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-rw-r--r--Build/source/texk/lcdf-typetools/lcdf-typetools-src/liblcdf/bezier.cc376
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diff --git a/Build/source/texk/lcdf-typetools/lcdf-typetools-src/liblcdf/bezier.cc b/Build/source/texk/lcdf-typetools/lcdf-typetools-src/liblcdf/bezier.cc
deleted file mode 100644
index c296a4b4aa3..00000000000
--- a/Build/source/texk/lcdf-typetools/lcdf-typetools-src/liblcdf/bezier.cc
+++ /dev/null
@@ -1,376 +0,0 @@
-// -*- related-file-name: "../include/lcdf/bezier.hh" -*-
-
-/* bezier.{cc,hh} -- cubic Bezier curves
- *
- * Copyright (c) 1998-2019 Eddie Kohler
- *
- * This program is free software; you can redistribute it and/or modify it
- * under the terms of the GNU General Public License as published by the Free
- * Software Foundation; either version 2 of the License, or (at your option)
- * any later version. This program is distributed in the hope that it will be
- * useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
- * Public License for more details.
- */
-
-#ifdef HAVE_CONFIG_H
-# include <config.h>
-#endif
-#include <lcdf/bezier.hh>
-
-//
-// bounding box
-//
-
-void
-Bezier::make_bb() const noexcept
-{
- _bb = 0;
- for (int i = 1; i < 4; i++) {
- if (_p[i].x > bb_right_x())
- _bb = (_bb & ~0x03) | (i << 0);
- else if (_p[i].x < bb_left_x())
- _bb = (_bb & ~0x0C) | (i << 2);
- if (_p[i].y > bb_top_x())
- _bb = (_bb & ~0x30) | (i << 4);
- else if (_p[i].y < bb_bottom_x())
- _bb = (_bb & ~0xC0) | (i << 6);
- }
-}
-
-
-//
-// is_flat, eval
-//
-
-bool
-Bezier::is_flat(double t) const noexcept
-{
- return (_p[2].on_segment(_p[0], _p[3], t)
- && _p[1].on_segment(_p[0], _p[3], t));
-}
-
-static Point
-eval_bezier(Point *b_in, int degree, double u)
-{
- assert(degree < 4);
- Point b[4];
- for (int i = 0; i <= degree; i++)
- b[i] = b_in[i];
-
- double m = 1.0 - u;
- for (int i = 1; i <= degree; i++)
- for (int j = 0; j <= degree - i; j++)
- b[j] = b[j]*m + b[j+1]*u;
- return b[0];
-}
-
-Point
-Bezier::eval(double u) const noexcept
-{
- Bezier b = *this;
- double m = 1.0 - u;
- for (int i = 1; i < 4; i++)
- for (int j = 0; j < 4 - i; j++)
- b._p[j] = m * b._p[j] + u * b._p[j+1];
- return b._p[0];
-}
-
-
-//
-// halve
-//
-
-void
-Bezier::halve(Bezier &l, Bezier &r) const noexcept
-{
- Point half = Point::midpoint(_p[1], _p[2]);
- l._p[0] = _p[0];
- l._p[1] = Point::midpoint(_p[0], _p[1]);
- l._p[2] = Point::midpoint(l._p[1], half);
- r._p[3] = _p[3];
- r._p[2] = Point::midpoint(_p[2], _p[3]);
- r._p[1] = Point::midpoint(r._p[2], half);
- r._p[0] = l._p[3] = Point::midpoint(l._p[2], r._p[1]);
-}
-
-
-//
-// hit testing
-//
-
-bool
-Bezier::in_bb(const Point &p, double tolerance) const noexcept
-{
- ensure_bb();
- if (bb_right() + tolerance < p.x
- || bb_left() - tolerance > p.x
- || bb_top() + tolerance < p.y
- || bb_bottom() - tolerance > p.y)
- return false;
- else
- return true;
-}
-
-double
-Bezier::hit_recurse(const Point &p, double tolerance, double leftd,
- double rightd, double leftt, double rightt) const noexcept
-{
- Bezier left, right;
- double middled, resultt;
-
- if (is_flat(tolerance)) {
- if (p.on_segment(_p[0], _p[3], tolerance))
