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+/* This file is part of the KDE project
+ Copyright (C) 2001, 2002, 2003 The Karbon Developers
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public
+ License as published by the Free Software Foundation; either
+ version 2 of the License, or (at your option) any later version.
+
+ This library 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public License
+ along with this library; see the file COPYING.LIB. If not, write to
+ the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+ * Boston, MA 02110-1301, USA.
+*/
+
+#include <math.h>
+
+#include <tqdom.h>
+
+#include "vpainter.h"
+#include "vpath.h"
+#include "vsegment.h"
+
+#include <kdebug.h>
+
+VSegment::VSegment( unsigned short deg )
+{
+ m_degree = deg;
+
+ m_nodes = new VNodeData[ degree() ];
+
+ for( unsigned short i = 0; i < degree(); ++i )
+ selectPoint( i );
+
+ m_state = normal;
+
+ m_prev = 0L;
+ m_next = 0L;
+}
+
+VSegment::VSegment( const VSegment& segment )
+{
+ m_degree = segment.degree();
+
+ m_nodes = new VNodeData[ degree() ];
+
+ m_state = segment.m_state;
+
+ // Copying the pointers m_prev/m_next has some advantages (see VSegment::length()).
+ // Inserting a segment into a path overwrites these anyway.
+ m_prev = segment.m_prev;
+ m_next = segment.m_next;
+
+ // Copy points.
+ for( unsigned short i = 0; i < degree(); i++ )
+ {
+ setPoint( i, segment.point( i ) );
+ selectPoint( i, segment.pointIsSelected( i ) );
+ }
+}
+
+VSegment::~VSegment()
+{
+ delete[]( m_nodes );
+}
+
+void
+VSegment::setDegree( unsigned short deg )
+{
+ // Do nothing if old and new degrees are identical.
+ if( degree() == deg )
+ return;
+
+ // TODO : this code is fishy, please make it sane
+
+ // Remember old nodes.
+ VNodeData* oldNodes = m_nodes;
+ KoPoint oldKnot = knot();
+
+ // Allocate new node data.
+ m_nodes = new VNodeData[ deg ];
+
+ if( deg == 1 )
+ m_nodes[ 0 ].m_vector = oldKnot;
+ else
+ {
+ // Copy old node data (from the knot "backwards".
+ unsigned short offset = kMax( 0, deg - m_degree );
+
+ for( unsigned short i = offset; i < deg; ++i )
+ {
+ m_nodes[ i ].m_vector = oldNodes[ i - offset ].m_vector;
+ }
+
+ // Fill with "zeros" if necessary.
+ for( unsigned short i = 0; i < offset; ++i )
+ {
+ m_nodes[ i ].m_vector = KoPoint( 0.0, 0.0 );
+ }
+ }
+
+ // Set new degree.
+ m_degree = deg;
+
+ // Delete old nodes.
+ delete[]( oldNodes );
+}
+
+void
+VSegment::draw( VPainter* painter ) const
+{
+ // Don't draw a deleted segment.
+ if( state() == deleted )
+ return;
+
+
+ if( prev() )
+ {
+ if( degree() == 3 )
+ {
+ painter->curveTo( point( 0 ), point( 1 ), point( 2 ) );
+ }
+ else
+ {
+ painter->lineTo( knot() );
+ }
+ }
+ else
+ {
+ painter->moveTo( knot() );
+ }
+}
+
+bool
+VSegment::isFlat( double flatness ) const
+{
+ // Lines and "begin" segments are flat.
+ if(
+ !prev() ||
+ degree() == 1 )
+ {
+ return true;
+ }
+
+
+ // Iterate over control points.
