259 lines
8.5 KiB
C++
259 lines
8.5 KiB
C++
//----------------------------------------------------------------------------
|
|
// 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 <cmath>
|
|
#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 = std::cos(sweep_angle / 2.0);
|
|
double y0 = std::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 = std::sin(start_angle + sweep_angle / 2.0);
|
|
double cs = std::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 = std::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(std::fabs(sweep_angle) < 1e-10)
|
|
{
|
|
m_num_vertices = 4;
|
|
m_cmd = path_cmd_line_to;
|
|
m_vertices[0] = x + rx * std::cos(start_angle);
|
|
m_vertices[1] = y + ry * std::sin(start_angle);
|
|
m_vertices[2] = x + rx * std::cos(start_angle + sweep_angle);
|
|
m_vertices[3] = y + ry * std::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 = std::cos(angle);
|
|
double sin_a = std::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 = std::sqrt(radii_check) * rx;
|
|
ry = std::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 * std::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 = std::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 * std::acos(v);
|
|
|
|
// Calculate the sweep angle
|
|
//------------------------
|
|
n = std::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 * std::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;
|
|
}
|
|
}
|
|
|
|
|
|
}
|