412 lines
13 KiB
C++
412 lines
13 KiB
C++
/************************************/
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/* routines to handle bezier curves */
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/************************************/
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#include "fctsys.h"
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#include "bezier_curves.h"
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#define add_segment(segment) if(s_bezier_Points_Buffer[s_bezier_Points_Buffer.size()-1] != segment) s_bezier_Points_Buffer.push_back(segment);
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// Local variables:
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static std::vector<wxPoint> s_bezier_Points_Buffer;
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static int bezier_recursion_limit = 12;
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static double bezier_approximation_scale = 0.5; // 1
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static double bezier_curve_collinearity_epsilon = 1e-30;
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static double bezier_curve_angle_tolerance_epsilon = 0.0001;
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static double bezier_distance_tolerance_square; // derived by approximation_scale
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static double bezier_angle_tolerance = 0.0;
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static double bezier_cusp_limit = 0.0;
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// Local functions:
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static void recursive_bezier( int x1, int y1, int x2, int y2, int x3, int y3, int level );
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static void recursive_bezier( int x1,
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int y1,
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int x2,
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int y2,
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int x3,
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int y3,
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int x4,
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int y4,
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int level );
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/***********************************************************************************/
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std::vector<wxPoint> Bezier2Poly( wxPoint c1, wxPoint c2, wxPoint c3, wxPoint c4 )
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{
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return Bezier2Poly( c1.x, c1.y, c2.x, c2.y, c3.x, c3.y, c4.x, c4.y );
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}
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std::vector<wxPoint> Bezier2Poly( wxPoint c1, wxPoint c2, wxPoint c3 )
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{
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return Bezier2Poly( c1.x, c1.y, c2.x, c2.y, c3.x, c3.y );
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}
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inline double calc_sq_distance( int x1, int y1, int x2, int y2 )
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{
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int dx = x2 - x1;
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int dy = y2 - y1;
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return (double)dx * dx + (double)dy * dy;
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}
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inline double sqrt_len( int dx, int dy )
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{
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return ((double)dx * dx) + ((double)dy * dy);
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}
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std::vector<wxPoint> Bezier2Poly( int x1, int y1, int x2, int y2, int x3, int y3 )
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{
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s_bezier_Points_Buffer.clear();
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bezier_distance_tolerance_square = 0.5 / bezier_approximation_scale;
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bezier_distance_tolerance_square *= bezier_distance_tolerance_square;
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s_bezier_Points_Buffer.push_back( wxPoint( x1, y1 ) );
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recursive_bezier( x1, y1, x2, y2, x3, y3, 0 );
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s_bezier_Points_Buffer.push_back( wxPoint( x3, y3 ) );
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wxLogDebug( wxT( "Bezier Conversion - End (%d vertex)" ), s_bezier_Points_Buffer.size() );
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return s_bezier_Points_Buffer;
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}
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std::vector<wxPoint> Bezier2Poly( int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4 )
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{
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s_bezier_Points_Buffer.clear();
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bezier_distance_tolerance_square = 0.5 / bezier_approximation_scale;
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bezier_distance_tolerance_square *= bezier_distance_tolerance_square;
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s_bezier_Points_Buffer.push_back( wxPoint( x1, y1 ) );
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recursive_bezier( x1, y1, x2, y2, x3, y3, x4, y4, 0 );
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s_bezier_Points_Buffer.push_back( wxPoint( x4, y4 ) );
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wxLogDebug( wxT( "Bezier Conversion - End (%d vertex)" ), s_bezier_Points_Buffer.size() );
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return s_bezier_Points_Buffer;
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}
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void recursive_bezier( int x1, int y1, int x2, int y2, int x3, int y3, int level )
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{
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if( abs( level ) > bezier_recursion_limit )
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{
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return;
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}
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// Calculate all the mid-points of the line segments
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//----------------------
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int x12 = (x1 + x2) / 2;
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int y12 = (y1 + y2) / 2;
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int x23 = (x2 + x3) / 2;
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int y23 = (y2 + y3) / 2;
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int x123 = (x12 + x23) / 2;
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int y123 = (y12 + y23) / 2;
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int dx = x3 - x1;
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int dy = y3 - y1;
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double d = fabs( ((double) (x2 - x3) * dy) - ((double) (y2 - y3) * dx ) );
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double da;
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if( d > bezier_curve_collinearity_epsilon )
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{
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// Regular case
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//-----------------
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if( d * d <= bezier_distance_tolerance_square * (dx * dx + dy * dy) )
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{
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// If the curvature doesn't exceed the distance_tolerance value
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// we tend to finish subdivisions.
