2011-10-12 03:02:50 +00:00
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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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// Stroke math
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//
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//----------------------------------------------------------------------------
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#ifndef AGG_STROKE_MATH_INCLUDED
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#define AGG_STROKE_MATH_INCLUDED
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#include "agg_math.h"
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#include "agg_vertex_sequence.h"
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namespace agg
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{
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//-------------------------------------------------------------line_cap_e
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enum line_cap_e
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{
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butt_cap,
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square_cap,
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round_cap
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};
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//------------------------------------------------------------line_join_e
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enum line_join_e
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{
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miter_join = 0,
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miter_join_revert = 1,
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round_join = 2,
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bevel_join = 3,
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miter_join_round = 4
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};
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//-----------------------------------------------------------inner_join_e
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enum inner_join_e
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{
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inner_bevel,
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inner_miter,
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inner_jag,
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inner_round
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};
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//------------------------------------------------------------math_stroke
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template<class VertexConsumer> class math_stroke
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{
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public:
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typedef typename VertexConsumer::value_type coord_type;
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math_stroke();
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void line_cap(line_cap_e lc) { m_line_cap = lc; }
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void line_join(line_join_e lj) { m_line_join = lj; }
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void inner_join(inner_join_e ij) { m_inner_join = ij; }
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line_cap_e line_cap() const { return m_line_cap; }
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line_join_e line_join() const { return m_line_join; }
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inner_join_e inner_join() const { return m_inner_join; }
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void width(double w);
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void miter_limit(double ml) { m_miter_limit = ml; }
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void miter_limit_theta(double t);
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void inner_miter_limit(double ml) { m_inner_miter_limit = ml; }
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void approximation_scale(double as) { m_approx_scale = as; }
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double width() const { return m_width * 2.0; }
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double miter_limit() const { return m_miter_limit; }
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double inner_miter_limit() const { return m_inner_miter_limit; }
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double approximation_scale() const { return m_approx_scale; }
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void calc_cap(VertexConsumer& vc,
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const vertex_dist& v0,
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const vertex_dist& v1,
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double len);
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void calc_join(VertexConsumer& vc,
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const vertex_dist& v0,
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const vertex_dist& v1,
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const vertex_dist& v2,
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double len1,
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double len2);
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private:
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AGG_INLINE void add_vertex(VertexConsumer& vc, double x, double y)
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{
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vc.add(coord_type(x, y));
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}
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void calc_arc(VertexConsumer& vc,
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double x, double y,
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double dx1, double dy1,
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double dx2, double dy2);
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void calc_miter(VertexConsumer& vc,
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const vertex_dist& v0,
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const vertex_dist& v1,
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const vertex_dist& v2,
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double dx1, double dy1,
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double dx2, double dy2,
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line_join_e lj,
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double mlimit,
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double dbevel);
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double m_width;
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double m_width_abs;
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double m_width_eps;
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int m_width_sign;
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double m_miter_limit;
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double m_inner_miter_limit;
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double m_approx_scale;
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line_cap_e m_line_cap;
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line_join_e m_line_join;
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inner_join_e m_inner_join;
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};
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//-----------------------------------------------------------------------
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template<class VC> math_stroke<VC>::math_stroke() :
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m_width(0.5),
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m_width_abs(0.5),
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m_width_eps(0.5/1024.0),
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m_width_sign(1),
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m_miter_limit(4.0),
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m_inner_miter_limit(1.01),
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m_approx_scale(1.0),
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m_line_cap(butt_cap),
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m_line_join(miter_join),
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m_inner_join(inner_miter)
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{
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}
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//-----------------------------------------------------------------------
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template<class VC> void math_stroke<VC>::width(double w)
