summaryrefslogtreecommitdiffstats
path: root/src/3rdparty/2geom/src/toys/elliptiarc-3point-center-fitting.cpp
diff options
context:
space:
mode:
Diffstat (limited to '')
-rw-r--r--src/3rdparty/2geom/src/toys/elliptiarc-3point-center-fitting.cpp266
1 files changed, 266 insertions, 0 deletions
diff --git a/src/3rdparty/2geom/src/toys/elliptiarc-3point-center-fitting.cpp b/src/3rdparty/2geom/src/toys/elliptiarc-3point-center-fitting.cpp
new file mode 100644
index 0000000..d2330a1
--- /dev/null
+++ b/src/3rdparty/2geom/src/toys/elliptiarc-3point-center-fitting.cpp
@@ -0,0 +1,266 @@
+/*
+ * make up an elliptical arc knowing 3 points lying on the arc
+ * and the ellipse centre
+ *
+ * Authors:
+ * Marco Cecchetti <mrcekets at gmail.com>
+ *
+ * Copyright 2008 authors
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it either under the terms of the GNU Lesser General Public
+ * License version 2.1 as published by the Free Software Foundation
+ * (the "LGPL") or, at your option, under the terms of the Mozilla
+ * Public License Version 1.1 (the "MPL"). If you do not alter this
+ * notice, a recipient may use your version of this file under either
+ * the MPL or the LGPL.
+ *
+ * You should have received a copy of the LGPL along with this library
+ * in the file COPYING-LGPL-2.1; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * You should have received a copy of the MPL along with this library
+ * in the file COPYING-MPL-1.1
+ *
+ * The contents of this file are subject to the Mozilla Public License
+ * Version 1.1 (the "License"); you may not use this file except in
+ * compliance with the License. You may obtain a copy of the License at
+ * http://www.mozilla.org/MPL/
+ *
+ * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
+ * OF ANY KIND, either express or implied. See the LGPL or the MPL for
+ * the specific language governing rights and limitations.
+ */
+
+#include <toys/path-cairo.h>
+#include <toys/toy-framework-2.h>
+
+#include <2geom/elliptical-arc.h>
+#include <2geom/numeric/linear_system.h>
+
+namespace Geom
+{
+
+bool make_elliptical_arc( EllipticalArc & ea,
+ Point const& centre,
+ Point const& initial,
+ Point const& final,
+ Point const& inner )
+{
+
+ Point p[3] = { initial, inner, final };
+ double x1, x2, x3, x4;
+ double y1, y2, y3, y4;
+ double x1y1, x2y2, x3y1, x1y3;
+ NL::Matrix m(3,3);
+ NL::Vector v(3);
+ NL::LinearSystem ls(m, v);
+
+ m.set_all(0);
+ v.set_all(0);
+ for (auto & k : p)
+ {
+ // init_x_y
+ x1 = k[X] - centre[X]; x2 = x1 * x1; x3 = x2 * x1; x4 = x3 * x1;
+ y1 = k[Y] - centre[Y]; y2 = y1 * y1; y3 = y2 * y1; y4 = y3 * y1;
+ x1y1 = x1 * y1;
+ x2y2 = x2 * y2;
+ x3y1 = x3 * y1; x1y3 = x1 * y3;
+
+ // init linear system
+ m(0,0) += x4;
+ m(0,1) += x3y1;
+ m(0,2) += x2y2;
+
+ m(1,0) += x3y1;
+ m(1,1) += x2y2;
+ m(1,2) += x1y3;
+
+ m(2,0) += x2y2;
+ m(2,1) += x1y3;
+ m(2,2) += y4;
+
+ v[0] += x2;
+ v[1] += x1y1;
+ v[2] += y2;
+ }
+
+ ls.SV_solve();
+
+ double A = ls.solution()[0];
+ double B = ls.solution()[1];
+ double C = ls.solution()[2];
+
+
+ //evaluate ellipse rotation angle
+ double rot = std::atan2( -B, -(A - C) )/2;
+ std::cerr << "rot = " << rot << std::endl;
+ bool swap_axes = false;
+ if ( are_near(rot, 0) ) rot = 0;
+ if ( are_near(rot, M_PI/2) || rot < 0 )
