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tdeedu/kig/misc/common.cpp

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/**
This file is part of Kig, a KDE program for Interactive Geometry...
Copyright (C) 2002 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 "common.h"
#include "../kig/kig_view.h"
#include "../objects/object_imp.h"
#include <cmath>
#include <kdebug.h>
#include <knumvalidator.h>
#include <klocale.h>
#if KDE_IS_VERSION( 3, 1, 90 )
#include <kinputdialog.h>
#else
#include <klineeditdlg.h>
#endif
Coordinate calcPointOnPerpend( const LineData& l, const Coordinate& t )
{
return calcPointOnPerpend( l.b - l.a, t );
}
Coordinate calcPointOnPerpend( const Coordinate& dir, const Coordinate& t )
{
return t + ( dir ).orthogonal();
}
Coordinate calcPointOnParallel( const LineData& l, const Coordinate& t )
{
return calcPointOnParallel( l.b - l.a, t );
}
Coordinate calcPointOnParallel( const Coordinate& dir, const Coordinate& t )
{
return t + dir*5;
}
Coordinate calcIntersectionPoint( const LineData& l1, const LineData& l2 )
{
const Coordinate& pa = l1.a;
const Coordinate& pb = l1.b;
const Coordinate& pc = l2.a;
const Coordinate& pd = l2.b;
double
xab = pb.x - pa.x,
xdc = pd.x - pc.x,
xac = pc.x - pa.x,
yab = pb.y - pa.y,
ydc = pd.y - pc.y,
yac = pc.y - pa.y;
double det = xab*ydc - xdc*yab;
double detn = xac*ydc - xdc*yac;
// test for parallelism
if ( fabs (det) < 1e-6 ) return Coordinate::invalidCoord();
double t = detn/det;
return pa + t*(pb - pa);
}
void calcBorderPoints( Coordinate& p1, Coordinate& p2, const Rect& r )
{
calcBorderPoints( p1.x, p1.y, p2.x, p2.y, r );
}
const LineData calcBorderPoints( const LineData& l, const Rect& r )
{
LineData ret( l );
calcBorderPoints( ret.a.x, ret.a.y, ret.b.x, ret.b.y, r );
return ret;
}
void calcBorderPoints( double& xa, double& ya, double& xb, double& yb, const Rect& r )
{
// we calc where the line through a(xa,ya) and b(xb,yb) intersects with r:
double left = (r.left()-xa)*(yb-ya)/(xb-xa)+ya;
double right = (r.right()-xa)*(yb-ya)/(xb-xa)+ya;
double top = (r.top()-ya)*(xb-xa)/(yb-ya)+xa;
double bottom = (r.bottom()-ya)*(xb-xa)/(yb-ya)+xa;
// now we go looking for valid points
int novp = 0; // number of valid points we have already found
if (!(top < r.left() || top > r.right())) {
// the line intersects with the top side of the rect.
++novp;
xa = top; ya = r.top();
};
if (!(left < r.bottom() || left > r.top())) {
// the line intersects with the left side of the rect.
if (novp++) { xb = r.left(); yb=left; }
else { xa = r.left(); ya=left; };
};
if (!(right < r.bottom() || right > r.top())) {
// the line intersects with the right side of the rect.
if (novp++) { xb = r.right(); yb=right; }
else { xa = r.right(); ya=right; };
};
if (!(bottom < r.left() || bottom > r.right())) {
// the line intersects with the bottom side of the rect.
++novp;
xb = bottom; yb = r.bottom();
};
if (novp < 2) {
// line is completely outside of the window...
xa = ya = xb = yb = 0;
};
}
void calcRayBorderPoints( const Coordinate& a, Coordinate& b, const Rect& r )
{
calcRayBorderPoints( a.x, a.y, b.x, b.y, r );
}
void calcRayBorderPoints( const double xa, const double ya, double& xb,
double& yb, const Rect& r )
{
// we calc where the line through a(xa,ya) and b(xb,yb) intersects with r:
double left = (r.left()-xa)*(yb-ya)/(xb-xa)+ya;
double right = (r.right()-xa)*(yb-ya)/(xb-xa)+ya;
double top = (r.top()-ya)*(xb-xa)/(yb-ya)+xa;
double bottom = (r.bottom()-ya)*(xb-xa)/(yb-ya)+xa;
// now we see which we can use...
if(
// the ray intersects with the top side of the rect..
top >= r.left() && top <= r.right()
// and b is above a
&& yb > ya )
{
xb = top;
yb = r.top();
return;
};
if(
// the ray intersects with the left side of the rect...
left >= r.bottom() && left <= r.top()
// and b is on the left of a..
