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tdeedu/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 <klocale.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.tqarg( mdata.coeffs[1], 0, 'g', 3 );
ret = ret.tqarg( mdata.coeffs[2], 0, 'g', 3 );
ret = ret.tqarg( mdata.coeffs[3], 0, 'g', 3 );
ret = ret.tqarg( mdata.coeffs[4], 0, 'g', 3 );
ret = ret.tqarg( mdata.coeffs[5], 0, 'g', 3 );
ret = ret.tqarg( mdata.coeffs[6], 0, 'g', 3 );
ret = ret.tqarg( mdata.coeffs[7], 0, 'g', 3 );
ret = ret.tqarg( mdata.coeffs[8], 0, 'g', 3 );
ret = ret.tqarg( mdata.coeffs[9], 0, 'g', 3 );
ret.append( i18n( " + %1 = 0" ) );
ret = ret.tqarg( mdata.coeffs[0], 0, 'g', 3 );
// we should find a common place to do this...
ret.replace( "+ -", "- " );
ret.replace( "+-", "-" );
return ret;
}