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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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