+ for( unsigned short i = 0; i < degree() - 1; ++i )
+ {
+ if(
+ height( prev()->knot(), point( i ), knot() ) / chordLength()
+ >= flatness )
+ {
+ return false;
+ }
+ }
+
+ return true;
+}
+
+KoPoint
+VSegment::pointAt( double t ) const
+{
+ KoPoint p;
+
+ pointDerivativesAt( t, &p );
+
+ return p;
+}
+
+void
+VSegment::pointDerivativesAt( double t, KoPoint* p,
+ KoPoint* d1, KoPoint* d2 ) const
+{
+ if( !prev() )
+ return;
+
+
+ // Optimise the line case.
+ if( degree() == 1 )
+ {
+ const KoPoint diff = knot() - prev()->knot();
+
+ if( p )
+ *p = prev()->knot() + diff * t;
+
+ if( d1 )
+ *d1 = diff;
+
+ if( d2 )
+ *d2 = KoPoint( 0.0, 0.0 );
+
+ return;
+ }
+
+
+ // Beziers.
+
+ // Copy points.
+ KoPoint* q = new KoPoint[ degree() + 1 ];
+
+ q[ 0 ] = prev()->knot();
+
+ for( unsigned short i = 0; i < degree(); ++i )
+ {
+ q[ i + 1 ] = point( i );
+ }
+
+
+ // The De Casteljau algorithm.
+ for( unsigned short j = 1; j <= degree(); j++ )
+ {
+ for( unsigned short i = 0; i <= degree() - j; i++ )
+ {
+ q[ i ] = ( 1.0 - t ) * q[ i ] + t * q[ i + 1 ];
+ }
+
+ // Save second derivative now that we have it.
+ if( j == degree() - 2 )
+ {
+ if( d2 )
+ *d2 = degree() * ( degree() - 1 )
+ * ( q[ 2 ] - 2 * q[ 1 ] + q[ 0 ] );
+ }
+
+ // Save first derivative now that we have it.
+ else if( j == degree() - 1 )
+ {
+ if( d1 )
+ *d1 = degree() * ( q[ 1 ] - q[ 0 ] );
+ }
+ }
+
+ // Save point.
+ if( p )
+ *p = q[ 0 ];
+
+ delete[]( q );
+
+
+ return;
+}
+
+KoPoint
+VSegment::tangentAt( double t ) const
+{
+ KoPoint tangent;
+
+ pointTangentNormalAt( t, 0L, &tangent );
+
+ return tangent;
+}
+
+void
+VSegment::pointTangentNormalAt( double t, KoPoint* p,
+ KoPoint* tn, KoPoint* n ) const
+{
+ // Calculate derivative if necessary.
+ KoPoint d;
+
+ pointDerivativesAt( t, p, tn || n ? &d : 0L );
+
+
+ // Normalize derivative.
+ if( tn || n )
+ {
+ const double norm =
+ sqrt( d.x() * d.x() + d.y() * d.y() );
+
+ d = norm ? d * ( 1.0 / norm ) : KoPoint( 0.0, 0.0 );
+ }
+
+ // Assign tangent vector.
+ if( tn )
+ *tn = d;
+
+ // Calculate normal vector.
+ if( n )
+ {
+ // Calculate vector product of "binormal" x tangent
+ // (0,0,1) x (dx,dy,0), which is simply (dy,-dx,0).
+ n->setX( d.y() );
+ n->setY( -d.x() );
+ }
+}
+
+double
+VSegment::length( double t ) const
+{
+ if( !prev() || t == 0.0 )
+ {
+ return 0.0;
+ }
+
+
+ // Optimise the line case.
+ if( degree() == 1 )
+ {
+ return
+ t * chordLength();
+ }
+
+
+ /* This algortihm is by Jens Gravesen <gravesen AT mat DOT dth DOT dk>.
+ * We calculate the chord length "chord"=|P0P3| and the length of the control point
+ * polygon "poly"=|P0P1|+|P1P2|+|P2P3|. The approximation for the bezier length is
+ * 0.5 * poly + 0.5 * chord. "poly - chord" is a measure for the error.