&& xb < xa )
{
xb = r.left();
yb=left;
return;
};
if (
// the ray intersects with the right side of the rect...
right >= r.bottom() && right <= r.top()
// and b is to the right of a..
&& xb > xa )
{
xb = r.right();
yb=right;
return;
};
if(
// the ray intersects with the bottom side of the rect...
bottom >= r.left() && bottom <= r.right()
// and b is under a..
&& yb < ya ) {
xb = bottom;
yb = r.bottom();
return;
};
kdError() << k_funcinfo << "damn" << endl;
}
bool isOnLine( const Coordinate& o, const Coordinate& a,
const Coordinate& b, const double fault )
{
double x1 = a.x;
double y1 = a.y;
double x2 = b.x;
double y2 = b.y;
// check your math theory ( homogeneous co<63>rdinates ) for this
double tmp = fabs( o.x * (y1-y2) + o.y*(x2-x1) + (x1*y2-y1*x2) );
return tmp < ( fault * (b-a).length());
// if o is on the line ( if the determinant of the matrix
// |---|---|---|
// | x | y | z |
// |---|---|---|
// | x1| y1| z1|
// |---|---|---|
// | x2| y2| z2|
// |---|---|---|
// equals 0, then p(x,y,z) is on the line containing points
// p1(x1,y1,z1) and p2 here, we're working with normal coords, no
// homogeneous ones, so all z's equal 1
}
bool isOnSegment( const Coordinate& o, const Coordinate& a,
const Coordinate& b, const double fault )
{
return isOnLine( o, a, b, fault )
// not too far to the right
&& (o.x - kigMax(a.x,b.x) < fault )
// not too far to the left
&& ( kigMin (a.x, b.x) - o.x < fault )
// not too high
&& ( kigMin (a.y, b.y) - o.y < fault )
// not too low
&& ( o.y - kigMax (a.y, b.y) < fault );
}
bool isOnRay( const Coordinate& o, const Coordinate& a,
const Coordinate& b, const double fault )
{
return isOnLine( o, a, b, fault )
// not too far in front of a horizontally..
// && ( a.x - b.x < fault ) == ( a.x - o.x < fault )
&& ( ( a.x < b.x ) ? ( a.x - o.x < fault ) : ( a.x - o.x > -fault ) )
// not too far in front of a vertically..
// && ( a.y - b.y < fault ) == ( a.y - o.y < fault );
&& ( ( a.y < b.y ) ? ( a.y - o.y < fault ) : ( a.y - o.y > -fault ) );
}
bool isOnArc( const Coordinate& o, const Coordinate& c, const double r,
const double sa, const double a, const double fault )
{
if ( fabs( ( c - o ).length() - r ) > fault )
return false;
Coordinate d = o - c;
double angle = atan2( d.y, d.x );
if ( angle < sa ) angle += 2 * M_PI;
return angle - sa - a < 1e-4;
}
const Coordinate calcMirrorPoint( const LineData& l,
const Coordinate& p )
{
Coordinate m =
calcIntersectionPoint( l,
LineData( p,
calcPointOnPerpend( l, p )
)
);
return 2*m - p;
}
const Coordinate calcCircleLineIntersect( const Coordinate& c,
const double sqr,
const LineData& l,
int side )
{
Coordinate proj = calcPointProjection( c, l );
Coordinate hvec = proj - c;
Coordinate lvec = -l.dir();
double sqdist = hvec.squareLength();
double sql = sqr - sqdist;
if ( sql < 0.0 )
return Coordinate::invalidCoord();
else
{
double l = sqrt( sql );
lvec = lvec.normalize( l );
lvec *= side;
return proj + lvec;
};
}
const Coordinate calcArcLineIntersect( const Coordinate& c, const double sqr,
