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438 lines
14 KiB
438 lines
14 KiB
2 years ago
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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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// Bessel function (besj) was adapted for use in AGG library by Andy Wilk
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// Contact: castor.vulgaris@gmail.com
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//----------------------------------------------------------------------------
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#ifndef AGG_MATH_INCLUDED
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#define AGG_MATH_INCLUDED
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#include <cmath>
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#include "agg_basics.h"
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namespace agg
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{
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//------------------------------------------------------vertex_dist_epsilon
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// Coinciding points maximal distance (Epsilon)
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const double vertex_dist_epsilon = 1e-14;
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//-----------------------------------------------------intersection_epsilon
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// See calc_intersection
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const double intersection_epsilon = 1.0e-30;
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//------------------------------------------------------------cross_product
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AGG_INLINE double cross_product(double x1, double y1,
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double x2, double y2,
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double x, double y)
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{
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return (x - x2) * (y2 - y1) - (y - y2) * (x2 - x1);
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}
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//--------------------------------------------------------point_in_triangle
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AGG_INLINE bool point_in_triangle(double x1, double y1,
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double x2, double y2,
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double x3, double y3,
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double x, double y)
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{
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bool cp1 = cross_product(x1, y1, x2, y2, x, y) < 0.0;
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bool cp2 = cross_product(x2, y2, x3, y3, x, y) < 0.0;
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bool cp3 = cross_product(x3, y3, x1, y1, x, y) < 0.0;
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return cp1 == cp2 && cp2 == cp3 && cp3 == cp1;
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}
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//-----------------------------------------------------------calc_distance
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AGG_INLINE double calc_distance(double x1, double y1, double x2, double y2)
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{
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double dx = x2-x1;
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double dy = y2-y1;
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return std::sqrt(dx * dx + dy * dy);
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}
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//--------------------------------------------------------calc_sq_distance
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AGG_INLINE double calc_sq_distance(double x1, double y1, double x2, double y2)
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{
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double dx = x2-x1;
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double dy = y2-y1;
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return dx * dx + dy * dy;
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}
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//------------------------------------------------calc_line_point_distance
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AGG_INLINE double calc_line_point_distance(double x1, double y1,
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double x2, double y2,
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double x, double y)
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{
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double dx = x2-x1;
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double dy = y2-y1;
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double d = std::sqrt(dx * dx + dy * dy);
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if(d < vertex_dist_epsilon)
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{
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return calc_distance(x1, y1, x, y);
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}
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return ((x - x2) * dy - (y - y2) * dx) / d;
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}
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//-------------------------------------------------------calc_line_point_u
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AGG_INLINE double calc_segment_point_u(double x1, double y1,
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double x2, double y2,
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double x, double y)
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{
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double dx = x2 - x1;
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double dy = y2 - y1;
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if(dx == 0 && dy == 0)
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{
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return 0;
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}
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double pdx = x - x1;
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double pdy = y - y1;
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return (pdx * dx + pdy * dy) / (dx * dx + dy * dy);
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}
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//---------------------------------------------calc_line_point_sq_distance
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AGG_INLINE double calc_segment_point_sq_distance(double x1, double y1,
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double x2, double y2,
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double x, double y,
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double u)
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{
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if(u <= 0)
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{
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return calc_sq_distance(x, y, x1, y1);
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}
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else
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if(u >= 1)
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{
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return calc_sq_distance(x, y, x2, y2);
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}
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return calc_sq_distance(x, y, x1 + u * (x2 - x1), y1 + u * (y2 - y1));
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}
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//---------------------------------------------calc_line_point_sq_distance
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AGG_INLINE double calc_segment_point_sq_distance(double x1, double y1,
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double x2, double y2,
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double x, double y)
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{
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return
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calc_segment_point_sq_distance(
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x1, y1, x2, y2, x, y,
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calc_segment_point_u(x1, y1, x2, y2, x, y));
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}
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//-------------------------------------------------------calc_intersection
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AGG_INLINE bool calc_intersection(double ax, double ay, double bx, double by,
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double cx, double cy, double dx, double dy,
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double* x, double* y)
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{
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double num = (ay-cy) * (dx-cx) - (ax-cx) * (dy-cy);
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double den = (bx-ax) * (dy-cy) - (by-ay) * (dx-cx);
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if(std::fabs(den) < intersection_epsilon) return false;
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double r = num / den;
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*x = ax + r * (bx-ax);
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*y = ay + r * (by-ay);
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return true;
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}
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//-----------------------------------------------------intersection_exists
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AGG_INLINE bool intersection_exists(double x1, double y1, double x2, double y2,
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double x3, double y3, double x4, double y4)
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{
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// It's less expensive but you can't control the
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// boundary conditions: Less or LessEqual
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double dx1 = x2 - x1;
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double dy1 = y2 - y1;
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double dx2 = x4 - x3;
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double dy2 = y4 - y3;
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return ((x3 - x2) * dy1 - (y3 - y2) * dx1 < 0.0) !=
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((x4 - x2) * dy1 - (y4 - y2) * dx1 < 0.0) &&
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((x1 - x4) * dy2 - (y1 - y4) * dx2 < 0.0) !=
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((x2 - x4) * dy2 - (y2 - y4) * dx2 < 0.0);
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// It's is more expensive but more flexible
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// in terms of boundary conditions.