+ * We subdivide each segment until the error is smaller than a given tolerance
+ * and add up the subresults.
+ */
+
+ // "Copy segment" splitted at t into a path.
+ VSubpath path( 0L );
+ path.moveTo( prev()->knot() );
+
+ // Optimize a bit: most of the time we'll need the
+ // length of the whole segment.
+ if( t == 1.0 )
+ path.append( this->clone() );
+ else
+ {
+ VSegment* copy = this->clone();
+ path.append( copy->splitAt( t ) );
+ delete copy;
+ }
+
+
+ double chord;
+ double poly;
+
+ double length = 0.0;
+
+ while( path.current() )
+ {
+ chord = path.current()->chordLength();
+ poly = path.current()->polyLength();
+
+ if(
+ poly &&
+ ( poly - chord ) / poly > VGlobal::lengthTolerance )
+ {
+ // Split at midpoint.
+ path.insert(
+ path.current()->splitAt( 0.5 ) );
+ }
+ else
+ {
+ length += 0.5 * poly + 0.5 * chord;
+ path.next();
+ }
+ }
+
+
+ return length;
+}
+
+double
+VSegment::chordLength() const
+{
+ if( !prev() )
+ return 0.0;
+
+
+ KoPoint d = knot() - prev()->knot();
+
+ return sqrt( d * d );
+}
+
+double
+VSegment::polyLength() const
+{
+ if( !prev() )
+ return 0.0;
+
+
+ // Start with distance |first point - previous knot|.
+ KoPoint d = point( 0 ) - prev()->knot();
+
+ double length = sqrt( d * d );
+
+ // Iterate over remaining points.
+ for( unsigned short i = 1; i < degree(); ++i )
+ {
+ d = point( i ) - point( i - 1 );
+ length += sqrt( d * d );
+ }
+
+
+ return length;
+}
+
+double
+VSegment::lengthParam( double len ) const
+{
+ if(
+ !prev() ||
+ len == 0.0 ) // We divide by len below.
+ {
+ return 0.0;
+ }
+
+
+ // Optimise the line case.
+ if( degree() == 1 )
+ {
+ return
+ len / chordLength();
+ }
+
+
+ // Perform a successive interval bisection.
+ double param1 = 0.0;
+ double paramMid = 0.5;
+ double param2 = 1.0;
+
+ double lengthMid = length( paramMid );
+
+ while( TQABS( lengthMid - len ) / len > VGlobal::paramLengthTolerance )
+ {
+ if( lengthMid < len )
+ param1 = paramMid;
+ else
+ param2 = paramMid;
+
+ paramMid = 0.5 * ( param2 + param1 );
+
+ lengthMid = length( paramMid );
+ }
+
+ return paramMid;
+}
+
+double
+VSegment::nearestPointParam( const KoPoint& p ) const
+{
+ if( !prev() )
+ {
+ return 1.0;
+ }
+
+
+ /* This function solves the "nearest point on curve" problem. That means, it
+ * calculates the point q (to be precise: it's parameter t) on this segment, which
+ * is located nearest to the input point P.
+ * The basic idea is best described (because it is freely available) in "Phoenix:
+ * An Interactive Curve Design System Based on the Automatic Fitting of
+ * Hand-Sketched Curves", Philip J. Schneider (Master thesis, University of
+ * Washington).
+ *
+ * For the nearest point q = C(t) on this segment, the first derivative is
+ * orthogonal to the distance vector "C(t) - P". In other words we are looking for
+ * solutions of f(t) = ( C(t) - P ) * C'(t) = 0.
+ * ( C(t) - P ) is a nth degree curve, C'(t) a n-1th degree curve => f(t) is a
+ * (2n - 1)th degree curve and thus has up to 2n - 1 distinct solutions.
+ * We solve the problem f(t) = 0 by using something called "Approximate Inversion Method".