const double sa, const double angle,
const LineData& l, int side )
{
const Coordinate possiblepoint = calcCircleLineIntersect( c, sqr, l, side );
if ( isOnArc( possiblepoint, c, sqrt( sqr ), sa, angle, test_threshold ) )
return possiblepoint;
else return Coordinate::invalidCoord();
}
const Coordinate calcPointProjection( const Coordinate& p,
const LineData& l )
{
Coordinate orth = l.dir().orthogonal();
return p + orth.normalize( calcDistancePointLine( p, l ) );
}
double calcDistancePointLine( const Coordinate& p,
const LineData& l )
{
double xa = l.a.x;
double ya = l.a.y;
double xb = l.b.x;
double yb = l.b.y;
double x = p.x;
double y = p.y;
double norm = l.dir().length();
return ( yb * x - ya * x - xb * y + xa * y + xb * ya - yb * xa ) / norm;
}
Coordinate calcRotatedPoint( const Coordinate& a, const Coordinate& c, const double arc )
{
// we take a point p on a line through c and parallel with the
// X-axis..
Coordinate p( c.x + 5, c.y );
// we then calc the arc that ac forms with cp...
Coordinate d = a - c;
d = d.normalize();
double aarc = std::acos( d.x );
if ( d.y < 0 ) aarc = 2*M_PI - aarc;
// we now take the sum of the two arcs to find the arc between
// pc and ca
double asum = aarc + arc;
Coordinate ret( std::cos( asum ), std::sin( asum ) );
ret = ret.normalize( ( a -c ).length() );
return ret + c;
}
Coordinate calcCircleRadicalStartPoint( const Coordinate& ca, const Coordinate& cb,
double sqra, double sqrb )
{
Coordinate direc = cb - ca;
Coordinate m = (ca + cb)/2;
double dsq = direc.squareLength();
double lambda = dsq == 0.0 ? 0.0
: (sqra - sqrb) / (2*dsq);
direc *= lambda;
return m + direc;
}
double getDoubleFromUser( const TQString& caption, const TQString& label, double value,
TQWidget* parent, bool* ok, double min, double max, int decimals )
{
#ifdef KIG_USE_KDOUBLEVALIDATOR
KDoubleValidator vtor( min, max, decimals, 0, 0 );
#else
KFloatValidator vtor( min, max, (TQWidget*) 0, 0 );
#endif
#if KDE_IS_VERSION( 3, 1, 90 )
TQString input = KInputDialog::getText(
caption, label, TDEGlobal::locale()->formatNumber( value, decimals ),
ok, parent, "getDoubleFromUserDialog", &vtor );
#else
TQString input =
KLineEditDlg::getText( caption, label,
TDEGlobal::locale()->formatNumber( value, decimals ),
ok, parent, &vtor );
#endif
bool myok = true;
double ret = TDEGlobal::locale()->readNumber( input, &myok );
if ( ! myok )
ret = input.toDouble( & myok );
if ( ok ) *ok = myok;
return ret;
}
const Coordinate calcCenter(
const Coordinate& a, const Coordinate& b, const Coordinate& c )
{
// this algorithm is written by my brother, Christophe Devriese
// <oelewapperke@ulyssis.org> ...
// I don't get it myself :)
double xdo = b.x-a.x;
double ydo = b.y-a.y;
double xao = c.x-a.x;
double yao = c.y-a.y;
double a2 = xdo*xdo + ydo*ydo;
double b2 = xao*xao + yao*yao;
double numerator = (xdo * yao - xao * ydo);
if ( numerator == 0 )
{
// problem: xdo * yao == xao * ydo <=> xdo/ydo == xao / yao
// this means that the lines ac and ab have the same direction,
// which means they're the same line..
