kicad/polygon/math_for_graphics.cpp

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// math for graphics utility routines, from FreePCB
using namespace std;
#include <vector>
#include <math.h>
#include <float.h>
#include <limits.h>
#include "fctsys.h"
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#include "PolyLine.h"
// test for hit on line segment
// i.e. cursor within a given distance from segment
// enter with: x,y = cursor coords
// (xi,yi) and (xf,yf) are the end-points of the line segment
// dist = maximum distance for hit
//
int TestLineHit( int xi, int yi, int xf, int yf, int x, int y, double dist )
{
double dd;
// test for vertical or horizontal segment
if( xf==xi )
{
// vertical segment
dd = fabs( (double)(x-xi) );
if( dd<dist && ( (yf>yi && y<yf && y>yi) || (yf<yi && y>yf && y<yi) ) )
return 1;
}
else if( yf==yi )
{
// horizontal segment
dd = fabs( (double)(y-yi) );
if( dd<dist && ( (xf>xi && x<xf && x>xi) || (xf<xi && x>xf && x<xi) ) )
return 1;
}
else
{
// oblique segment
// find a,b such that (xi,yi) and (xf,yf) lie on y = a + bx
double b = (double)(yf-yi)/(xf-xi);
double a = (double)yi-b*xi;
// find c,d such that (x,y) lies on y = c + dx where d=(-1/b)
double d = -1.0/b;
double c = (double)y-d*x;
// find nearest point to (x,y) on line segment (xi,yi) to (xf,yf)
double xp = (a-c)/(d-b);
double yp = a + b*xp;
// find distance
dd = sqrt((x-xp)*(x-xp)+(y-yp)*(y-yp));
if( fabs(b)>0.7 )
{
// line segment more vertical than horizontal
if( dd<dist && ( (yf>yi && yp<yf && yp>yi) || (yf<yi && yp>yf && yp<yi) ) )
return 1;
}
else
{
// line segment more horizontal than vertical
if( dd<dist && ( (xf>xi && xp<xf && xp>xi) || (xf<xi && xp>xf && xp<xi) ) )
return 1;
}
}
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return 0; // no hit
}
// set EllipseKH struct to describe the ellipse for an arc
//
int MakeEllipseFromArc( int xi, int yi, int xf, int yf, int style, EllipseKH * el )
{
// arc (quadrant of ellipse)
// convert to clockwise arc
int xxi, xxf, yyi, yyf;
if( style == CPolyLine::ARC_CCW )
{
xxi = xf;
xxf = xi;
yyi = yf;
yyf = yi;
}
else
{
xxi = xi;
xxf = xf;
yyi = yi;
yyf = yf;
}
// find center and radii of ellipse
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double xo=0, yo=0;
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if( xxf > xxi && yyf > yyi )
{
xo = xxf;
yo = yyi;
el->theta1 = M_PI;
el->theta2 = M_PI/2.0;
}
else if( xxf < xxi && yyf > yyi )
{
xo = xxi;
yo = yyf;
el->theta1 = -M_PI/2.0;
el->theta2 = -M_PI;
}
else if( xxf < xxi && yyf < yyi )
{
xo = xxf;
yo = yyi;
el->theta1 = 0.0;
el->theta2 = -M_PI/2.0;
}
else if( xxf > xxi && yyf < yyi )
{
xo = xxi;
yo = yyf;
el->theta1 = M_PI/2.0;
el->theta2 = 0.0;
}
el->Center.X = xo;
el->Center.Y = yo;
el->xrad = abs(xf-xi);
el->yrad = abs(yf-yi);
#if 0
el->Phi = 0.0;
el->MaxRad = el->xrad;
el->MinRad = el->yrad;
if( el->MaxRad < el->MinRad )
{
el->MaxRad = el->yrad;
el->MinRad = el->xrad;
el->Phi = M_PI/2.0;
}
#endif
return 0;
}
// find intersections between line segment (xi,yi) to (xf,yf)
// and line segment (xi2,yi2) to (xf2,yf2)
// the line segments may be arcs (i.e. quadrant of an ellipse) or straight
// returns number of intersections found (max of 2)
// returns coords of intersections in arrays x[2], y[2]
