259 lines
8.5 KiB
C++
259 lines
8.5 KiB
C++
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//----------------------------------------------------------------------------
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// Anti-Grain Geometry - Version 2.4
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// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
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//
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// Permission to copy, use, modify, sell and distribute this software
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// is granted provided this copyright notice appears in all copies.
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// This software is provided "as is" without express or implied
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// warranty, and with no claim as to its suitability for any purpose.
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//
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//----------------------------------------------------------------------------
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// Contact: mcseem@antigrain.com
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// mcseemagg@yahoo.com
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// http://www.antigrain.com
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//----------------------------------------------------------------------------
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//
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// Arc generator. Produces at most 4 consecutive cubic bezier curves, i.e.,
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// 4, 7, 10, or 13 vertices.
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//
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//----------------------------------------------------------------------------
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#include <math.h>
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#include "agg_bezier_arc.h"
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namespace agg
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{
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// This epsilon is used to prevent us from adding degenerate curves
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// (converging to a single point).
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// The value isn't very critical. Function arc_to_bezier() has a limit
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// of the sweep_angle. If fabs(sweep_angle) exceeds pi/2 the curve
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// becomes inaccurate. But slight exceeding is quite appropriate.
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//-------------------------------------------------bezier_arc_angle_epsilon
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const double bezier_arc_angle_epsilon = 0.01;
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//------------------------------------------------------------arc_to_bezier
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void arc_to_bezier(double cx, double cy, double rx, double ry,
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double start_angle, double sweep_angle,
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double* curve)
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{
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double x0 = cos(sweep_angle / 2.0);
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double y0 = sin(sweep_angle / 2.0);
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double tx = (1.0 - x0) * 4.0 / 3.0;
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double ty = y0 - tx * x0 / y0;
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double px[4];
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double py[4];
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px[0] = x0;
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py[0] = -y0;
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px[1] = x0 + tx;
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py[1] = -ty;
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px[2] = x0 + tx;
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py[2] = ty;
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px[3] = x0;
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py[3] = y0;
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double sn = sin(start_angle + sweep_angle / 2.0);
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double cs = cos(start_angle + sweep_angle / 2.0);
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unsigned i;
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for(i = 0; i < 4; i++)
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{
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curve[i * 2] = cx + rx * (px[i] * cs - py[i] * sn);
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curve[i * 2 + 1] = cy + ry * (px[i] * sn + py[i] * cs);
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}
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}
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//------------------------------------------------------------------------
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void bezier_arc::init(double x, double y,
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double rx, double ry,
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double start_angle,
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double sweep_angle)
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{
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start_angle = fmod(start_angle, 2.0 * pi);
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if(sweep_angle >= 2.0 * pi) sweep_angle = 2.0 * pi;
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if(sweep_angle <= -2.0 * pi) sweep_angle = -2.0 * pi;
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if(fabs(sweep_angle) < 1e-10)
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{
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m_num_vertices = 4;
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m_cmd = path_cmd_line_to;
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m_vertices[0] = x + rx * cos(start_angle);
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m_vertices[1] = y + ry * sin(start_angle);
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m_vertices[2] = x + rx * cos(start_angle + sweep_angle);
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m_vertices[3] = y + ry * sin(start_angle + sweep_angle);
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return;
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}
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double total_sweep = 0.0;
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double local_sweep = 0.0;
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double prev_sweep;
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m_num_vertices = 2;
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m_cmd = path_cmd_curve4;
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bool done = false;
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do
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{
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if(sweep_angle < 0.0)
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{
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prev_sweep = total_sweep;
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local_sweep = -pi * 0.5;
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total_sweep -= pi * 0.5;
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if(total_sweep <= sweep_angle + bezier_arc_angle_epsilon)
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{
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local_sweep = sweep_angle - prev_sweep;
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done = true;
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}
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}
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else
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{
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prev_sweep = total_sweep;
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local_sweep = pi * 0.5;
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total_sweep += pi * 0.5;
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if(total_sweep >= sweep_angle - bezier_arc_angle_epsilon)
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{
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local_sweep = sweep_angle - prev_sweep;
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done = true;
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}
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}
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arc_to_bezier(x, y, rx, ry,
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start_angle,
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local_sweep,