+ * Let's write f(t) explicitly (with c_i = p_i - P and d_j = p_{j+1} - p_j):
+ *
+ * n n-1
+ * f(t) = SUM c_i * B^n_i(t) * SUM d_j * B^{n-1}_j(t)
+ * i=0 j=0
+ *
+ * n n-1
+ * = SUM SUM w_{ij} * B^{2n-1}_{i+j}(t)
+ * i=0 j=0
+ *
+ * with w_{ij} = c_i * d_j * z_{ij} and
+ *
+ * BinomialCoeff( n, i ) * BinomialCoeff( n - i ,j )
+ * z_{ij} = -----------------------------------------------
+ * BinomialCoeff( 2n - 1, i + j )
+ *
+ * This Bernstein-Bezier polynom representation can now be solved for it's roots.
+ */
+
+
+ // Calculate the c_i = point( i ) - P.
+ KoPoint* c = new KoPoint[ degree() + 1 ];
+
+ c[ 0 ] = prev()->knot() - p;
+
+ for( unsigned short i = 1; i <= degree(); ++i )
+ {
+ c[ i ] = point( i - 1 ) - p;
+ }
+
+
+ // Calculate the d_j = point( j + 1 ) - point( j ).
+ KoPoint* d = new KoPoint[ degree() ];
+
+ d[ 0 ] = point( 0 ) - prev()->knot();
+
+ for( unsigned short j = 1; j <= degree() - 1; ++j )
+ {
+ d[ j ] = 3.0 * ( point( j ) - point( j - 1 ) );
+ }
+
+
+ // Calculate the z_{ij}.
+ double* z = new double[ degree() * ( degree() + 1 ) ];
+
+ for( unsigned short j = 0; j <= degree() - 1; ++j )
+ {
+ for( unsigned short i = 0; i <= degree(); ++i )
+ {
+ z[ j * ( degree() + 1 ) + i ] =
+ static_cast<double>(
+ VGlobal::binomialCoeff( degree(), i ) *
+ VGlobal::binomialCoeff( degree() - i, j ) )
+ /
+ static_cast<double>(
+ VGlobal::binomialCoeff( 2 * degree() - 1, i + j ) );
+ }
+ }
+
+
+ // Calculate the dot products of c_i and d_i.
+ double* products = new double[ degree() * ( degree() + 1 ) ];
+
+ for( unsigned short j = 0; j <= degree() - 1; ++j )
+ {
+ for( unsigned short i = 0; i <= degree(); ++i )
+ {
+ products[ j * ( degree() + 1 ) + i ] =
+ d[ j ] * c[ i ];
+ }
+ }
+
+ // We don't need the c_i and d_i anymore.
+ delete[]( d );
+ delete[]( c );
+
+
+ // Calculate the control points of the new 2n-1th degree curve.
+ VSubpath newCurve( 0L );
+ newCurve.append( new VSegment( 2 * degree() - 1 ) );
+
+ // Set up control points in the ( u, f(u) )-plane.
+ for( unsigned short u = 0; u <= 2 * degree() - 1; ++u )
+ {
+ newCurve.current()->setP(
+ u,
+ KoPoint(
+ static_cast<double>( u ) / static_cast<double>( 2 * degree() - 1 ),
+ 0.0 ) );
+ }
+
+
+ // Set f(u)-values.
+ for( unsigned short k = 0; k <= 2 * degree() - 1; ++k )
+ {
+ unsigned short min = kMin( k, degree() );
+
+ for(
+ unsigned short i = kMax( 0, k - ( degree() - 1 ) );
+ i <= min;
+ ++i )
+ {
+ unsigned short j = k - i;
+
+ // p_k += products[j][i] * z[j][i].
+ newCurve.getLast()->setP(
+ k,
+ KoPoint(
+ newCurve.getLast()->p( k ).x(),
+ newCurve.getLast()->p( k ).y() +
+ products[ j * ( degree() + 1 ) + i ] *
+ z[ j * ( degree() + 1 ) + i ] ) );
+ }
+ }
+
+ // We don't need the c_i/d_i dot products and the z_{ij} anymore.