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{
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m_width = w * 0.5;
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if(m_width < 0)
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{
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m_width_abs = -m_width;
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m_width_sign = -1;
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}
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else
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{
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m_width_abs = m_width;
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m_width_sign = 1;
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}
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m_width_eps = m_width / 1024.0;
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}
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//-----------------------------------------------------------------------
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template<class VC> void math_stroke<VC>::miter_limit_theta(double t)
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{
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2014-08-30 22:13:26 +00:00
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m_miter_limit = 1.0 / std::sin(t * 0.5) ;
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2011-10-12 03:02:50 +00:00
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}
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//-----------------------------------------------------------------------
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template<class VC>
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void math_stroke<VC>::calc_arc(VC& vc,
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double x, double y,
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double dx1, double dy1,
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double dx2, double dy2)
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{
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2014-08-30 22:13:26 +00:00
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double a1 = std::atan2(dy1 * m_width_sign, dx1 * m_width_sign);
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double a2 = std::atan2(dy2 * m_width_sign, dx2 * m_width_sign);
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2011-10-12 03:02:50 +00:00
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double da = a1 - a2;
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int i, n;
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2014-08-30 22:13:26 +00:00
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da = std::acos(m_width_abs / (m_width_abs + 0.125 / m_approx_scale)) * 2;
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2011-10-12 03:02:50 +00:00
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add_vertex(vc, x + dx1, y + dy1);
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if(m_width_sign > 0)
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{
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if(a1 > a2) a2 += 2 * pi;
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n = int((a2 - a1) / da);
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da = (a2 - a1) / (n + 1);
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a1 += da;
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for(i = 0; i < n; i++)
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{
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2014-08-30 22:13:26 +00:00
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add_vertex(vc, x + std::cos(a1) * m_width, y + std::sin(a1) * m_width);
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2011-10-12 03:02:50 +00:00
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a1 += da;
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}
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}
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else
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{
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if(a1 < a2) a2 -= 2 * pi;
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n = int((a1 - a2) / da);
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da = (a1 - a2) / (n + 1);
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a1 -= da;
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for(i = 0; i < n; i++)
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{
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2014-08-30 22:13:26 +00:00
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add_vertex(vc, x + std::cos(a1) * m_width, y + std::sin(a1) * m_width);
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2011-10-12 03:02:50 +00:00
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a1 -= da;
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}
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}
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add_vertex(vc, x + dx2, y + dy2);
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}
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//-----------------------------------------------------------------------
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template<class VC>
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void math_stroke<VC>::calc_miter(VC& vc,
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const vertex_dist& v0,
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const vertex_dist& v1,
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const vertex_dist& v2,
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double dx1, double dy1,
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double dx2, double dy2,
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line_join_e lj,
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double mlimit,
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double dbevel)
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{
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double xi = v1.x;
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double yi = v1.y;
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double di = 1;
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double lim = m_width_abs * mlimit;
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bool miter_limit_exceeded = true; // Assume the worst
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bool intersection_failed = true; // Assume the worst
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if(calc_intersection(v0.x + dx1, v0.y - dy1,
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v1.x + dx1, v1.y - dy1,
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v1.x + dx2, v1.y - dy2,
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v2.x + dx2, v2.y - dy2,
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&xi, &yi))
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{
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// Calculation of the intersection succeeded
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//---------------------
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di = calc_distance(v1.x, v1.y, xi, yi);
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if(di <= lim)
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{
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// Inside the miter limit
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//---------------------
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add_vertex(vc, xi, yi);
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miter_limit_exceeded = false;
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}
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intersection_failed = false;
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}
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else
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{
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// Calculation of the intersection failed, most probably
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// the three points lie one straight line.
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// First check if v0 and v2 lie on the opposite sides of vector:
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// (v1.x, v1.y) -> (v1.x+dx1, v1.y-dy1), that is, the perpendicular
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// to the line determined by vertices v0 and v1.
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// This condition determines whether the next line segments continues
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// the previous one or goes back.