// FIXME: i would normally throw an error here, but KDE doesn't
// use exceptions, so i'm returning a bogus point :(
return a.invalidCoord();
/* return (a+c)/2; */
};
double denominator = 0.5 / numerator;
double centerx = a.x - (ydo * b2 - yao * a2) * denominator;
double centery = a.y + (xdo * b2 - xao * a2) * denominator;
return Coordinate(centerx, centery);
}
bool lineInRect( const Rect& r, const Coordinate& a, const Coordinate& b,
const int width, const ObjectImp* imp, const KigWidget& w )
{
double miss = w.screenInfo().normalMiss( width );
//mp: the following test didn't work for vertical segments;
// fortunately the ieee floating point standard allows us to avoid
// the test altogether, since it would produce an infinity value that
// makes the final r.contains to fail
// in any case the corresponding test for a.y - b.y was missing.
// if ( fabs( a.x - b.x ) <= 1e-7 )
// {
// // too small to be useful..
// return r.contains( Coordinate( a.x, r.center().y ), miss );
// }
// in case we have a segment we need also to check for the case when
// the segment is entirely contained in the rect, in which case the
// final tests all fail.
// it is ok to just check for the midpoint in the rect since:
// - if we have a segment completely contained in the rect this is true
// - if the midpoint is in the rect than returning true is safe (also
// in the cases where we have a ray or a line)
if ( r.contains( 0.5*( a + b ), miss ) ) return true;
Coordinate dir = b - a;
double m = dir.y / dir.x;
double lefty = a.y + m * ( r.left() - a.x );
double righty = a.y + m * ( r.right() - a.x );
double minv = dir.x / dir.y;
double bottomx = a.x + minv * ( r.bottom() - a.y );
double topx = a.x + minv * ( r.top() - a.y );
// these are the intersections between the line, and the lines
// defined by the sides of the rectangle.
Coordinate leftint( r.left(), lefty );
Coordinate rightint( r.right(), righty );
Coordinate bottomint( bottomx, r.bottom() );
Coordinate topint( topx, r.top() );
// For each intersection, we now check if we contain the
// intersection ( this might not be the case for a segment, when the
// intersection is not between the begin and end point.. ) and if
// the rect contains the intersection.. If it does, we have a winner..
return
( imp->contains( leftint, width, w ) && r.contains( leftint, miss ) ) ||
( imp->contains( rightint, width, w ) && r.contains( rightint, miss ) ) ||
( imp->contains( bottomint, width, w ) && r.contains( bottomint, miss ) ) ||
( imp->contains( topint, width, w ) && r.contains( topint, miss ) );
}
bool operator==( const LineData& l, const LineData& r )
{
return l.a == r.a && l.b == r.b;
}
bool LineData::isParallelTo( const LineData& l ) const
{
const Coordinate& p1 = a;
const Coordinate& p2 = b;
const Coordinate& p3 = l.a;
const Coordinate& p4 = l.b;
double dx1 = p2.x - p1.x;
double dy1 = p2.y - p1.y;
double dx2 = p4.x - p3.x;
double dy2 = p4.y - p3.y;
return isSingular( dx1, dy1, dx2, dy2 );
}
bool LineData::isOrthogonalTo( const LineData& l ) const
{
const Coordinate& p1 = a;
const Coordinate& p2 = b;
const Coordinate& p3 = l.a;
const Coordinate& p4 = l.b;
double dx1 = p2.x - p1.x;
double dy1 = p2.y - p1.y;
double dx2 = p4.x - p3.x;
double dy2 = p4.y - p3.y;
return isSingular( dx1, dy1, -dy2, dx2 );
}
bool areCollinear( const Coordinate& p1,
const Coordinate& p2, const Coordinate& p3 )
{
return isSingular( p2.x - p1.x, p2.y - p1.y, p3.x - p1.x, p3.y - p1.y );
}
bool isSingular( const double& a, const double& b,
const double& c, const double& d )
{
double det = a*d - b*c;
double norm1 = std::fabs(a) + std::fabs(b);
double norm2 = std::fabs(c) + std::fabs(d);
/*
* test must be done relative to the magnitude of the two
* row (or column) vectors!
*/
return ( std::fabs(det) < test_threshold*norm1*norm2 );
}
const double double_inf = HUGE_VAL;
const double test_threshold = 1e-6;