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diff --git a/kig/objects/cubic_imp.cc b/kig/objects/cubic_imp.cc
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-// Copyright (C) 2003 Dominique Devriese <devriese@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.
-
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-// GNU General Public License for more details.
-
-// You should have received a copy of the GNU General Public License
-// along with this program; if not, write to the Free Software
-// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
-// 02110-1301, USA.
-
-#include "cubic_imp.h"
-
-#include "bogus_imp.h"
-
-#include "../misc/kigpainter.h"
-#include "../misc/screeninfo.h"
-#include "../misc/kignumerics.h"
-#include "../misc/common.h"
-#include "../kig/kig_view.h"
-
-#include <math.h>
-#include <tdelocale.h>
-
-CubicImp::CubicImp( const CubicCartesianData& data )
- : CurveImp(), mdata( data )
-{
-}
-
-CubicImp::~CubicImp()
-{
-}
-
-ObjectImp* CubicImp::transform( const Transformation& t ) const
-{
- bool valid = true;
- CubicCartesianData d = calcCubicTransformation( data(), t, valid );
- if ( valid ) return new CubicImp( d );
- else return new InvalidImp;
-}
-
-void CubicImp::draw( KigPainter& p ) const
-{
- p.drawCurve( this );
-}
-
-bool CubicImp::contains( const Coordinate& o, int width, const KigWidget& w ) const
-{
- return internalContainsPoint( o, w.screenInfo().normalMiss( width ) );
-}
-
-bool CubicImp::inRect( const Rect&, int, const KigWidget& ) const
-{
- // TODO ?
- return false;
-}
-
-CubicImp* CubicImp::copy() const
-{
- return new CubicImp( mdata );
-}
-
-double CubicImp::getParam( const Coordinate& p, const KigDocument& ) const
-{
- double x = p.x;
- double y = p.y;
- double t;
-
- double a000 = mdata.coeffs[0];
- double a001 = mdata.coeffs[1];
- double a002 = mdata.coeffs[2];
- double a011 = mdata.coeffs[3];
- double a012 = mdata.coeffs[4];
- double a022 = mdata.coeffs[5];
- double a111 = mdata.coeffs[6];
- double a112 = mdata.coeffs[7];
- double a122 = mdata.coeffs[8];
- double a222 = mdata.coeffs[9];
-
- /*
- * first project p onto the cubic. This is done by computing the
- * line through p in the direction of the gradient
- */
-
- double f = a000 + a001*x + a002*y + a011*x*x + a012*x*y + a022*y*y +
- a111*x*x*x + a112*x*x*y + a122*x*y*y + a222*y*y*y;
- if ( f != 0 )
- {
- double fx = a001 + 2*a011*x + a012*y + 3*a111*x*x + 2*a112*x*y + a122*y*y;
- double fy = a002 + 2*a022*y + a012*x + 3*a222*y*y + 2*a122*x*y + a112*x*x;
- Coordinate v = Coordinate (fx, fy);
- if ( f < 0 ) v = -v; // the line points away from the intersection
- double a, b, c, d;
- calcCubicLineRestriction ( mdata, p, v, a, b, c, d );
- if ( a < 0 )
- {
- a *= -1;
- b *= -1;
- c *= -1;
- d *= -1;
- }
-
- // computing the coefficients of the Sturm sequence
- double p1a = 2*b*b - 6*a*c;
- double p1b = b*c - 9*a*d;
- double p0a = c*p1a*p1a + p1b*(3*a*p1b - 2*b*p1a);
- // compute the number of roots for negative lambda
- int variations = calcCubicVariations ( 0, a, b, c, d, p1a, p1b, p0a );
- bool valid;
- int numroots;
- double lambda = calcCubicRoot ( -1e10, 1e10, a, b, c, d, variations, valid,
- numroots );
- if ( valid )
- {
- Coordinate pnew = p + lambda*v;
- x = pnew.x;
- y = pnew.y;
- }
- }
-
- if (x > 0) t = x/(1+x);
- else t = x/(1-x);
- t = 0.5*(t + 1);
- t /= 3;
-
- Coordinate p1 = getPoint ( t );
- Coordinate p2 = getPoint ( t + 1.0/3.0 );
- Coordinate p3 = getPoint ( t + 2.0/3.0 );
-
- double mint = t;
- double mindist = p1.valid() ? fabs ( y - p1.y ) : double_inf;
- if ( p2.valid() && fabs ( y - p2.y ) < mindist )
- {
- mint = t + 1.0/3.0;
- mindist = fabs ( y - p2.y );
- }
- if ( p3.valid() && fabs ( y - p3.y ) < mindist )
- {
- mint = t + 2.0/3.0;
- }
-
- return mint;
-}
-
-const Coordinate CubicImp::getPoint( double p, const KigDocument& ) const
-{
- return getPoint( p );
-}
-
-const Coordinate CubicImp::getPoint( double p ) const
-{
- /*
- * this isn't really elegant...