//
int FindSegmentIntersections( int xi, int yi, int xf, int yf, int style,
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int xi2, int yi2, int xf2, int yf2, int style2,
double x[], double y[] )
{
double xr[12], yr[12];
int iret = 0;
if( max(xi,xf) < min(xi2,xf2)
|| min(xi,xf) > max(xi2,xf2)
|| max(yi,yf) < min(yi2,yf2)
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|| min(yi,yf) > max(yi2,yf2) )
return 0;
if( style != CPolyLine::STRAIGHT && style2 != CPolyLine::STRAIGHT )
{
// two identical arcs intersect
if( style == style2 && xi == xi2 && yi == yi2 && xf == xf2 && yf == yf2 )
{
if( x && y )
{
x[0] = xi;
y[0] = yi;
}
return 1;
}
else if( style != style2 && xi == xf2 && yi == yf2 && xf == xi2 && yf == yi2 )
{
if( x && y )
{
x[0] = xi;
y[0] = yi;
}
return 1;
}
}
if( style == CPolyLine::STRAIGHT && style2 == CPolyLine::STRAIGHT )
{
// both straight-line segments
int x, y;
bool bYes = TestForIntersectionOfStraightLineSegments( xi, yi, xf, yf, xi2, yi2, xf2, yf2, &x, &y );
if( !bYes )
return 0;
xr[0] = x;
yr[0] = y;
iret = 1;
}
else if( style == CPolyLine::STRAIGHT )
{
// first segment is straight, second segment is an arc
int ret;
double x1r, y1r, x2r, y2r;
if( xf == xi )
{
// vertical first segment
double a = xi;
double b = DBL_MAX/2.0;
ret = FindLineSegmentIntersection( a, b, xi2, yi2, xf2, yf2, style2,
&x1r, &y1r, &x2r, &y2r );
}
else
{
double b = (double)(yf-yi)/(double)(xf-xi);
double a = yf - b*xf;
ret = FindLineSegmentIntersection( a, b, xi2, yi2, xf2, yf2, style2,
&x1r, &y1r, &x2r, &y2r );
}
if( ret == 0 )
return 0;
if( InRange( x1r, xi, xf ) && InRange( y1r, yi, yf ) )
{
xr[iret] = x1r;
yr[iret] = y1r;
iret++;
}
if( ret == 2 )
{
if( InRange( x2r, xi, xf ) && InRange( y2r, yi, yf ) )
{
xr[iret] = x2r;
yr[iret] = y2r;
iret++;
}
}
}
else if( style2 == CPolyLine::STRAIGHT )
{
// first segment is an arc, second segment is straight
int ret;
double x1r, y1r, x2r, y2r;
if( xf2 == xi2 )
{
// vertical second segment
double a = xi2;
double b = DBL_MAX/2.0;
ret = FindLineSegmentIntersection( a, b, xi, yi, xf, yf, style,
&x1r, &y1r, &x2r, &y2r );
}
else
{
double b = (double)(yf2-yi2)/(double)(xf2-xi2);
double a = yf2 - b*xf2;
ret = FindLineSegmentIntersection( a, b, xi, yi, xf, yf, style,
&x1r, &y1r, &x2r, &y2r );
}
if( ret == 0 )
return 0;
if( InRange( x1r, xi2, xf2 ) && InRange( y1r, yi2, yf2 ) )
{
xr[iret] = x1r;
yr[iret] = y1r;
iret++;
}
if( ret == 2 )
{
if( InRange( x2r, xi2, xf2 ) && InRange( y2r, yi2, yf2 ) )
{
xr[iret] = x2r;
yr[iret] = y2r;
iret++;
}
}
}
else
{
// both segments are arcs
EllipseKH el1;
EllipseKH el2;
MakeEllipseFromArc( xi, yi, xf, yf, style, &el1 );
MakeEllipseFromArc( xi2, yi2, xf2, yf2, style2, &el2 );
int n;
if( el1.xrad+el1.yrad > el2.xrad+el2.yrad )
n = GetArcIntersections( &el1, &el2 );
else
n = GetArcIntersections( &el2, &el1 );
iret = n;
}
if( x && y )
{
for( int i=0; i<iret; i++ )
{
x[i] = xr[i];
y[i] = yr[i];
}
}
return iret;
}
// find intersection between line y = a + bx and line segment (xi,yi) to (xf,yf)
// if b > DBL_MAX/10, assume vertical line at x = a
// the line segment may be an arc (i.e. quadrant of an ellipse)
// return 0 if no intersection
// returns 1 or 2 if intersections found