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//----------------
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double x2 = v1.x + dx1;
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double y2 = v1.y - dy1;
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if((cross_product(v0.x, v0.y, v1.x, v1.y, x2, y2) < 0.0) ==
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(cross_product(v1.x, v1.y, v2.x, v2.y, x2, y2) < 0.0))
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{
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// This case means that the next segment continues
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// the previous one (straight line)
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//-----------------
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add_vertex(vc, v1.x + dx1, v1.y - dy1);
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miter_limit_exceeded = false;
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}
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}
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if(miter_limit_exceeded)
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{
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// Miter limit exceeded
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//------------------------
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switch(lj)
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{
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case miter_join_revert:
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// For the compatibility with SVG, PDF, etc,
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// we use a simple bevel join instead of
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// "smart" bevel
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//-------------------
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add_vertex(vc, v1.x + dx1, v1.y - dy1);
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add_vertex(vc, v1.x + dx2, v1.y - dy2);
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break;
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case miter_join_round:
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calc_arc(vc, v1.x, v1.y, dx1, -dy1, dx2, -dy2);
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break;
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default:
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// If no miter-revert, calculate new dx1, dy1, dx2, dy2
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//----------------
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if(intersection_failed)
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{
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mlimit *= m_width_sign;
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add_vertex(vc, v1.x + dx1 + dy1 * mlimit,
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v1.y - dy1 + dx1 * mlimit);
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add_vertex(vc, v1.x + dx2 - dy2 * mlimit,
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v1.y - dy2 - dx2 * mlimit);
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}
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else
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{
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double x1 = v1.x + dx1;
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double y1 = v1.y - dy1;
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double x2 = v1.x + dx2;
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double y2 = v1.y - dy2;
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di = (lim - dbevel) / (di - dbevel);
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add_vertex(vc, x1 + (xi - x1) * di,