+ delete[]( products );
+ delete[]( z );
+
+kdDebug(38000) << "results" << endl;
+for( int i = 0; i <= 2 * degree() - 1; ++i )
+{
+kdDebug(38000) << newCurve.getLast()->p( i ).x() << " "
+<< newCurve.getLast()->p( i ).y() << endl;
+}
+kdDebug(38000) << endl;
+
+ // Find roots.
+ TQValueList<double> params;
+
+ newCurve.getLast()->rootParams( params );
+
+
+ // Now compare the distances of the candidate points.
+ double resultParam;
+ double distanceSquared;
+ double oldDistanceSquared;
+ KoPoint dist;
+
+ // First candidate is the previous knot.
+ dist = prev()->knot() - p;
+ distanceSquared = dist * dist;
+ resultParam = 0.0;
+
+ // Iterate over the found candidate params.
+ for( TQValueListConstIterator<double> itr = params.begin(); itr != params.end(); ++itr )
+ {
+ pointDerivativesAt( *itr, &dist );
+ dist -= p;
+ oldDistanceSquared = distanceSquared;
+ distanceSquared = dist * dist;
+
+ if( distanceSquared < oldDistanceSquared )
+ resultParam = *itr;
+ }
+
+ // Last candidate is the knot.
+ dist = knot() - p;
+ oldDistanceSquared = distanceSquared;
+ distanceSquared = dist * dist;
+
+ if( distanceSquared < oldDistanceSquared )
+ resultParam = 1.0;
+
+
+ return resultParam;
+}
+
+void
+VSegment::rootParams( TQValueList<double>& params ) const
+{
+ if( !prev() )
+ {
+ return;
+ }
+
+
+ // Calculate how often the control polygon crosses the x-axis
+ // This is the upper limit for the number of roots.
+ switch( controlPolygonZeros() )
+ {
+ // No solutions.
+ case 0:
+ return;
+ // Exactly one solution.
+ case 1:
+ if( isFlat( VGlobal::flatnessTolerance / chordLength() ) )
+ {
+ // Calculate intersection of chord with x-axis.
+ KoPoint chord = knot() - prev()->knot();
+
+kdDebug(38000) << prev()->knot().x() << " " << prev()->knot().y()
+<< knot().x() << " " << knot().y() << " ---> "
+<< ( chord.x() * prev()->knot().y() - chord.y() * prev()->knot().x() ) / - chord.y() << endl;
+ params.append(
+ ( chord.x() * prev()->knot().y() - chord.y() * prev()->knot().x() )
+ / - chord.y() );
+
+ return;
+ }
+ break;
+ }
+
+ // Many solutions. Do recursive midpoint subdivision.
+ VSubpath path( *this );
+ path.insert( path.current()->splitAt( 0.5 ) );
+
+ path.current()->rootParams( params );
+ path.next()->rootParams( params );
+}
+
+int
+VSegment::controlPolygonZeros() const
+{
+ if( !prev() )
+ {
+ return 0;
+ }
+
+
+ int signChanges = 0;
+
+ int sign = VGlobal::sign( prev()->knot().y() );
+ int oldSign;
+
+ for( unsigned short i = 0; i < degree(); ++i )
+ {
+ oldSign = sign;
+ sign = VGlobal::sign( point( i ).y() );
+
+ if( sign != oldSign )
+ {
+ ++signChanges;
+ }
+ }
+
+
+ return signChanges;
+}
+
+bool
+VSegment::isSmooth( const VSegment& next ) const
+{
+ // Return false if this segment is a "begin".
+ if( !prev() )
+ return false;
+
+
+ // Calculate tangents.