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m_vertices + m_num_vertices - 2);
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m_num_vertices += 6;
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start_angle += local_sweep;
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}
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while(!done && m_num_vertices < 26);
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}
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//--------------------------------------------------------------------
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void bezier_arc_svg::init(double x0, double y0,
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double rx, double ry,
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double angle,
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bool large_arc_flag,
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bool sweep_flag,
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double x2, double y2)
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{
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m_radii_ok = true;
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if(rx < 0.0) rx = -rx;
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if(ry < 0.0) ry = -rx;
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// Calculate the middle point between
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// the current and the final points
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//------------------------
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double dx2 = (x0 - x2) / 2.0;
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double dy2 = (y0 - y2) / 2.0;
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double cos_a = cos(angle);
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double sin_a = sin(angle);
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// Calculate (x1, y1)
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//------------------------
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double x1 = cos_a * dx2 + sin_a * dy2;
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double y1 = -sin_a * dx2 + cos_a * dy2;
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// Ensure radii are large enough
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//------------------------
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double prx = rx * rx;
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double pry = ry * ry;
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double px1 = x1 * x1;
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double py1 = y1 * y1;
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// Check that radii are large enough
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//------------------------
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double radii_check = px1/prx + py1/pry;
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if(radii_check > 1.0)
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{
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rx = sqrt(radii_check) * rx;
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ry = sqrt(radii_check) * ry;
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prx = rx * rx;
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pry = ry * ry;
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if(radii_check > 10.0) m_radii_ok = false;
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}
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// Calculate (cx1, cy1)
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//------------------------
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double sign = (large_arc_flag == sweep_flag) ? -1.0 : 1.0;
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double sq = (prx*pry - prx*py1 - pry*px1) / (prx*py1 + pry*px1);
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double coef = sign * sqrt((sq < 0) ? 0 : sq);
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double cx1 = coef * ((rx * y1) / ry);
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double cy1 = coef * -((ry * x1) / rx);
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//
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// Calculate (cx, cy) from (cx1, cy1)
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//------------------------
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double sx2 = (x0 + x2) / 2.0;
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double sy2 = (y0 + y2) / 2.0;
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double cx = sx2 + (cos_a * cx1 - sin_a * cy1);
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double cy = sy2 + (sin_a * cx1 + cos_a * cy1);
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// Calculate the start_angle (angle1) and the sweep_angle (dangle)
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//------------------------
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double ux = (x1 - cx1) / rx;
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double uy = (y1 - cy1) / ry;
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double vx = (-x1 - cx1) / rx;
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double vy = (-y1 - cy1) / ry;
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double p, n;
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// Calculate the angle start
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//------------------------
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n = sqrt(ux*ux + uy*uy);
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p = ux; // (1 * ux) + (0 * uy)
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sign = (uy < 0) ? -1.0 : 1.0;
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double v = p / n;
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if(v < -1.0) v = -1.0;
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if(v > 1.0) v = 1.0;
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double start_angle = sign * acos(v);
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// Calculate the sweep angle
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//------------------------
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n = sqrt((ux*ux + uy*uy) * (vx*vx + vy*vy));
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p = ux * vx + uy * vy;
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sign = (ux * vy - uy * vx < 0) ? -1.0 : 1.0;
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v = p / n;
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if(v < -1.0) v = -1.0;
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if(v > 1.0) v = 1.0;
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double sweep_angle = sign * acos(v);
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if(!sweep_flag && sweep_angle > 0)
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{
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sweep_angle -= pi * 2.0;
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}
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else
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if (sweep_flag && sweep_angle < 0)
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{
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sweep_angle += pi * 2.0;
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}
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// We can now build and transform the resulting arc
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//------------------------
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m_arc.init(0.0, 0.0, rx, ry, start_angle, sweep_angle);
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trans_affine mtx = trans_affine_rotation(angle);
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mtx *= trans_affine_translation(cx, cy);
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for(unsigned i = 2; i < m_arc.num_vertices()-2; i += 2)
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{
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mtx.transform(m_arc.vertices() + i, m_arc.vertices() + i + 1);
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}
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// We must make sure that the starting and ending points
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// exactly coincide with the initial (x0,y0) and (x2,y2)
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m_arc.vertices()[0] = x0;
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m_arc.vertices()[1] = y0;
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if(m_arc.num_vertices() > 2)
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{
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m_arc.vertices()[m_arc.num_vertices() - 2] = x2;
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m_arc.vertices()[m_arc.num_vertices() - 1] = y2;
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}
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}
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}
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