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y1 + (yi - y1) * di);
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add_vertex(vc, x2 + (xi - x2) * di,
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y2 + (yi - y2) * di);
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}
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break;
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}
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}
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}
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//--------------------------------------------------------stroke_calc_cap
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template<class VC>
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void math_stroke<VC>::calc_cap(VC& vc,
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const vertex_dist& v0,
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const vertex_dist& v1,
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double len)
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{
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vc.remove_all();
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double dx1 = (v1.y - v0.y) / len;
|
|
|
|
|
double dy1 = (v1.x - v0.x) / len;
|
|
|
|
|
double dx2 = 0;
|
|
|
|
|
double dy2 = 0;
|
|
|
|
|
|
|
|
|
|
dx1 *= m_width;
|
|
|
|
|
dy1 *= m_width;
|
|
|
|
|
|
|
|
|
|
if(m_line_cap != round_cap)
|
|
|
|
|
{
|
|
|
|
|
if(m_line_cap == square_cap)
|
|
|
|
|
{
|
|
|
|
|
dx2 = dy1 * m_width_sign;
|
|
|
|
|
dy2 = dx1 * m_width_sign;
|
|
|
|
|
}
|
|
|
|
|
add_vertex(vc, v0.x - dx1 - dx2, v0.y + dy1 - dy2);
|
|
|
|
|
add_vertex(vc, v0.x + dx1 - dx2, v0.y - dy1 - dy2);
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
{
|
2014-08-30 22:13:26 +00:00
|
|
|
double da = std::acos(m_width_abs / (m_width_abs + 0.125 / m_approx_scale)) * 2;
|
2011-10-12 03:02:50 +00:00
|
|
|
double a1;
|
|
|
|
|
int i;
|
|
|
|
|
int n = int(pi / da);
|
|
|
|
|
|
|
|
|
|
da = pi / (n + 1);
|
|
|
|
|
add_vertex(vc, v0.x - dx1, v0.y + dy1);
|
|
|
|
|
if(m_width_sign > 0)
|
|
|
|
|
{
|
2014-08-30 22:13:26 +00:00
|
|
|
a1 = std::atan2(dy1, -dx1);
|
2011-10-12 03:02:50 +00:00
|
|
|
a1 += da;
|
|
|
|
|
for(i = 0; i < n; i++)
|
|
|
|
|
{
|
2014-08-30 22:13:26 +00:00
|
|
|
add_vertex(vc, v0.x + std::cos(a1) * m_width,
|
|
|
|
|
v0.y + std::sin(a1) * m_width);
|
2011-10-12 03:02:50 +00:00
|
|
|
a1 += da;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
{
|
2014-08-30 22:13:26 +00:00
|
|
|
a1 = std::atan2(-dy1, dx1);
|
2011-10-12 03:02:50 +00:00
|
|
|
a1 -= da;
|
|
|
|
|
for(i = 0; i < n; i++)
|
|
|
|
|
{
|
2014-08-30 22:13:26 +00:00
|
|
|
add_vertex(vc, v0.x + std::cos(a1) * m_width,
|
|
|
|
|
v0.y + std::sin(a1) * m_width);
|
2011-10-12 03:02:50 +00:00
|
|
|
a1 -= da;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
add_vertex(vc, v0.x + dx1, v0.y - dy1);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------
|
|
|
|
|
template<class VC>
|
|
|
|
|
void math_stroke<VC>::calc_join(VC& vc,
|
|
|
|
|
const vertex_dist& v0,
|
|
|
|
|
const vertex_dist& v1,
|
|
|
|
|
const vertex_dist& v2,
|
|
|
|
|
double len1,
|
|
|
|
|
double len2)
|
|
|
|
|
{
|
|
|
|
|
double dx1 = m_width * (v1.y - v0.y) / len1;
|
|
|
|
|
double dy1 = m_width * (v1.x - v0.x) / len1;
|
|
|
|
|
double dx2 = m_width * (v2.y - v1.y) / len2;
|
|
|
|
|
double dy2 = m_width * (v2.x - v1.x) / len2;
|
|
|
|
|
|
|
|
|
|
vc.remove_all();
|
|
|
|
|
|
|
|
|
|
double cp = cross_product(v0.x, v0.y, v1.x, v1.y, v2.x, v2.y);
|
|
|
|
|
if(cp != 0 && (cp > 0) == (m_width > 0))
|
|
|
|
|
{
|
|
|
|
|
// Inner join
|
|
|
|
|
//---------------
|
|
|
|
|
double limit = ((len1 < len2) ? len1 : len2) / m_width_abs;
|
|
|
|
|
if(limit < m_inner_miter_limit)
|
|
|
|
|
{
|
|
|
|
|