+ KoPoint t1;
+ KoPoint t2;
+
+ pointTangentNormalAt( 1.0, 0L, &t1 );
+
+ next.pointTangentNormalAt( 0.0, 0L, &t2 );
+
+
+ // Dot product.
+ if( t1 * t2 >= VGlobal::parallelTolerance )
+ return true;
+
+ return false;
+}
+
+KoRect
+VSegment::boundingBox() const
+{
+ // Initialize with knot.
+ KoRect rect( knot(), knot() );
+
+ // Add p0, if it exists.
+ if( prev() )
+ {
+ if( prev()->knot().x() < rect.left() )
+ rect.setLeft( prev()->knot().x() );
+
+ if( prev()->knot().x() > rect.right() )
+ rect.setRight( prev()->knot().x() );
+
+ if( prev()->knot().y() < rect.top() )
+ rect.setTop( prev()->knot().y() );
+
+ if( prev()->knot().y() > rect.bottom() )
+ rect.setBottom( prev()->knot().y() );
+ }
+
+ if( degree() == 3 )
+ {
+ /*
+ The basic idea for calculating the axis aligned bounding box (AABB) for bezier segments
+ was found in comp.graphics.algorithms:
+
+ Both the x coordinate and the y coordinate are polynomial. Newton told
+ us that at a maximum or minimum the derivative will be zero. Take all
+ those points, and take the ends; their AABB will be that of the curve.
+
+ We have a helpful trick for the derivatives: use the curve defined by
+ differences of successive control points.
+ This is a quadratic Bezier curve:
+
+ 2
+ r(t) = Sum Bi,2(t) *Pi = B0,2(t) * P0 + B1,2(t) * P1 + B2,2(t) * P2
+ i=0
+
+ r(t) = (1-t)^2 * P0 + 2t(1-t) * P1 + t^2 * P2
+
+ r(t) = (P2 - 2*P1 + P0) * t^2 + (2*P1 - 2*P0) * t + P0
+
+ Setting r(t) to zero and using the x and y coordinates of differences of
+ successive control points lets us find the paramters t, where the original
+ bezier curve has a minimum or a maximum.
+ */
+ double t[4];
+
+ // calcualting the differnces between successive control points
+ KoPoint x0 = p(1)-p(0);
+ KoPoint x1 = p(2)-p(1);
+ KoPoint x2 = p(3)-p(2);
+
+ // calculating the coefficents
+ KoPoint a = x2 - 2.0*x1 + x0;
+ KoPoint b = 2.0*x1 - 2.0*x0;
+ KoPoint c = x0;
+
+ // calculating parameter t at minimum/maximum in x-direction
+ if( a.x() == 0.0 )
+ {
+ t[0] = - c.x() / b.x();
+ t[1] = -1.0;
+ }
+ else
+ {
+ double rx = b.x()*b.x() - 4.0*a.x()*c.x();
+ if( rx < 0.0 )
+ rx = 0.0;
+ t[0] = ( -b.x() + sqrt( rx ) ) / (2.0*a.x());
+ t[1] = ( -b.x() - sqrt( rx ) ) / (2.0*a.x());
+ }
+
+ // calculating parameter t at minimum/maximum in y-direction
+ if( a.y() == 0.0 )
+ {
+ t[2] = - c.y() / b.y();
+ t[3] = -1.0;
+ }
+ else
+ {
+ double ry = b.y()*b.y() - 4.0*a.y()*c.y();
+ if( ry < 0.0 )
+ ry = 0.0;
+ t[2] = ( -b.y() + sqrt( ry ) ) / (2.0*a.y());
+ t[3] = ( -b.y() - sqrt( ry ) ) / (2.0*a.y());
+ }
+
+ // calculate points at found minimum/maximum and update bounding box
+ for( int i = 0; i < 4; ++i )
+ {
+ if( t[i] >= 0.0 && t[i] <= 1.0 )
+ {
+ KoPoint p = pointAt( t[i] );
+
+ if( p.x() < rect.left() )
+ rect.setLeft( p.x() );
+
+ if( p.x() > rect.right() )
+ rect.setRight( p.x() );
+
+ if( p.y() < rect.top() )
+ rect.setTop( p.y() );
+
+ if( p.y() > rect.bottom() )
+ rect.setBottom( p.y() );
+ }
+ }
+
+ return rect;
+ }
+
+ for( unsigned short i = 0; i < degree() - 1; ++i )
+ {
+ if( point( i ).x() < rect.left() )
+ rect.setLeft( point( i ).x() );
+
+ if( point( i ).x() > rect.right() )
+ rect.setRight( point( i ).x() );
+
+ if( point( i ).y() < rect.top() )
+ rect.setTop( point( i ).y() );
+
+ if( point( i ).y() > rect.bottom() )
+ rect.setBottom( point( i ).y() );
+ }
+
+
+ return rect;
+}
+
+VSegment*
+VSegment::splitAt( double t )
+{
+ if( !prev() )
+ {
+ return 0L;
+ }
+
+
+ // Create new segment.