- return (leftt + rightt) / 2;
- else
- return -1;
- }
-
- if (leftd < tolerance * tolerance)
- return leftt;
- if (rightd < tolerance * tolerance)
- return rightt;
-
- if (!in_bb(p, tolerance))
- return -1;
-
- halve(left, right);
- middled = (right._p[0] - p).squared_length();
- resultt = left.hit_recurse
- (p, tolerance, leftd, middled, leftt, (leftt + rightt) / 2);
- if (resultt >= 0)
- return resultt;
-
- return right.hit_recurse
- (p, tolerance, middled, rightd, (leftt + rightt) / 2, rightt);
-}
-
-bool
-Bezier::hit(const Point &p, double tolerance) const noexcept
-{
- double leftd = (_p[0] - p).squared_length();
- double rightd = (_p[3] - p).squared_length();
- double resultt = hit_recurse(p, tolerance, leftd, rightd, 0, 1);
- return resultt >= 0;
-}
-
-
-//
-// segmentize to list of points
-//
-// uses recursive subdivision
-//
-
-void
-Bezier::segmentize(Vector<Point> &v, bool first) const
-{
- if (is_flat(0.5)) {
- if (first)
- v.push_back(_p[0]);
- v.push_back(_p[3]);
- } else {
- Bezier left, right;
- halve(left, right);
- left.segmentize(v, first);
- right.segmentize(v, false);
- }
-}
-
-
-//
-// curve fitting
-//
-// code after Philip J. Schneider's algorithm described, with code, in the
-// first Graphics Gems
-//
-
-static void
-chord_length_parameterize(const Point *d, int nd, Vector<double> &result)
-{
- assert(result.size() == 0);
- result.reserve(nd);
- result.push_back(0);
- for (int i = 1; i < nd; i++)
- result.push_back(result.back() + Point::distance(d[i-1], d[i]));
- double last_dist = result.back();
- for (int i = 1; i < nd; i++)
- result[i] /= last_dist;
-}
-
-static inline double
-B0(double u)
-{
- double m = 1.0 - u;
- return m*m*m;
-}
-
-static inline double
-B1(double u)
-{
- double m = 1.0 - u;
- return 3*m*m*u;
-}
-
-static inline double
-B2(double u)
-{
- double m = 1.0 - u;
- return 3*m*u*u;
-}
-
-static inline double
-B3(double u)
-{
- return u*u*u;
-}
-
-static Bezier
-generate_bezier(const Point *d, int nd, const Vector<double> &parameters,
- const Point &left_tangent, const Point &right_tangent)
-{
- Point *a0 = new Point[nd];
- Point *a1 = new Point[nd];
-
- for (int i = 0; i < nd; i++) {
- a0[i] = left_tangent * B1(parameters[i]);
- a1[i] = right_tangent * B2(parameters[i]);
- }
-
- double c[2][2], x[2];
- c[0][0] = c[0][1] = c[1][0] = c[1][1] = x[0] = x[1] = 0.0;
-
- int last = nd - 1;
- for (int i = 0; i < nd; i++) {
- c[0][0] += Point::dot(a0[i], a0[i]);
- c[0][1] += Point::dot(a0[i], a1[i]);
- c[1][1] += Point::dot(a1[i], a1[i]);
-
- Point tmp = d[i] - (d[0] * (B0(parameters[i]) + B1(parameters[i]))
- + d[last] * (B2(parameters[i]) + B3(parameters[i])));
- x[0] += Point::dot(a0[i], tmp);
- x[1] += Point::dot(a1[i], tmp);
- }
- c[1][0] = c[0][1];
-
- // compute determinants
- double det_c0_c1 = c[0][0]*c[1][1] - c[1][0]*c[0][1];
- double det_c0_x = c[0][0]*x[1] - c[0][1]*x[0];
- double det_x_c1 = x[0]*c[1][1] - x[1]*c[0][1];
-
- // finally, derive alpha values
- if (det_c0_c1 == 0.0)
- det_c0_c1 = c[0][0]*c[1][1] * 10e-12;
- double alpha_l = det_x_c1 / det_c0_c1;
- double alpha_r = det_c0_x / det_c0_c1;
-
- // if alpha negative, use the Wu/Barsky heuristic
- if (alpha_l < 0.0 || alpha_r < 0.0) {