// sets coords of intersections in *x1, *y1, *x2, *y2
// if no intersection, returns min distance in dist
//
int FindLineSegmentIntersection( double a, double b, int xi, int yi, int xf, int yf, int style,
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double * x1, double * y1, double * x2, double * y2,
double * dist )
{
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double xx = 0, yy = 0; //Init made to avoid C compil "uninitialized" warning
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bool bVert = false;
if( b > DBL_MAX/10.0 )
bVert = true;
if( xf != xi )
{
// non-vertical segment, get intersection
if( style == CPolyLine::STRAIGHT || yf == yi )
{
// horizontal or oblique straight segment
// put into form y = c + dx;
double d = (double)(yf-yi)/(double)(xf-xi);
double c = yf - d*xf;
if( bVert )
{
// if vertical line, easy
if( InRange( a, xi, xf ) )
{
*x1 = a;
*y1 = c + d*a;
return 1;
}
else
{
if( dist )
*dist = min( abs(a-xi), abs(a-xf) );
return 0;
}
}
if( fabs(b-d) < 1E-12 )
{
// parallel lines
if( dist )
{
*dist = GetPointToLineDistance( a, b, xi, xf );
}
return 0; // lines parallel
}
// calculate intersection
xx = (c-a)/(b-d);
yy = a + b*(xx);
// see if intersection is within the line segment
if( yf == yi )
{
// horizontal line
if( (xx>=xi && xx>xf) || (xx<=xi && xx<xf) )
return 0;
}
else
{
// oblique line
if( (xx>=xi && xx>xf) || (xx<=xi && xx<xf)
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|| (yy>yi && yy>yf) || (yy<yi && yy<yf) )
return 0;
}
}
else if( style == CPolyLine::ARC_CW || style == CPolyLine::ARC_CCW )
{
// arc (quadrant of ellipse)
// convert to clockwise arc
int xxi, xxf, yyi, yyf;
if( style == CPolyLine::ARC_CCW )
{
xxi = xf;
xxf = xi;
yyi = yf;
yyf = yi;
}
else
{
xxi = xi;
xxf = xf;
yyi = yi;
yyf = yf;
}
// find center and radii of ellipse
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double xo = xxf, yo = yyi, rx, ry; // Init made to avoid C compil warnings
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if( xxf > xxi && yyf > yyi )
{
xo = xxf;
yo = yyi;
}
else if( xxf < xxi && yyf > yyi )
{
xo = xxi;
yo = yyf;
}
else if( xxf < xxi && yyf < yyi )
{
xo = xxf;
yo = yyi;
}
else if( xxf > xxi && yyf < yyi )
{
xo = xxi;
yo = yyf;
}
rx = fabs( (double)(xxi-xxf) );
ry = fabs( (double)(yyi-yyf) );
bool test;
double xx1, xx2, yy1, yy2, aa;
if( bVert )
{
// shift vertical line to coordinate system of ellipse
aa = a - xo;
test = FindVerticalLineEllipseIntersections( rx, ry, aa, &yy1, &yy2 );
if( !test )
return 0;
// shift back to PCB coordinates
yy1 += yo;
yy2 += yo;
xx1 = a;
xx2 = a;
}
else
{
// shift line to coordinate system of ellipse
aa = a + b*xo - yo;
test = FindLineEllipseIntersections( rx, ry, aa, b, &xx1, &xx2 );
if( !test )
return 0;
// shift back to PCB coordinates
yy1 = aa + b*xx1;
xx1 += xo;
yy1 += yo;
yy2 = aa + b*xx2;
xx2 += xo;
yy2 += yo;
}
int npts = 0;
if( (xxf>xxi && xx1<xxf && xx1>xxi) || (xxf<xxi && xx1<xxi && xx1>xxf) )
{
if( (yyf>yyi && yy1<yyf && yy1>yyi) || (yyf<yyi && yy1<yyi && yy1>yyf) )
{
*x1 = xx1;
*y1 = yy1;
npts = 1;
}
}
if( (xxf>xxi && xx2<xxf && xx2>xxi) || (xxf<xxi && xx2<xxi && xx2>xxf) )
{
if( (yyf>yyi && yy2<yyf && yy2>yyi) || (yyf<yyi && yy2<yyi && yy2>yyf) )
{
if( npts == 0 )
{
*x1 = xx2;
*y1 = yy2;
npts = 1;
}