+ {
+ swap_axes = true;
+ }
+
+ // evaluate the length of the ellipse rays
+ double cosrot = std::cos(rot);
+ double sinrot = std::sin(rot);
+ double cos2 = cosrot * cosrot;
+ double sin2 = sinrot * sinrot;
+ double cossin = cosrot * sinrot;
+
+ double den = A * cos2 + B * cossin + C * sin2;
+ if ( den <= 0 )
+ {
+ std::cerr << "!(den > 0) error" << std::endl;
+ std::cerr << "evaluating rx" << std::endl;
+ return false;
+ }
+ double rx = std::sqrt(1/den);
+
+ den = C * cos2 - B * cossin + A * sin2;
+ if ( den <= 0 )
+ {
+ std::cerr << "!(den > 0) error" << std::endl;
+ std::cerr << "evaluating ry" << std::endl;
+ return false;
+ }
+ double ry = std::sqrt(1/den);
+
+
+ // the solution is not unique so we choose always the ellipse
+ // with a rotation angle between 0 and PI/2
+ if ( swap_axes ) std::swap(rx, ry);
+ if ( are_near(rot, M_PI/2)
+ || are_near(rot, -M_PI/2)
+ || are_near(rx, ry) )
+ {
+ rot = 0;
+ }
+ else if ( rot < 0 )
+ {
+ rot += M_PI/2;
+ }
+
+ std::cerr << "swap axes: " << swap_axes << std::endl;
+ std::cerr << "rx = " << rx << " ry = " << ry << std::endl;
+ std::cerr << "rot = " << deg_from_rad(rot) << std::endl;
+ std::cerr << "centre: " << centre << std::endl;
+
+
+ // find out how we should set the large_arc_flag and sweep_flag
+ bool large_arc_flag = true;
+ bool sweep_flag = true;
+
+ Point sp_cp = initial - centre;
+ Point ep_cp = final - centre;
+ Point ip_cp = inner - centre;
+
+ double angle1 = angle_between(sp_cp, ep_cp);
+ double angle2 = angle_between(sp_cp, ip_cp);
+ double angle3 = angle_between(ip_cp, ep_cp);
+
+ if ( angle1 > 0 )
+ {
+ if ( angle2 > 0 && angle3 > 0 )
+ {
+ large_arc_flag = false;
+ sweep_flag = true;
+ }
+ else
+ {
+ large_arc_flag = true;
+ sweep_flag = false;
+ }
+ }
+ else
+ {
+ if ( angle2 < 0 && angle3 < 0 )
+ {
+ large_arc_flag = false;
+ sweep_flag = false;
+ }
+ else
+ {
+ large_arc_flag = true;
+ sweep_flag = true;
+ }
+ }
+
+ // finally we're going to create the elliptical arc!
+ try
+ {
+ ea.set( initial, rx, ry, rot,
+ large_arc_flag, sweep_flag, final );
+ }
+ catch( RangeError e )
+ {
+ std::cerr << e.what() << std::endl;
+ return false;
+ }
+
+ return true;
+}
+
+
+}
+
+
+
+using namespace Geom;
+
+class ElliptiArcMaker : public Toy
+{
+ private:
+ void draw( cairo_t *cr, std::ostringstream *notify,
+ int width, int height, bool save, std::ostringstream *timer_stream) override
+ {
+ cairo_set_line_width (cr, 0.3);
+ cairo_set_source_rgb(cr, 0,0,0.3);
+ draw_text(cr, O.pos, "centre");
+ draw_text(cr, A.pos, "initial");
+ draw_text(cr, B.pos, "final");
+ draw_text(cr, C.pos, "inner");
+ cairo_stroke(cr);
+ cairo_set_source_rgb(cr, 0.7,0,0);
+ bool status
+ = make_elliptical_arc(ea, O.pos, A.pos, B.pos, C.pos);
+ if (status)
+ {
+ D2<Geom::SBasis> easb = ea.toSBasis();
+ cairo_d2_sb(cr, easb);
+ }
+ cairo_stroke(cr);
+ Toy::draw(cr, notify, width, height, save,timer_stream);
+ }
+
+ public:
+ ElliptiArcMaker()
+ : O(443, 441),
+ A(516, 275),
+ B(222, 455),
+ C(190, 234)
+ {
+ handles.push_back(&O);
+ handles.push_back(&A);
+ handles.push_back(&B);
+ handles.push_back(&C);
+ }
+
+ private:
+ PointHandle O, A, B, C;
+ EllipticalArc ea;
+};
+
+
+
+
+
+
+
+
+int main(int argc, char **argv)
+{
+ init( argc, argv, new ElliptiArcMaker() );
+ return 0;
+}
+