+ VSegment* segment = new VSegment( degree() );
+
+ // Set segment state.
+ segment->m_state = m_state;
+
+
+ // Lines are easy: no need to modify the current segment.
+ if( degree() == 1 )
+ {
+ segment->setKnot(
+ prev()->knot() +
+ ( knot() - prev()->knot() ) * t );
+
+ return segment;
+ }
+
+
+ // Beziers.
+
+ // Copy points.
+ KoPoint* q = new KoPoint[ degree() + 1 ];
+
+ q[ 0 ] = prev()->knot();
+
+ for( unsigned short i = 0; i < degree(); ++i )
+ {
+ q[ i + 1 ] = point( i );
+ }
+
+
+ // The De Casteljau algorithm.
+ for( unsigned short j = 1; j <= degree(); ++j )
+ {
+ for( unsigned short i = 0; i <= degree() - j; ++i )
+ {
+ q[ i ] = ( 1.0 - t ) * q[ i ] + t * q[ i + 1 ];
+ }
+
+ // Modify the new segment.
+ segment->setPoint( j - 1, q[ 0 ] );
+ }
+
+ // Modify the current segment (no need to modify the knot though).
+ for( unsigned short i = 1; i < degree(); ++i )
+ {
+ setPoint( i - 1, q[ i ] );
+ }
+
+
+ delete[]( q );
+
+
+ return segment;
+}
+
+double
+VSegment::height(
+ const KoPoint& a,
+ const KoPoint& p,
+ const KoPoint& b )
+{
+ // Calculate determinant of AP and AB to obtain projection of vector AP to
+ // the orthogonal vector of AB.
+ const double det =
+ p.x() * a.y() + b.x() * p.y() - p.x() * b.y() -
+ a.x() * p.y() + a.x() * b.y() - b.x() * a.y();
+
+ // Calculate norm = length(AB).
+ const KoPoint ab = b - a;
+ const double norm = sqrt( ab * ab );
+
+ // If norm is very small, simply use distance AP.
+ if( norm < VGlobal::verySmallNumber )
+ return
+ sqrt(
+ ( p.x() - a.x() ) * ( p.x() - a.x() ) +
+ ( p.y() - a.y() ) * ( p.y() - a.y() ) );
+
+ // Normalize.
