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