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99 lines
3.8 KiB
C++
99 lines
3.8 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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// 2-D projective geometry utilities for the Euclidean signature.
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// Ported from de.jreality.math.P2 and de.varylab.discreteconformal.math.P2Big.
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//
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// Points and lines are represented as homogeneous 3-vectors (x, y, w).
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// In the Euclidean case a finite point (px, py) is stored as (px, py, 1).
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#include <Eigen/Dense>
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#include <cmath>
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namespace conformallab {
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// ── Point / line duality ──────────────────────────────────────────────────────
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/// Cross-product point–line duality in P²: returns the intersection
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/// of two lines (or the line through two points). Same as Java
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/// `P2.pointFromLines` / `P2.lineFromPoints`.
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inline Eigen::Vector3d pointFromLines(const Eigen::Vector3d& l1,
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const Eigen::Vector3d& l2) {
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return l1.cross(l2);
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}
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// ── Euclidean perpendicular bisector ─────────────────────────────────────────
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/// Homogeneous line coordinates `(a, b, c)` of the perpendicular
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/// bisector of `[p, q]` in the Euclidean plane (`ax + by + c = 0`).
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/// Same as Java `P2.perpendicularBisector(p, q, Pn.EUCLIDEAN)`.
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inline Eigen::Vector3d perpendicularBisectorEuclidean(const Eigen::Vector3d& p_h,
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const Eigen::Vector3d& q_h) {
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// Dehomogenize
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Eigen::Vector2d p = p_h.head<2>() / p_h(2);
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Eigen::Vector2d q = q_h.head<2>() / q_h(2);
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// Direction vector (p → direction, matching jReality sign convention)
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Eigen::Vector2d d = p - q;
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// Midpoint
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Eigen::Vector2d m = (p + q) * 0.5;
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// Line: d[0]*(x - m[0]) + d[1]*(y - m[1]) = 0
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// = d[0]*x + d[1]*y - (d[0]*m[0] + d[1]*m[1])
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double c = -(d(0) * m(0) + d(1) * m(1));
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return {d(0), d(1), c};
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}
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/// Euclidean distance between two P² homogeneous points (dehomogenises both).
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inline double euclideanDistanceP2(const Eigen::Vector3d& p_h,
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const Eigen::Vector3d& q_h) {
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Eigen::Vector2d p = p_h.head<2>() / p_h(2);
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Eigen::Vector2d q = q_h.head<2>() / q_h(2);
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return (p - q).norm();
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}
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// ── Direct Euclidean isometry from two point-frames ──────────────────────────
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/// Build the 3×3 projective frame matrix anchored at `p0` with `p1`
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/// defining the positive x-direction (Euclidean case). Columns:
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/// `[dehom(p0), unit_dir(p0→p1), perp_dir]`.
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template <typename S>
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Eigen::Matrix<S, 3, 3> makeFrameMatrix(Eigen::Matrix<S, 3, 1> p0_h,
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Eigen::Matrix<S, 3, 1> p1_h) {
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// Dehomogenize
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Eigen::Matrix<S, 3, 1> p0 = p0_h / p0_h(2); // (px, py, 1)
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Eigen::Matrix<S, 3, 1> p1_d = p1_h / p1_h(2);
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// Unit direction p0 → p1
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Eigen::Matrix<S, 2, 1> dir2 = (p1_d - p0).template head<2>();
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dir2.normalize();
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Eigen::Matrix<S, 3, 1> p1n(dir2(0), dir2(1), S(0));
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// Perpendicular direction
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Eigen::Matrix<S, 3, 1> p2(-dir2(1), dir2(0), S(0));
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Eigen::Matrix<S, 3, 3> M;
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M.col(0) = p0;
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M.col(1) = p1n;
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M.col(2) = p2;
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return M;
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}
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/// 3×3 Euclidean isometry (as a projective matrix) that maps the
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/// frame `(s1, s2)` to the frame `(t1, t2)`. Same as Java
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/// `P2.makeDirectIsometryFromFrames(..., Pn.EUCLIDEAN)`.
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template <typename S>
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Eigen::Matrix<S, 3, 3> makeDirectIsometryFromFramesEuclidean(
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Eigen::Matrix<S, 3, 1> s1, Eigen::Matrix<S, 3, 1> s2,
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Eigen::Matrix<S, 3, 1> t1, Eigen::Matrix<S, 3, 1> t2)
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{
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auto toS = makeFrameMatrix<S>(s1, s2);
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auto toT = makeFrameMatrix<S>(t1, t2);
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return toT * toS.inverse();
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}
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} // namespace conformallab
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