- * the magnitude of p tells which one of the maximum 3 intersections
- * of the vertical line with the cubic to take.
- */
-
- p *= 3;
- int root = (int) p;
- assert ( root >= 0 );
- assert ( root <= 3 );
- if ( root == 3 ) root = 2;
-
- p -= root;
-
- assert ( 0 <= p && p <= 1 );
- if ( p <= 0. ) p = 1e-6;
- if ( p >= 1. ) p = 1 - 1e-6;
- root++;
- p = 2*p - 1;
- double x;
- if (p > 0) x = p/(1 - p);
- else x = p/(1 + p);
-
- // calc the third degree polynomial:
- // compute the third degree polinomial:
-// double a000 = mdata.coeffs[0];
-// double a001 = mdata.coeffs[1];
-// double a002 = mdata.coeffs[2];
-// double a011 = mdata.coeffs[3];
-// double a012 = mdata.coeffs[4];
-// double a022 = mdata.coeffs[5];
-// double a111 = mdata.coeffs[6];
-// double a112 = mdata.coeffs[7];
-// double a122 = mdata.coeffs[8];
-// double a222 = mdata.coeffs[9];
-//
-// // first the y^3 coefficient, it coming only from a222:
-// double a = a222;
-// // next the y^2 coefficient (from a122 and a022):
-// double b = a122*x + a022;
-// // next the y coefficient (from a112, a012 and a002):
-// double c = a112*x*x + a012*x + a002;
-// // finally the constant coefficient (from a111, a011, a001 and a000):
-// double d = a111*x*x*x + a011*x*x + a001*x + a000;
-
-// commented out, since the bound is already computed when passing a huge
-// interval; the normalization is not needed also
-
- // renormalize: positive a
-// if ( a < 0 )
-// {
-// a *= -1;
-// b *= -1;
-// c *= -1;
-// d *= -1;
-// }
-//
-// const double small = 1e-7;
-// int degree = 3;
-// if ( fabs(a) < small*fabs(b) ||
-// fabs(a) < small*fabs(c) ||
-// fabs(a) < small*fabs(d) )
-// {
-// degree = 2;
-// if ( fabs(b) < small*fabs(c) ||
-// fabs(b) < small*fabs(d) )
-// {
-// degree = 1;
-// }
-// }
-
-// and a bound for all the real roots:
-
-// double bound;
-// switch (degree)
-// {
-// case 3:
-// bound = fabs(d/a);
-// if ( fabs(c/a) + 1 > bound ) bound = fabs(c/a) + 1;
-// if ( fabs(b/a) + 1 > bound ) bound = fabs(b/a) + 1;
-// break;
-//
-// case 2:
-// bound = fabs(d/b);
-// if ( fabs(c/b) + 1 > bound ) bound = fabs(c/b) + 1;
-// break;
-//
-// case 1:
-// default:
-// bound = fabs(d/c) + 1;
-// break;
-// }
-
- int numroots;
- bool valid = true;
- double y = calcCubicYvalue ( x, -double_inf, double_inf, root, mdata, valid,
- numroots );
- if ( ! valid ) return Coordinate::invalidCoord();
- else return Coordinate(x,y);
-// if ( valid ) return Coordinate(x,y);
-// root--; if ( root <= 0) root += 3;
-// y = calcCubicYvalue ( x, -bound, bound, root, mdata, valid,
-// numroots );
-// if ( valid ) return Coordinate(x,y);
-// root--; if ( root <= 0) root += 3;
-// y = calcCubicYvalue ( x, -bound, bound, root, mdata, valid,
-// numroots );
-// assert ( valid );
-// return Coordinate(x,y);
-}
-
-const uint CubicImp::numberOfProperties() const
-{
- return Parent::numberOfProperties() + 1;
-}
-
-const QCStringList CubicImp::propertiesInternalNames() const
-{
- QCStringList l = Parent::propertiesInternalNames();
- l << "cartesian-equation";
- assert( l.size() == CubicImp::numberOfProperties() );
- return l;
-
-}
-
-/*
- * cartesian equation property contributed by Carlo Sardi
- */
-
-const QCStringList CubicImp::properties() const
-{
- QCStringList l = Parent::properties();
- l << I18N_NOOP( "Cartesian Equation" );
- assert( l.size() == CubicImp::numberOfProperties() );
- return l;
-
-}
-
-const ObjectImpType* CubicImp::impRequirementForProperty( uint which ) const
-{
- if ( which < Parent::numberOfProperties() )
- return Parent::impRequirementForProperty( which );
- else return CubicImp::stype();
-}
-
-const char* CubicImp::iconForProperty( uint which ) const
-{
- int pnum = 0;
- if ( which < Parent::numberOfProperties() )
- return Parent::iconForProperty( which );
- if ( which == Parent::numberOfProperties() + pnum++ )