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//--------------------
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//double den = (x2-x1) * (y4-y3) - (y2-y1) * (x4-x3);
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//if(fabs(den) < intersection_epsilon) return false;
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//double nom1 = (x4-x3) * (y1-y3) - (y4-y3) * (x1-x3);
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//double nom2 = (x2-x1) * (y1-y3) - (y2-y1) * (x1-x3);
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//double ua = nom1 / den;
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//double ub = nom2 / den;
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//return ua >= 0.0 && ua <= 1.0 && ub >= 0.0 && ub <= 1.0;
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}
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//--------------------------------------------------------calc_orthogonal
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AGG_INLINE void calc_orthogonal(double thickness,
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double x1, double y1,
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double x2, double y2,
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double* x, double* y)
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{
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double dx = x2 - x1;
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double dy = y2 - y1;
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double d = std::sqrt(dx*dx + dy*dy);
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*x = thickness * dy / d;
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*y = -thickness * dx / d;
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}
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//--------------------------------------------------------dilate_triangle
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AGG_INLINE void dilate_triangle(double x1, double y1,
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double x2, double y2,
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double x3, double y3,
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double *x, double* y,
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double d)
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{
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double dx1=0.0;
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double dy1=0.0;
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double dx2=0.0;
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double dy2=0.0;
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double dx3=0.0;
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double dy3=0.0;
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double loc = cross_product(x1, y1, x2, y2, x3, y3);
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if(std::fabs(loc) > intersection_epsilon)
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{
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if(cross_product(x1, y1, x2, y2, x3, y3) > 0.0)
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{
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d = -d;
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}
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calc_orthogonal(d, x1, y1, x2, y2, &dx1, &dy1);
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calc_orthogonal(d, x2, y2, x3, y3, &dx2, &dy2);
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calc_orthogonal(d, x3, y3, x1, y1, &dx3, &dy3);
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}
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*x++ = x1 + dx1; *y++ = y1 + dy1;
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*x++ = x2 + dx1; *y++ = y2 + dy1;
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*x++ = x2 + dx2; *y++ = y2 + dy2;
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*x++ = x3 + dx2; *y++ = y3 + dy2;
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*x++ = x3 + dx3; *y++ = y3 + dy3;
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*x++ = x1 + dx3; *y++ = y1 + dy3;
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}
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//------------------------------------------------------calc_triangle_area
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AGG_INLINE double calc_triangle_area(double x1, double y1,
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double x2, double y2,
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double x3, double y3)
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{
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return (x1*y2 - x2*y1 + x2*y3 - x3*y2 + x3*y1 - x1*y3) * 0.5;
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}
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//-------------------------------------------------------calc_polygon_area
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template<class Storage> double calc_polygon_area(const Storage& st)
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{
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unsigned i;
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double sum = 0.0;
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double x = st[0].x;
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double y = st[0].y;
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double xs = x;
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double ys = y;
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for(i = 1; i < st.size(); i++)
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{
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const typename Storage::value_type& v = st[i];
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sum += x * v.y - y * v.x;
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x = v.x;
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y = v.y;
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}
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return (sum + x * ys - y * xs) * 0.5;
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}
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//------------------------------------------------------------------------
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// Tables for fast sqrt
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extern int16u g_sqrt_table[1024];
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extern int8 g_elder_bit_table[256];
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//---------------------------------------------------------------fast_sqrt
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//Fast integer Sqrt - really fast: no cycles, divisions or multiplications
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#if defined(_MSC_VER)
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#pragma warning(push)
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#pragma warning(disable : 4035) //Disable warning "no return value"
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#endif
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AGG_INLINE unsigned fast_sqrt(unsigned val)
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{
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#if defined(_M_IX86) && defined(_MSC_VER) && !defined(AGG_NO_ASM)
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//For Ix86 family processors this assembler code is used.
