cross(ps1.head<3>());
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if (cross.norm() > 1e-7) return false;
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// Betweenness check: dot product of the two direction vectors must be ≤ 0.
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double dot = ps0.dot(ps1);
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if (dot > 0.0) return false;
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return true;
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}
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/// Find the point on the target segment `(tgt0, tgt1)` corresponding
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/// to `p` on the source segment `(src0, src1)`, parametrised by
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/// hyperbolic distance ratios on the source. Same as Java
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/// `SurfaceCurveUtility.getPointOnCorrespondingSegment()`.
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inline Eigen::VectorXd getPointOnCorrespondingSegment(
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const Eigen::VectorXd& p,
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const Eigen::VectorXd& src0,
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const Eigen::VectorXd& src1,
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const Eigen::VectorXd& tgt0,
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const Eigen::VectorXd& tgt1)
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{
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double l = hyperbolicDistance(src0, src1);
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double l1 = hyperbolicDistance(src0, p) / l; // weight for tgt1
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double l2 = hyperbolicDistance(src1, p) / l; // weight for tgt0
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if (std::isnan(l1)) return dehomogenize(tgt0);
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if (std::isnan(l2)) return dehomogenize(tgt1);
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Eigen::VectorXd t0d = dehomogenize(tgt0);
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Eigen::VectorXd t1d = dehomogenize(tgt1);
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return l1 * t1d + l2 * t0d;
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}
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} // namespace conformallab
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