else
{
*x2 = xx2;
*y2 = yy2;
npts = 2;
}
}
}
return npts;
}
else
wxASSERT(0);
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}
else
{
// vertical line segment
if( bVert )
return 0;
xx = xi;
yy = a + b*xx;
if( (yy>=yi && yy>yf) || (yy<=yi && yy<yf) )
return 0;
}
*x1 = xx;
*y1 = yy;
return 1;
}
// Test for intersection of line segments
// If lines are parallel, returns false
// If true, returns intersection coords in x, y
// if false, returns min. distance in dist (may be 0.0 if parallel)
// and coords on nearest point in one of the segments in (x,y)
//
bool TestForIntersectionOfStraightLineSegments( int x1i, int y1i, int x1f, int y1f,
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int x2i, int y2i, int x2f, int y2f,
int * x, int * y, double * d )
{
double a, b, dist;
// first, test for intersection
if( x1i == x1f && x2i == x2f )
{
// both segments are vertical, can't intersect
}
else if( y1i == y1f && y2i == y2f )
{
// both segments are horizontal, can't intersect
}
else if( x1i == x1f && y2i == y2f )
{
// first seg. vertical, second horizontal, see if they cross
if( InRange( x1i, x2i, x2f )
&& InRange( y2i, y1i, y1f ) )
{
if( x )
*x = x1i;
if( y )
*y = y2i;
if( d )
*d = 0.0;
return true;
}
}
else if( y1i == y1f && x2i == x2f )
{
// first seg. horizontal, second vertical, see if they cross
if( InRange( y1i, y2i, y2f )
&& InRange( x2i, x1i, x1f ) )
{
if( x )
*x = x2i;
if( y )
*y = y1i;
if( d )
*d = 0.0;
return true;
}
}
else if( x1i == x1f )
{
// first segment vertical, second oblique
// get a and b for second line segment, so that y = a + bx;
b = (double)(y2f-y2i)/(x2f-x2i);
a = (double)y2i - b*x2i;
double x1, y1, x2, y2;
int test = FindLineSegmentIntersection( a, b, x1i, y1i, x1f, y1f, CPolyLine::STRAIGHT,
&x1, &y1, &x2, &y2 );
if( test )
{
if( InRange( y1, y1i, y1f ) && InRange( x1, x2i, x2f ) && InRange( y1, y2i, y2f ) )
{
if( x )
*x = (int) x1;
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if( y )
*y = (int) y1;
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if( d )
*d = 0.0;
return true;
}
}
}
else if( y1i == y1f )
{
// first segment horizontal, second oblique
// get a and b for second line segment, so that y = a + bx;
b = (double)(y2f-y2i)/(x2f-x2i);
a = (double)y2i - b*x2i;
double x1, y1, x2, y2;
int test = FindLineSegmentIntersection( a, b, x1i, y1i, x1f, y1f, CPolyLine::STRAIGHT,
&x1, &y1, &x2, &y2 );
if( test )
{
if( InRange( x1, x1i, x1f ) && InRange( x1, x2i, x2f ) && InRange( y1, y2i, y2f ) )
{
if( x )
*x = (int) x1;
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if( y )
*y = (int) y1;
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if( d )
*d = 0.0;
return true;
}
}
}
else if( x2i == x2f )
{
// second segment vertical, first oblique
// get a and b for first line segment, so that y = a + bx;
b = (double)(y1f-y1i)/(x1f-x1i);
a = (double)y1i - b*x1i;
double x1, y1, x2, y2;
int test = FindLineSegmentIntersection( a, b, x2i, y2i, x2f, y2f, CPolyLine::STRAIGHT,
&x1, &y1, &x2, &y2 );
if( test )
{
if( InRange( x1, x1i, x1f ) && InRange( y1, y1i, y1f ) && InRange( y1, y2i, y2f ) )
{
if( x )
*x = (int) x1;
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if( y )
*y = (int) y1;
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if( d )