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//----------------------
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if( bezier_angle_tolerance < bezier_curve_angle_tolerance_epsilon )
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{
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add_segment( wxPoint( x123, y123 ) );
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return;
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}
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// Angle & Cusp Condition
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//----------------------
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da = fabs( atan2( (double) ( y3 - y2 ), (double) ( x3 - x2 ) ) -
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atan2( (double) ( y2 - y1 ), (double) ( x2 - x1 ) ) );
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if( da >=M_PI )
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da = 2 * M_PI - da;
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if( da < bezier_angle_tolerance )
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{
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// Finally we can stop the recursion
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//----------------------
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add_segment( wxPoint( x123, y123 ) );
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return;
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}
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}
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}
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else
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{
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// Collinear case
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//------------------
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da = sqrt_len(dx, dy);
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if( da == 0 )
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{
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d = calc_sq_distance( x1, y1, x2, y2 );
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}
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else
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{
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d = ( (double)(x2 - x1) * dx + (double)(y2 - y1) * dy ) / da;
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if( d > 0 && d < 1 )
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{
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// Simple collinear case, 1---2---3
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// We can leave just two endpoints
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return;
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}
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if( d <= 0 )
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d = calc_sq_distance( x2, y2, x1, y1 );
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else if( d >= 1 )
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d = calc_sq_distance( x2, y2, x3, y3 );
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else
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d = calc_sq_distance( x2, y2, x1 + (int) d * dx,
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y1 + (int) d * dy );
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}
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if( d < bezier_distance_tolerance_square )
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{
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add_segment( wxPoint( x2, y2 ) );
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return;
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}
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}
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// Continue subdivision
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//----------------------
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recursive_bezier( x1, y1, x12, y12, x123, y123, level + 1 );
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recursive_bezier( x123, y123, x23, y23, x3, y3, -(level + 1) );
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}
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void recursive_bezier( int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4, int level )
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{
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if( abs( level ) > bezier_recursion_limit )
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{
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return;
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}
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// Calculate all the mid-points of the line segments
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//----------------------
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int x12 = (x1 + x2) / 2;
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int y12 = (y1 + y2) / 2;
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int x23 = (x2 + x3) / 2;
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int y23 = (y2 + y3) / 2;
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int x34 = (x3 + x4) / 2;
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int y34 = (y3 + y4) / 2;
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int x123 = (x12 + x23) / 2;
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int y123 = (y12 + y23) / 2;
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int x234 = (x23 + x34) / 2;
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int y234 = (y23 + y34) / 2;
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int x1234 = (x123 + x234) / 2;
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int y1234 = (y123 + y234) / 2;
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// Try to approximate the full cubic curve by a single straight line
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//------------------
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int dx = x4 - x1;
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int dy = y4 - y1;
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double d2 = fabs( (double) ( (x2 - x4) * dy - (y2 - y4) * dx ) );
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double d3 = fabs( (double) ( (x3 - x4) * dy - (y3 - y4) * dx ) );
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double da1, da2, k;
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switch( (int(d2 > bezier_curve_collinearity_epsilon) << 1) +
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int(d3 > bezier_curve_collinearity_epsilon) )
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{
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case 0:
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// All collinear OR p1==p4
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//----------------------
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k = dx * dx + dy * dy;
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if( k == 0 )
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{
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d2 = calc_sq_distance( x1, y1, x2, y2 );
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d3 = calc_sq_distance( x4, y4, x3, y3 );
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}
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else
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{
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k = 1 / k;
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da1 = x2 - x1;
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da2 = y2 - y1;
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d2 = k * (da1 * dx + da2 * dy);
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da1 = x3 - x1;
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da2 = y3 - y1;
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d3 = k * (da1 * dx + da2 * dy);
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if( d2 > 0 && d2 < 1 && d3 > 0 && d3 < 1 )
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{
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// Simple collinear case, 1---2---3---4
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// We can leave just two endpoints
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return;
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}
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if( d2 <= 0 )
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d2 = calc_sq_distance( x2, y2, x1, y1 );
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else if( d2 >= 1 )
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d2 = calc_sq_distance( x2, y2, x4, y4 );
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else
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d2 = calc_sq_distance( x2, y2, x1 + (int) d2 * dx,
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y1 + (int) d2 * dy );
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if( d3 <= 0 )
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d3 = calc_sq_distance( x3, y3, x1, y1 );
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else if( d3 >= 1 )
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d3 = calc_sq_distance( x3, y3, x4, y4 );
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else
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d3 = calc_sq_distance( x3, y3, x1 + (int) d3 * dx,
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y1 + (int) d3 * dy );
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}
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if( d2 > d3 )
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{
