//-*-C++-*- /* ************************************************************************** description -------------------- copyright : (C) 2002 by Andreas Zehender email : zehender@kde.org ************************************************************************** ************************************************************************** * * * This program is free software; you can redistribute it and/or modify * * it under the terms of the GNU General Public License as published by * * the Free Software Foundation; either version 2 of the License, or * * (at your option) any later version. * * * **************************************************************************/ #include "pmsorsegment.h" #include "pmmath.h" #include "pmmatrix.h" #include "pmdebug.h" #include PMVector PMSorSegment::point( double t ) const { t = m_t + t * m_s; double r2 = t * ( t * ( t * m_a + m_b ) + m_c ) + m_d; if( r2 < 0.0 ) r2 = 0.0; return PMVector( sqrt( r2 ), t ); } void PMSorSegment::calculateSor( const PMVector& p0, const PMVector& p1, const PMVector& p2, const PMVector& p3 ) { double b[4], h; PMMatrix m; m_t = p1[1]; m_s = p2[1] - p1[1]; if( approxZero( p2[1] - p0[1] ) || approxZero( p3[1] - p1[1] ) ) { kdError( PMArea ) << "Incorrect points in PMSorSegment::calculateSor\n"; m_a = m_b = m_c = m_d = 0.0; return; } // interpolate the points // see povray documentation b[0] = p1[0] * p1[0]; b[1] = p2[0] * p2[0]; b[2] = 2.0 * p1[0] * ( p2[0] - p0[0] ) / ( p2[1] - p0[1] ); b[3] = 2.0 * p2[0] * ( p3[0] - p1[0] ) / ( p3[1] - p1[1] ); h = p1[1]; m[0][0] = h * h * h; m[0][1] = h * h; m[0][2] = h; m[0][3] = 1.0; m[2][0] = 3.0 * h * h; m[2][1] = 2.0 * h; m[2][2] = 1.0; m[2][3] = 0.0; h = p2[1]; m[1][0] = h * h * h; m[1][1] = h * h; m[1][2] = h; m[1][3] = 1.0; m[3][0] = 3.0 * h * h; m[3][1] = 2.0 * h; m[3][2] = 1.0; m[3][3] = 0.0; // Calculate the coefficients // x = M^-1 * b; m = m.inverse( ); m_a = b[0] * m[0][0] + b[1] * m[0][1] + b[2] * m[0][2] + b[3] * m[0][3]; m_b = b[0] * m[1][0] + b[1] * m[1][1] + b[2] * m[1][2] + b[3] * m[1][3]; m_c = b[0] * m[2][0] + b[1] * m[2][1] + b[2] * m[2][2] + b[3] * m[2][3]; m_d = b[0] * m[3][0] + b[1] * m[3][1] + b[2] * m[3][2] + b[3] * m[3][3]; if( approxZero( m_a ) ) m_a = 0.0; if( approxZero( m_b ) ) m_b = 0.0; if( approxZero( m_c ) ) m_c = 0.0; if( approxZero( m_d ) ) m_d = 0.0; }