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