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//The key command here is bsr - determination the number of the most
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//significant bit of the value. For other processors
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//(and maybe compilers) the pure C "#else" section is used.
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__asm
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{
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mov ebx, val
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mov edx, 11
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bsr ecx, ebx
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sub ecx, 9
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jle less_than_9_bits
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shr ecx, 1
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adc ecx, 0
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sub edx, ecx
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shl ecx, 1
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shr ebx, cl
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less_than_9_bits:
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xor eax, eax
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mov ax, g_sqrt_table[ebx*2]
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mov ecx, edx
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shr eax, cl
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}
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#else
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//This code is actually pure C and portable to most
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//arcitectures including 64bit ones.
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unsigned t = val;
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int bit=0;
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unsigned shift = 11;
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//The following piece of code is just an emulation of the
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//Ix86 assembler command "bsr" (see above). However on old
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//Intels (like Intel MMX 233MHz) this code is about twice
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//faster (sic!) then just one "bsr". On PIII and PIV the
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//bsr is optimized quite well.
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bit = t >> 24;
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if(bit)
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{
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bit = g_elder_bit_table[bit] + 24;
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}
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else
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{
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bit = (t >> 16) & 0xFF;
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if(bit)
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{
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bit = g_elder_bit_table[bit] + 16;
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}
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else
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{
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bit = (t >> 8) & 0xFF;
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if(bit)
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{
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bit = g_elder_bit_table[bit] + 8;
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}
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else
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{
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bit = g_elder_bit_table[t];
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}
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}
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}
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//This code calculates the sqrt.
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bit -= 9;
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if(bit > 0)
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{
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bit = (bit >> 1) + (bit & 1);
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shift -= bit;
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val >>= (bit << 1);
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}
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return g_sqrt_table[val] >> shift;
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#endif
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}
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#if defined(_MSC_VER)
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#pragma warning(pop)
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#endif
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//--------------------------------------------------------------------besj
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// Function BESJ calculates Bessel function of first kind of order n
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// Arguments:
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// n - an integer (>=0), the order
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// x - value at which the Bessel function is required
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//--------------------
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// C++ Mathematical Library
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// Convereted from equivalent FORTRAN library
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// Converetd by Gareth Walker for use by course 392 computational project
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// All functions tested and yield the same results as the corresponding
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// FORTRAN versions.
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//
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// If you have any problems using these functions please report them to
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// M.Muldoon@UMIST.ac.uk
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//
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// Documentation available on the web
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// http://www.ma.umist.ac.uk/mrm/Teaching/392/libs/392.html
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// Version 1.0 8/98
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// 29 October, 1999
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//--------------------
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// Adapted for use in AGG library by Andy Wilk (castor.vulgaris@gmail.com)
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//------------------------------------------------------------------------
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inline double besj(double x, int n)
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{
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if(n < 0)
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{
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return 0;
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}
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double d = 1E-6;
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double b = 0;
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if(std::fabs(x) <= d)
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{
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if(n != 0) return 0;
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return 1;
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}
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double b1 = 0; // b1 is the value from the previous iteration
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// Set up a starting order for recurrence
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int m1 = (int)std::fabs(x) + 6;
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if(std::fabs(x) > 5)
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{
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m1 = (int)(std::fabs(1.4 * x + 60 / x));
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}
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int m2 = (int)(n + 2 + std::fabs(x) / 4);
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if (m1 > m2)
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{
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m2 = m1;
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}
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// Apply recurrence down from curent max order
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for(;;)
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{
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double c3 = 0;
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double c2 = 1E-30;
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double c4 = 0;
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int m8 = 1;
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if (m2 / 2 * 2 == m2)
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{
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m8 = -1;
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}
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int imax = m2 - 2;
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for (int i = 1; i <= imax; i++)
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{
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double c6 = 2 * (m2 - i) * c2 / x - c3;
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c3 = c2;
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c2 = c6;
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if(m2 - i - 1 == n)
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{
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b = c6;
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}
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m8 = -1 * m8;
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if (m8 > 0)
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{
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c4 = c4 + 2 * c6;
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}
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}
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double c6 = 2 * c2 / x - c3;
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if(n == 0)
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{
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b = c6;
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}
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c4 += c6;
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b /= c4;
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if(std::fabs(b - b1) < d)
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{
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return b;
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}
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b1 = b;
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m2 += 3;
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}
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}
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}
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#endif
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