- return "kig_text"; // cartesian equation string
- else
- assert( false );
- return "";
-}
-
-ObjectImp* CubicImp::property( uint which, const KigDocument& w ) const
-{
- int pnum = 0;
-
- if ( which < Parent::numberOfProperties() )
- return Parent::property( which, w );
- if ( which == Parent::numberOfProperties() + pnum++ )
- return new StringImp( cartesianEquationString( w ) );
- else
- assert( false );
- return new InvalidImp;
-}
-
-const CubicCartesianData CubicImp::data() const
-{
- return mdata;
-}
-
-void CubicImp::visit( ObjectImpVisitor* vtor ) const
-{
- vtor->visit( this );
-}
-
-bool CubicImp::equals( const ObjectImp& rhs ) const
-{
- return rhs.inherits( CubicImp::stype() ) &&
- static_cast<const CubicImp&>( rhs ).data() == data();
-}
-
-const ObjectImpType* CubicImp::type() const
-{
- return CubicImp::stype();
-}
-
-const ObjectImpType* CubicImp::stype()
-{
- static const ObjectImpType t(
- Parent::stype(), "cubic",
- I18N_NOOP( "cubic curve" ),
- I18N_NOOP( "Select this cubic curve" ),
- I18N_NOOP( "Select cubic curve %1" ),
- I18N_NOOP( "Remove a Cubic Curve" ),
- I18N_NOOP( "Add a Cubic Curve" ),
- I18N_NOOP( "Move a Cubic Curve" ),
- I18N_NOOP( "Attach to this cubic curve" ),
- I18N_NOOP( "Show a Cubic Curve" ),
- I18N_NOOP( "Hide a Cubic Curve" )
- );
- return &t;
-}
-
-bool CubicImp::containsPoint( const Coordinate& p, const KigDocument& ) const
-{
- return internalContainsPoint( p, test_threshold );
-}
-
-bool CubicImp::internalContainsPoint( const Coordinate& p, double threshold ) const
-{
- double a000 = mdata.coeffs[0];
- double a001 = mdata.coeffs[1];
- double a002 = mdata.coeffs[2];
- double a011 = mdata.coeffs[3];
- double a012 = mdata.coeffs[4];
- double a022 = mdata.coeffs[5];
- double a111 = mdata.coeffs[6];
- double a112 = mdata.coeffs[7];
- double a122 = mdata.coeffs[8];
- double a222 = mdata.coeffs[9];
-
- double x = p.x;
- double y = p.y;
-
- double f = a000 + a001*x + a002*y + a011*x*x + a012*x*y + a022*y*y +
- a111*x*x*x + a112*x*x*y + a122*x*y*y + a222*y*y*y;
- double fx = a001 + 2*a011*x + a012*y + 3*a111*x*x + 2*a112*x*y + a122*y*y;
- double fy = a002 + a012*x + 2*a022*y + a112*x*x + 2*a122*x*y + 3*a222*y*y;
-
- double dist = fabs(f)/(fabs(fx) + fabs(fy));
-
- return dist <= threshold;
-}
-
-bool CubicImp::isPropertyDefinedOnOrThroughThisImp( uint which ) const
-{
- return Parent::isPropertyDefinedOnOrThroughThisImp( which );
-}
-
-Rect CubicImp::surroundingRect() const
-{
- // it's probably possible to calculate this if it exists, but for
- // now we don't.
- return Rect::invalidRect();
-}
-
-TQString CubicImp::cartesianEquationString( const KigDocument& ) const
-{
- /*
- * unfortunately TQStrings.arg method is limited to %1, %9, so we cannot
- * treat all 10 arguments! Let's split the equation in two parts...
- * Now this ends up also in the translation machinery, is this really
- * necessary? Otherwise we could do a little bit of tidy up on the
- * the equation (removal of zeros, avoid " ... + -1234 x ", etc.)
- */
-
- TQString ret = i18n( "%6 x³ + %9 y³ + %7 x²y + %8 xy² + %5 y² + %3 x² + %4 xy + %1 x + %2 y" );
- ret = ret.arg( mdata.coeffs[1], 0, 'g', 3 );
- ret = ret.arg( mdata.coeffs[2], 0, 'g', 3 );
- ret = ret.arg( mdata.coeffs[3], 0, 'g', 3 );
- ret = ret.arg( mdata.coeffs[4], 0, 'g', 3 );
- ret = ret.arg( mdata.coeffs[5], 0, 'g', 3 );
- ret = ret.arg( mdata.coeffs[6], 0, 'g', 3 );
- ret = ret.arg( mdata.coeffs[7], 0, 'g', 3 );
- ret = ret.arg( mdata.coeffs[8], 0, 'g', 3 );
- ret = ret.arg( mdata.coeffs[9], 0, 'g', 3 );
-
- ret.append( i18n( " + %1 = 0" ) );
- ret = ret.arg( mdata.coeffs[0], 0, 'g', 3 );
-
- // we should find a common place to do this...
- ret.replace( "+ -", "- " );
- ret.replace( "+-", "-" );
- return ret;
-}
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