*d = 0.0;
return true;
}
}
}
else if( y2i == y2f )
{
// second segment horizontal, first oblique
// get a and b for second line segment, so that y = a + bx;
b = (double)(y1f-y1i)/(x1f-x1i);
a = (double)y1i - b*x1i;
double x1, y1, x2, y2;
int test = FindLineSegmentIntersection( a, b, x2i, y2i, x2f, y2f, CPolyLine::STRAIGHT,
&x1, &y1, &x2, &y2 );
if( test )
{
if( InRange( x1, x1i, x1f ) && InRange( y1, y1i, y1f ) )
{
if( x )
*x = (int) x1;
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if( y )
*y = (int) y1;
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if( d )
*d = 0.0;
return true;
}
}
}
else
{
// both segments oblique
if( (long)(y1f-y1i)*(x2f-x2i) != (long)(y2f-y2i)*(x1f-x1i) )
{
// not parallel, get a and b for first line segment, so that y = a + bx;
b = (double)(y1f-y1i)/(x1f-x1i);
a = (double)y1i - b*x1i;
double x1, y1, x2, y2;
int test = FindLineSegmentIntersection( a, b, x2i, y2i, x2f, y2f, CPolyLine::STRAIGHT,
&x1, &y1, &x2, &y2 );
// both segments oblique
if( test )
{
if( InRange( x1, x1i, x1f ) && InRange( y1, y1i, y1f ) )
{
if( x )
*x = (int) x1;
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if( y )
*y = (int) y1;
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if( d )
*d = 0.0;
return true;
}
}
}
}
// don't intersect, get shortest distance between each endpoint and the other line segment
dist = GetPointToLineSegmentDistance( x1i, y1i, x2i, y2i, x2f, y2f );
double xx = x1i;
double yy = y1i;
double dd = GetPointToLineSegmentDistance( x1f, y1f, x2i, y2i, x2f, y2f );
if( dd < dist )
{
dist = dd;
xx = x1f;
yy = y1f;
}
dd = GetPointToLineSegmentDistance( x2i, y2i, x1i, y1i, x1f, y1f );
if( dd < dist )
{
dist = dd;
xx = x2i;
yy = y2i;
}
dd = GetPointToLineSegmentDistance( x2f, y2f, x1i, y1i, x1f, y1f );
if( dd < dist )
{
dist = dd;
xx = x2f;
yy = y2f;
}
if( x )
*x = (int) xx;
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if( y )
*y = (int) yy;
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if( d )
*d = dist;
return false;
}
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/*solves the Quadratic equation = a*x*x + b*x + c
*/
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bool Quadratic( double a, double b, double c, double *x1, double *x2 )
{
double root = b*b - 4.0*a*c;
if( root < 0.0 )
return false;
root = sqrt( root );
*x1 = (-b+root)/(2.0*a);
*x2 = (-b-root)/(2.0*a);
return true;
}
// finds intersections of vertical line at x
// with ellipse defined by (x^2)/(a^2) + (y^2)/(b^2) = 1;
// returns true if solution exist, with solutions in y1 and y2
// else returns false
//
bool FindVerticalLineEllipseIntersections( double a, double b, double x, double *y1, double *y2 )
{
double y_sqr = (1.0-(x*x)/(a*a))*b*b;
if( y_sqr < 0.0 )
return false;
*y1 = sqrt(y_sqr);
*y2 = -*y1;
return true;
}
// finds intersections of straight line y = c + dx
// with ellipse defined by (x^2)/(a^2) + (y^2)/(b^2) = 1;
// returns true if solution exist, with solutions in x1 and x2
// else returns false
//
bool FindLineEllipseIntersections( double a, double b, double c, double d, double *x1, double *x2 )
{
// quadratic terms
double A = d*d+b*b/(a*a);
double B = 2.0*c*d;
double C = c*c-b*b;
return Quadratic( A, B, C, x1, x2 );
}
// Get clearance between 2 segments
