a2876b9cbf
- include/matrix_utility.hpp: 4x4 mapping matrix R·from=to (Eigen) - include/projective_math.hpp: dehomogenize, hyperbolicDistance, isOnSegment (collinearity + betweenness via 3D cross/dot), getPointOnCorrespondingSegment (parameter by arc-length ratio) - test_matrix_utility.cpp: port of MatrixUtilityTest (1 test) - test_surface_curve_utility.cpp: port of SurfaceCurveUtilityTest testIsBetween and testGetPointOnSegment_SegmentEdge (2 tests) - tolerance adjusted to 1e-12 for matrix inversion (2.7e-15 rounding from Eigen vs jReality's LU; both well within meaningful accuracy) Total: 16/16 tests pass Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
90 lines
3.5 KiB
C++
90 lines
3.5 KiB
C++
#pragma once
|
|
|
|
// Projective and hyperbolic geometry utilities.
|
|
// Ported from de.jreality.math.Pn / Rn and
|
|
// de.varylab.discreteconformal.uniformization.SurfaceCurveUtility (Java).
|
|
|
|
#include <Eigen/Dense>
|
|
#include <cmath>
|
|
#include <algorithm>
|
|
#include <array>
|
|
#include <cassert>
|
|
|
|
namespace conformallab {
|
|
|
|
// Divide a homogeneous vector by its last component.
|
|
// Corresponds to Java Pn.dehomogenize().
|
|
inline Eigen::VectorXd dehomogenize(const Eigen::VectorXd& p) {
|
|
return p / p(p.size() - 1);
|
|
}
|
|
|
|
// Hyperbolic distance between two homogeneous vectors of the same dimension.
|
|
// The last component is the "timelike" coordinate (jReality convention).
|
|
// Inner product: <p,q> = -sum_i p_i*q_i + p_last * q_last
|
|
// Distance: arcosh(<p̂, q̂>) where p̂ normalises to the hyperboloid.
|
|
// Corresponds to Java Pn.distanceBetween(p, q, Pn.HYPERBOLIC).
|
|
inline double hyperbolicDistance(const Eigen::VectorXd& p,
|
|
const Eigen::VectorXd& q) {
|
|
int n = static_cast<int>(p.size());
|
|
double normP = std::sqrt(p(n-1)*p(n-1) - p.head(n-1).squaredNorm());
|
|
double normQ = std::sqrt(q(n-1)*q(n-1) - q.head(n-1).squaredNorm());
|
|
double inner = (-p.head(n-1).dot(q.head(n-1)) + p(n-1)*q(n-1))
|
|
/ (normP * normQ);
|
|
// clamp to [1, inf) to guard against floating-point rounding below 1
|
|
return std::acosh(std::max(1.0, inner));
|
|
}
|
|
|
|
// Check whether a homogeneous point p lies on the segment [s[0], s[1]].
|
|
// Works for n-dimensional homogeneous coords; cross product uses the first
|
|
// 3 spatial components after dehomogenization (matching jReality's Rn behaviour).
|
|
// Corresponds to Java SurfaceCurveUtility.isOnSegment().
|
|
inline bool isOnSegment(const Eigen::VectorXd& p_h,
|
|
const Eigen::VectorXd& s0_h,
|
|
const Eigen::VectorXd& s1_h) {
|
|
// Dehomogenize all points.
|
|
Eigen::VectorXd p = dehomogenize(p_h);
|
|
Eigen::VectorXd s0 = dehomogenize(s0_h);
|
|
Eigen::VectorXd s1 = dehomogenize(s1_h);
|
|
|
|
// Vectors from p to each endpoint.
|
|
Eigen::VectorXd ps0 = s0 - p;
|
|
Eigen::VectorXd ps1 = s1 - p;
|
|
|
|
// Collinearity check: 3D cross product of first 3 spatial components
|
|
// (after dehomogenize the w-component differences cancel to 0).
|
|
// head<3>() gives compile-time size needed by Eigen's cross().
|
|
Eigen::Vector3d cross = ps0.head<3>().cross(ps1.head<3>());
|
|
if (cross.norm() > 1e-7) return false;
|
|
|
|
// Betweenness check: dot product of the two direction vectors must be ≤ 0.
|
|
double dot = ps0.dot(ps1);
|
|
if (dot > 0.0) return false;
|
|
|
|
return true;
|
|
}
|
|
|
|
// Find the point on `target` that corresponds to `p` on `source`.
|
|
// The parameter t is determined by hyperbolic distance ratios on `source`,
|
|
// then applied as a linear interpolation on the dehomogenized `target`.
|
|
// Corresponds to Java SurfaceCurveUtility.getPointOnCorrespondingSegment().
|
|
inline Eigen::VectorXd getPointOnCorrespondingSegment(
|
|
const Eigen::VectorXd& p,
|
|
const Eigen::VectorXd& src0,
|
|
const Eigen::VectorXd& src1,
|
|
const Eigen::VectorXd& tgt0,
|
|
const Eigen::VectorXd& tgt1)
|
|
{
|
|
double l = hyperbolicDistance(src0, src1);
|
|
double l1 = hyperbolicDistance(src0, p) / l; // weight for tgt1
|
|
double l2 = hyperbolicDistance(src1, p) / l; // weight for tgt0
|
|
|
|
if (std::isnan(l1)) return dehomogenize(tgt0);
|
|
if (std::isnan(l2)) return dehomogenize(tgt1);
|
|
|
|
Eigen::VectorXd t0d = dehomogenize(tgt0);
|
|
Eigen::VectorXd t1d = dehomogenize(tgt1);
|
|
return l1 * t1d + l2 * t0d;
|
|
}
|
|
|
|
} // namespace conformallab
|