+ return TQABS( det ) / norm;
+}
+
+bool
+VSegment::linesIntersect(
+ const KoPoint& a0,
+ const KoPoint& a1,
+ const KoPoint& b0,
+ const KoPoint& b1 )
+{
+ const KoPoint delta_a = a1 - a0;
+ const double det_a = a1.x() * a0.y() - a1.y() * a0.x();
+
+ const double r_b0 = delta_a.y() * b0.x() - delta_a.x() * b0.y() + det_a;
+ const double r_b1 = delta_a.y() * b1.x() - delta_a.x() * b1.y() + det_a;
+
+ if( r_b0 != 0.0 && r_b1 != 0.0 && r_b0 * r_b1 > 0.0 )
+ return false;
+
+ const KoPoint delta_b = b1 - b0;
+
+ const double det_b = b1.x() * b0.y() - b1.y() * b0.x();
+
+ const double r_a0 = delta_b.y() * a0.x() - delta_b.x() * a0.y() + det_b;
+ const double r_a1 = delta_b.y() * a1.x() - delta_b.x() * a1.y() + det_b;
+
+ if( r_a0 != 0.0 && r_a1 != 0.0 && r_a0 * r_a1 > 0.0 )
+ return false;
+
+ return true;
+}
+
+bool
+VSegment::intersects( const VSegment& segment ) const
+{
+ if(
+ !prev() ||
+ !segment.prev() )
+ {
+ return false;
+ }
+
+
+ //TODO: this just dumbs down beziers to lines!
+ return linesIntersect( segment.prev()->knot(), segment.knot(), prev()->knot(), knot() );
+}
+
+// TODO: Move this function into "userland"
+uint
+VSegment::nodeNear( const KoPoint& p, double isNearRange ) const
+{
+ int index = 0;
+
+ for( unsigned short i = 0; i < degree(); ++i )
+ {
+ if( point( 0 ).isNear( p, isNearRange ) )
+ {
+ index = i + 1;
+ break;
+ }
+ }
+
+ return index;
+}
+
+VSegment*
+VSegment::revert() const
+{
+ if( !prev() )
+ return 0L;
+
+ // Create new segment.
+ VSegment* segment = new VSegment( degree() );
+
+ segment->m_state = m_state;
+
+
+ // Swap points.
+ for( unsigned short i = 0; i < degree() - 1; ++i )
+ {
+ segment->setPoint( i, point( degree() - 2 - i ) );
+ }
+
+ segment->setKnot( prev()->knot() );
+
+
+ // TODO swap node attributes (selected)
+
+ return segment;
+}
+
+VSegment*
+VSegment::prev() const
+{
+ VSegment* segment = m_prev;
+
+ while( segment && segment->state() == deleted )
+ {
+ segment = segment->m_prev;
+ }
+
+ return segment;
+}
+
+VSegment*
+VSegment::next() const
+{
+ VSegment* segment = m_next;
+
+ while( segment && segment->state() == deleted )
+ {
+ segment = segment->m_next;
+ }
+
+ return segment;
+}
+
+// TODO: remove this backward compatibility function after koffice 1.3.x
+void
+VSegment::load( const TQDomElement& element )
+{
+ if( element.tagName() == "CURVE" )
+ {
+ setDegree( 3 );
+
+ setPoint(
+ 0,
+ KoPoint(
+ element.attribute( "x1" ).toDouble(),
+ element.attribute( "y1" ).toDouble() ) );
+
+ setPoint(
+ 1,
+ KoPoint(
+ element.attribute( "x2" ).toDouble(),
+ element.attribute( "y2" ).toDouble() ) );
+
+ setKnot(
+ KoPoint(
+ element.attribute( "x3" ).toDouble(),
+ element.attribute( "y3" ).toDouble() ) );
+ }
+ else if( element.tagName() == "LINE" )
+ {
+ setDegree( 1 );
+
+ setKnot(
+ KoPoint(
+ element.attribute( "x" ).toDouble(),
+ element.attribute( "y" ).toDouble() ) );
+ }
+ else if( element.tagName() == "MOVE" )
+ {
+ setDegree( 1 );
+
+ setKnot(
+ KoPoint(
+ element.attribute( "x" ).toDouble(),
+ element.attribute( "y" ).toDouble() ) );
+ }
+}
+
+VSegment*
+VSegment::clone() const
+{
+ return new VSegment( *this );
+}
+
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-01 07:05:12 +0000