- double distance = Point::distance(d[0], d[last]) / 3;
- return Bezier(d[0], d[0] + left_tangent*distance,
- d[last] + right_tangent*distance, d[last]);
- } else
- return Bezier(d[0], d[0] + left_tangent*alpha_l,
- d[last] + right_tangent*alpha_r, d[last]);
-}
-
-static double
-newton_raphson_root_find(const Bezier &b, const Point &p, double u)
-{
- const Point *b_pts = b.points();
-
- Point b_det[3];
- for (int i = 0; i < 3; i++)
- b_det[i] = (b_pts[i+1] - b_pts[i]) * 3;
-
- Point b_det_det[2];
- for (int i = 0; i < 2; i++)
- b_det_det[i] = (b_det[i+1] - b_det[i]) * 2;
-
- Point b_u = b.eval(u);
- Point b_det_u = eval_bezier(b_det, 2, u);
- Point b_det_det_u = eval_bezier(b_det_det, 1, u);
-
- double numerator = Point::dot(b_u - p, b_det_u);
- double denominator = Point::dot(b_det_u, b_det_u) +
- Point::dot(b_u - p, b_det_det_u);
-
- return u - numerator/denominator;
-}
-
-static void
-reparameterize(const Point *d, int nd, Vector<double> &parameters,
- const Bezier &b)
-{
- for (int i = 0; i < nd; i++)
- parameters[i] = newton_raphson_root_find(b, d[i], parameters[i]);
-}
-
-static double
-compute_max_error(const Point *d, int nd, const Bezier &b,
- const Vector<double> &parameters, int *split_point)
-{
- *split_point = nd/2;
- double max_dist = 0.0;
- for (int i = 1; i < nd - 1; i++) {
- double dist = (b.eval(parameters[i]) - d[i]).squared_length();
- if (dist >= max_dist) {
- max_dist = dist;
- *split_point = i;
- }
- }
- return max_dist;
-}
-
-static void
-fit0(const Point *d, int nd, Point left_tangent, Point right_tangent,
- double error, Vector<Bezier> &result)
-{
- // Use a heuristic for small regions (only two points)
- if (nd == 2) {
- double dist = Point::distance(d[0], d[1]) / 3;
- result.push_back(Bezier(d[0],
- d[0] + dist*left_tangent,
- d[1] + dist*right_tangent,
- d[1]));
- return;
- }
-
- // Parameterize points and attempt to fit curve
- Vector<double> parameters;
- chord_length_parameterize(d, nd, parameters);
- Bezier b = generate_bezier(d, nd, parameters, left_tangent, right_tangent);
-
- // find max error
- int split_point;
- double max_error = compute_max_error(d, nd, b, parameters, &split_point);
- if (max_error < error) {
- result.push_back(b);
- return;
- }
-
- // if error not too large, try iteration and reparameterization
- if (max_error < error*error)
- for (int i = 0; i < 4; i++) {
- reparameterize(d, nd, parameters, b);
- b = generate_bezier(d, nd, parameters, left_tangent, right_tangent);
- max_error = compute_max_error(d, nd, b, parameters, &split_point);
- if (max_error < error) {
- result.push_back(b);
- return;
- }
- }
-
- // fitting failed -- split at max error point and fit again
- Point center_tangent = ((d[split_point-1] - d[split_point+1])/2).normal();
- fit0(d, split_point+1, left_tangent, center_tangent, error, result);
- fit0(d+split_point, nd-split_point, -center_tangent, right_tangent, error, result);
-}
-
-void
-Bezier::fit(const Vector<Point> &points, double error, Vector<Bezier> &result)
-{
- int npoints = points.size();
- Point left_tangent = (points[1] - points[0]).normal();
- Point right_tangent = (points[npoints-2] - points[npoints-1]).normal();
- fit0(&points[0], npoints, left_tangent, right_tangent, error, result);
-}