//---------------------------------------------------------------------------- // 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 //---------------------------------------------------------------------------- // // Stroke math // //---------------------------------------------------------------------------- #ifndef AGG_STROKE_MATH_INCLUDED #define AGG_STROKE_MATH_INCLUDED #include "agg_math.h" #include "agg_vertex_sequence.h" namespace agg { //-------------------------------------------------------------line_cap_e enum line_cap_e { butt_cap, square_cap, round_cap }; //------------------------------------------------------------line_join_e enum line_join_e { miter_join = 0, miter_join_revert = 1, round_join = 2, bevel_join = 3, miter_join_round = 4 }; //-----------------------------------------------------------inner_join_e enum inner_join_e { inner_bevel, inner_miter, inner_jag, inner_round }; //------------------------------------------------------------math_stroke template<class VertexConsumer> class math_stroke { public: typedef typename VertexConsumer::value_type coord_type; math_stroke(); void line_cap(line_cap_e lc) { m_line_cap = lc; } void line_join(line_join_e lj) { m_line_join = lj; } void inner_join(inner_join_e ij) { m_inner_join = ij; } line_cap_e line_cap() const { return m_line_cap; } line_join_e line_join() const { return m_line_join; } inner_join_e inner_join() const { return m_inner_join; } void width(double w); void miter_limit(double ml) { m_miter_limit = ml; } void miter_limit_theta(double t); void inner_miter_limit(double ml) { m_inner_miter_limit = ml; } void approximation_scale(double as) { m_approx_scale = as; } double width() const { return m_width * 2.0; } double miter_limit() const { return m_miter_limit; } double inner_miter_limit() const { return m_inner_miter_limit; } double approximation_scale() const { return m_approx_scale; } void calc_cap(VertexConsumer& vc, const vertex_dist& v0, const vertex_dist& v1, double len); void calc_join(VertexConsumer& vc, const vertex_dist& v0, const vertex_dist& v1, const vertex_dist& v2, double len1, double len2); private: AGG_INLINE void add_vertex(VertexConsumer& vc, double x, double y) { vc.add(coord_type(x, y)); } void calc_arc(VertexConsumer& vc, double x, double y, double dx1, double dy1, double dx2, double dy2); void calc_miter(VertexConsumer& vc, const vertex_dist& v0, const vertex_dist& v1, const vertex_dist& v2, double dx1, double dy1, double dx2, double dy2, line_join_e lj, double mlimit, double dbevel); double m_width; double m_width_abs; double m_width_eps; int m_width_sign; double m_miter_limit; double m_inner_miter_limit; double m_approx_scale; line_cap_e m_line_cap; line_join_e m_line_join; inner_join_e m_inner_join; }; //----------------------------------------------------------------------- template<class VC> math_stroke<VC>::math_stroke() : m_width(0.5), m_width_abs(0.5), m_width_eps(0.5/1024.0), m_width_sign(1), m_miter_limit(4.0), m_inner_miter_limit(1.01), m_approx_scale(1.0), m_line_cap(butt_cap), m_line_join(miter_join), m_inner_join(inner_miter) { } //----------------------------------------------------------------------- template<class VC> void math_stroke<VC>::width(double w) { m_width = w * 0.5; if(m_width < 0) { m_width_abs = -m_width; m_width_sign = -1; } else { m_width_abs = m_width; m_width_sign = 1; } m_width_eps = m_width / 1024.0; } //----------------------------------------------------------------------- template<class VC> void math_stroke<VC>::miter_limit_theta(double t) { m_miter_limit = 1.0 / std::sin(t * 0.5) ; } //----------------------------------------------------------------------- template<class VC> void math_stroke<VC>::calc_arc(VC& vc, double x, double y, double dx1, double dy1, double dx2, double dy2) { double a1 = std::atan2(dy1 * m_width_sign, dx1 * m_width_sign); double a2 = std::atan2(dy2 * m_width_sign, dx2 * m_width_sign); double da = a1 - a2; int i, n; da = std::acos(m_width_abs / (m_width_abs + 0.125 / m_approx_scale)) * 2; add_vertex(vc, x + dx1, y + dy1); if(m_width_sign > 0) { if(a1 > a2) a2 += 2 * pi; n = int((a2 - a1) / da); da = (a2 - a1) / (n + 1); a1 += da; for(i = 0; i < n; i++) { add_vertex(vc, x + std::cos(a1) * m_width, y + std::sin(a1) * m_width); a1 += da; } } else { if(a1 < a2) a2 -= 2 * pi; n = int((a1 - a2) / da); da = (a1 - a2) / (n + 1); a1 -= da; for(i = 0; i < n; i++) { add_vertex(vc, x + std::cos(a1) * m_width, y + std::sin(a1) * m_width); a1 -= da; } } add_vertex(vc, x + dx2, y + dy2); } //----------------------------------------------------------------------- template<class VC> void math_stroke<VC>::calc_miter(VC& vc, const vertex_dist& v0, const vertex_dist& v1, const vertex_dist& v2, double dx1, double dy1, double dx2, double dy2, line_join_e lj, double mlimit, double dbevel) { double xi = v1.x; double yi = v1.y; double di = 1; double lim = m_width_abs * mlimit; bool miter_limit_exceeded = true; // Assume the worst bool intersection_failed = true; // Assume the worst 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, &xi, &yi)) { // Calculation of the intersection succeeded //--------------------- di = calc_distance(v1.x, v1.y, xi, yi); if(di <= lim) { // Inside the miter limit //--------------------- add_vertex(vc, xi, yi); miter_limit_exceeded = false; } intersection_failed = false; } else { // Calculation of the intersection failed, most probably // the three points lie one straight line. // First check if v0 and v2 lie on the opposite sides of vector: // (v1.x, v1.y) -> (v1.x+dx1, v1.y-dy1), that is, the perpendicular // to the line determined by vertices v0 and v1. // This condition determines whether the next line segments continues // the previous one or goes back. //---------------- double x2 = v1.x + dx1; double y2 = v1.y - dy1; if((cross_product(v0.x, v0.y, v1.x, v1.y, x2, y2) < 0.0) == (cross_product(v1.x, v1.y, v2.x, v2.y, x2, y2) < 0.0)) { // This case means that the next segment continues // the previous one (straight line) //----------------- add_vertex(vc, v1.x + dx1, v1.y - dy1); miter_limit_exceeded = false; } } if(miter_limit_exceeded) { // Miter limit exceeded //------------------------ switch(lj) { case miter_join_revert: // For the compatibility with SVG, PDF, etc, // we use a simple bevel join instead of // "smart" bevel //------------------- add_vertex(vc, v1.x + dx1, v1.y - dy1); add_vertex(vc, v1.x + dx2, v1.y - dy2); break; case miter_join_round: calc_arc(vc, v1.x, v1.y, dx1, -dy1, dx2, -dy2); break; default: // If no miter-revert, calculate new dx1, dy1, dx2, dy2 //---------------- if(intersection_failed) { mlimit *= m_width_sign; add_vertex(vc, v1.x + dx1 + dy1 * mlimit, v1.y - dy1 + dx1 * mlimit); add_vertex(vc, v1.x + dx2 - dy2 * mlimit, v1.y - dy2 - dx2 * mlimit); } else { double x1 = v1.x + dx1; double y1 = v1.y - dy1; double x2 = v1.x + dx2; double y2 = v1.y - dy2; di = (lim - dbevel) / (di - dbevel); add_vertex(vc, x1 + (xi - x1) * di, y1 + (yi - y1) * di); add_vertex(vc, x2 + (xi - x2) * di, y2 + (yi - y2) * di); } break; } } } //--------------------------------------------------------stroke_calc_cap template<class VC> void math_stroke<VC>::calc_cap(VC& vc, const vertex_dist& v0, const vertex_dist& v1, double len) { vc.remove_all(); 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 { double da = std::acos(m_width_abs / (m_width_abs + 0.125 / m_approx_scale)) * 2; 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) { a1 = std::atan2(dy1, -dx1); a1 += da; for(i = 0; i < n; i++) { add_vertex(vc, v0.x + std::cos(a1) * m_width, v0.y + std::sin(a1) * m_width); a1 += da; } } else { a1 = std::atan2(-dy1, dx1); a1 -= da; for(i = 0; i < n; i++) { add_vertex(vc, v0.x + std::cos(a1) * m_width, v0.y + std::sin(a1) * m_width); 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