limit = m_inner_miter_limit;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
switch(m_inner_join)
|
|
|
|
|
{
|
|
|
|
|
default: // inner_bevel
|
|
|
|
|
add_vertex(vc, v1.x + dx1, v1.y - dy1);
|
|
|
|
|
add_vertex(vc, v1.x + dx2, v1.y - dy2);
|
|
|
|
|
break;
|
|
|
|
|
|
|
|
|
|
case inner_miter:
|
|
|
|
|
calc_miter(vc,
|
|
|
|
|
v0, v1, v2, dx1, dy1, dx2, dy2,
|
|
|
|
|
miter_join_revert,
|
|
|
|
|
limit, 0);
|
|
|
|
|
break;
|
|
|
|
|
|
|
|
|
|
case inner_jag:
|
|
|
|
|
case inner_round:
|
|
|
|
|
cp = (dx1-dx2) * (dx1-dx2) + (dy1-dy2) * (dy1-dy2);
|
|
|
|
|
if(cp < len1 * len1 && cp < len2 * len2)
|
|
|
|
|
{
|
|
|
|
|
calc_miter(vc,
|
|
|
|
|
v0, v1, v2, dx1, dy1, dx2, dy2,
|
|
|
|
|
miter_join_revert,
|
|
|
|
|
limit, 0);
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
{
|
|
|
|
|
if(m_inner_join == inner_jag)
|
|
|
|
|
{
|
|
|
|
|
add_vertex(vc, v1.x + dx1, v1.y - dy1);
|
|
|
|
|
add_vertex(vc, v1.x, v1.y );
|
|
|
|
|
add_vertex(vc, v1.x + dx2, v1.y - dy2);
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
{
|
|
|
|
|
add_vertex(vc, v1.x + dx1, v1.y - dy1);
|
|
|
|
|
add_vertex(vc, v1.x, v1.y );
|
|
|
|
|
calc_arc(vc, v1.x, v1.y, dx2, -dy2, dx1, -dy1);
|
|
|
|
|
add_vertex(vc, v1.x, v1.y );
|
|
|
|
|
add_vertex(vc, v1.x + dx2, v1.y - dy2);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
{
|
|
|
|
|
// Outer join
|
|
|
|
|
//---------------
|
|
|
|
|
|
|
|
|
|
// Calculate the distance between v1 and
|
|
|
|
|
// the central point of the bevel line segment
|
|
|
|
|
//---------------
|
|
|
|
|
double dx = (dx1 + dx2) / 2;
|
|
|
|
|
double dy = (dy1 + dy2) / 2;
|
|
|
|
|
double dbevel = sqrt(dx * dx + dy * dy);
|
|
|
|
|
|
|
|
|
|
if(m_line_join == round_join || m_line_join == bevel_join)
|
|
|
|
|
{
|
|
|
|
|
// This is an optimization that reduces the number of points
|
|
|
|
|
// in cases of almost collinear segments. If there's no
|
|
|
|
|
// visible difference between bevel and miter joins we'd rather
|
|
|
|
|
// use miter join because it adds only one point instead of two.
|
|
|
|
|
//
|
|
|
|
|
// Here we calculate the middle point between the bevel points
|
|
|
|
|
// and then, the distance between v1 and this middle point.
|
|
|
|
|
// At outer joins this distance always less than stroke width,
|
|
|
|
|
// because it's actually the height of an isosceles triangle of
|
|
|
|
|
// v1 and its two bevel points. If the difference between this
|
|
|
|
|
// width and this value is small (no visible bevel) we can
|
|
|
|
|
// add just one point.
|
|
|
|
|
//
|
|
|
|
|
// The constant in the expression makes the result approximately
|
|
|
|
|
// the same as in round joins and caps. You can safely comment
|
|
|
|
|
// out this entire "if".
|
|
|
|
|
//-------------------
|
|
|
|
|
if(m_approx_scale * (m_width_abs - dbevel) < m_width_eps)
|
|
|
|
|
{
|
|
|
|
|
if(calc_intersection(v0.x + dx1, v0.y - dy1,
|
|
|
|
|
v1.x + dx1, v1.y - dy1,
|
|
|
|
|
v1.x + dx2, v1.y - dy2,
|
|
|
|
|
v2.x + dx2, v2.y - dy2,
|
|
|
|
|
&dx, &dy))
|
|
|
|
|
{
|
|
|
|
|
add_vertex(vc, dx, dy);
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
{
|
|
|
|
|
add_vertex(vc, v1.x + dx1, v1.y - dy1);
|
|
|
|
|
}
|
|
|
|
|
return;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
switch(m_line_join)
|
|
|
|
|
{
|
|
|
|
|
case miter_join:
|
|
|
|
|
case miter_join_revert:
|
|
|
|
|
case miter_join_round:
|
|
|
|
|
calc_miter(vc,
|
|
|
|
|
v0, v1, v2, dx1, dy1, dx2, dy2,
|
|
|
|
|
m_line_join,
|
|
|
|
|
m_miter_limit,
|
|
|
|
|
dbevel);
|
|
|
|
|
break;
|
|
|
|
|
|
|
|
|
|
case round_join:
|
|
|
|
|
calc_arc(vc, v1.x, v1.y, dx1, -dy1, dx2, -dy2);
|
|
|
|
|
break;
|
|
|
|
|
|
|
|
|
|
default: // Bevel join
|
|
|
|
|
add_vertex(vc, v1.x + dx1, v1.y - dy1);
|
|
|
|
|
add_vertex(vc, v1.x + dx2, v1.y - dy2);
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#endif
|