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if( d2 < bezier_distance_tolerance_square )
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{
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add_segment( wxPoint( x2, y2 ) );
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return;
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}
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}
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else
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{
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if( d3 < bezier_distance_tolerance_square )
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{
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add_segment( wxPoint( x3, y3 ) );
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return;
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}
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}
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break;
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case 1:
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// p1,p2,p4 are collinear, p3 is significant
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//----------------------
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if( d3 * d3 <= bezier_distance_tolerance_square * sqrt_len(dx, dy) )
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{
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if( bezier_angle_tolerance < bezier_curve_angle_tolerance_epsilon )
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{
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add_segment( wxPoint( x23, y23 ) );
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return;
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}
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// Angle Condition
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//----------------------
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da1 = fabs( atan2( (double) ( y4 - y3 ), (double) ( x4 - x3 ) ) -
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atan2( (double) ( y3 - y2 ), (double) ( x3 - x2 ) ) );
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if( da1 >= M_PI )
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da1 = 2 * M_PI - da1;
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if( da1 < bezier_angle_tolerance )
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{
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add_segment( wxPoint( x2, y2 ) );
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add_segment( wxPoint( x3, y3 ) );
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return;
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}
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if( bezier_cusp_limit != 0.0 )
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{
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if( da1 > bezier_cusp_limit )
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{
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add_segment( wxPoint( x3, y3 ) );
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return;
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}
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}
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}
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break;
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case 2:
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// p1,p3,p4 are collinear, p2 is significant
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//----------------------
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if( d2 * d2 <= bezier_distance_tolerance_square * sqrt_len(dx, dy) )
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{
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if( bezier_angle_tolerance < bezier_curve_angle_tolerance_epsilon )
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{
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add_segment( wxPoint( x23, y23 ) );
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return;
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}
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// Angle Condition
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//----------------------
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da1 = fabs( atan2( (double) ( y3 - y2 ), (double) ( x3 - x2 ) ) -
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atan2( (double) ( y2 - y1 ), (double) ( x2 - x1 ) ) );
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if( da1 >= M_PI )
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da1 = 2 * M_PI - da1;
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if( da1 < bezier_angle_tolerance )
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{
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add_segment( wxPoint( x2, y2 ) );
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add_segment( wxPoint( x3, y3 ) );
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return;
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}
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if( bezier_cusp_limit != 0.0 )
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{
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if( da1 > bezier_cusp_limit )
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{
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add_segment( wxPoint( x2, y2 ) );
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return;
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}
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}
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}
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break;
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case 3:
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// Regular case
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//-----------------
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if( (d2 + d3) * (d2 + d3) <= bezier_distance_tolerance_square * sqrt_len(dx, dy) )
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{
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// If the curvature doesn't exceed the distance_tolerance value
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// we tend to finish subdivisions.
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//----------------------
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if( bezier_angle_tolerance < bezier_curve_angle_tolerance_epsilon )
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{
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add_segment( wxPoint( x23, y23 ) );
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return;
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}
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// Angle & Cusp Condition
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//----------------------
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k = atan2( (double) ( y3 - y2 ), (double) ( x3 - x2 ) );
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da1 = fabs( k - atan2( (double) ( y2 - y1 ),
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(double) ( x2 - x1 ) ) );
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da2 = fabs( atan2( (double) ( y4 - y3 ),
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(double) ( x4 - x3 ) ) - k );
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if( da1 >= M_PI )
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da1 = 2 * M_PI - da1;
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if( da2 >= M_PI )
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da2 = 2 * M_PI - da2;
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if( da1 + da2 < bezier_angle_tolerance )
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{
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// Finally we can stop the recursion
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//----------------------
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add_segment( wxPoint( x23, y23 ) );
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return;
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}
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if( bezier_cusp_limit != 0.0 )
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{
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if( da1 > bezier_cusp_limit )
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{
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add_segment( wxPoint( x2, y2 ) );
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return;
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}
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if( da2 > bezier_cusp_limit )
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{
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add_segment( wxPoint( x3, y3 ) );
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return;
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}
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}
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}
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break;
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}
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// Continue subdivision
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//----------------------
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recursive_bezier( x1, y1, x12, y12, x123, y123, x1234, y1234, level + 1 );
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recursive_bezier( x1234, y1234, x234, y234, x34, y34, x4, y4, level + 1 );
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}
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