// Returns point in segment closest to other segment in x, y
// in clearance > max_cl, just returns max_cl and doesn't return x,y
//
int GetClearanceBetweenSegments( int x1i, int y1i, int x1f, int y1f, int style1, int w1,
int x2i, int y2i, int x2f, int y2f, int style2, int w2,
int max_cl, int * x, int * y )
{
// check clearance between bounding rectangles
int test = max_cl + w1/2 + w2/2;
if( min(x1i,x1f)-max(x2i,x2f) > test )
return max_cl;
if( min(x2i,x2f)-max(x1i,x1f) > test )
return max_cl;
if( min(y1i,y1f)-max(y2i,y2f) > test )
return max_cl;
if( min(y2i,y2f)-max(y1i,y1f) > test )
return max_cl;
if( style1 == CPolyLine::STRAIGHT && style1 == CPolyLine::STRAIGHT )
{
// both segments are straight lines
int xx, yy;
double dd;
TestForIntersectionOfStraightLineSegments( x1i, y1i, x1f, y1f,
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x2i, y2i, x2f, y2f, &xx, &yy, &dd );
int d = max( 0, (int)dd - w1/2 - w2/2 );
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if( x )
*x = xx;
if( y )
*y = yy;
return d;
}
// not both straight-line segments
// see if segments intersect
double xr[2];
double yr[2];
test = FindSegmentIntersections( x1i, y1i, x1f, y1f, style1, x2i, y2i, x2f, y2f, style2, xr, yr );
if( test )
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{
if( x )
*x = (int) xr[0];
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if( y )
*y = (int) yr[0];
return 0;
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}
// at least one segment is an arc
EllipseKH el1;
EllipseKH el2;
bool bArcs;
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int xi=0, yi=0, xf=0, yf=0;
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if( style2 == CPolyLine::STRAIGHT )
{
// style1 = arc, style2 = straight
MakeEllipseFromArc( x1i, y1i, x1f, y1f, style1, &el1 );
xi = x2i;
yi = y2i;
xf = x2f;
yf = y2f;
bArcs = false;
}
else if( style1 == CPolyLine::STRAIGHT )
{
// style2 = arc, style1 = straight
xi = x1i;
yi = y1i;
xf = x1f;
yf = y1f;
MakeEllipseFromArc( x2i, y2i, x2f, y2f, style2, &el1 );
bArcs = false;
}
else
{
// style1 = arc, style2 = arc
MakeEllipseFromArc( x1i, y1i, x1f, y1f, style1, &el1 );
MakeEllipseFromArc( x2i, y2i, x2f, y2f, style2, &el2 );
bArcs = true;
}
const int NSTEPS = 32;
if( el1.theta2 > el1.theta1 )
wxASSERT(0);
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if( bArcs && el2.theta2 > el2.theta1 )
wxASSERT(0);
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// test multiple points in both segments
double th1;
double th2;
double len2;
if( bArcs )
{
th1 = el2.theta1;
th2 = el2.theta2;
len2 = max(el2.xrad, el2.yrad);
}
else
{
th1 = 1.0;
th2 = 0.0;
len2 = abs(xf-xi)+abs(yf-yi);
}
double s_start = el1.theta1;
double s_end = el1.theta2;
double s_start2 = th1;
double s_end2 = th2;
double dmin = DBL_MAX;
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double xmin = 0, ymin = 0, smin = 0, smin2 = 0; // Init made to avoid C compil warnings
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int nsteps = NSTEPS;
int nsteps2 = NSTEPS;
double step = (s_start-s_end)/(nsteps-1);
double step2 = (s_start2-s_end2)/(nsteps2-1);
while( (step * max(el1.xrad, el1.yrad)) > 0.1*NM_PER_MIL
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&& (step2 * len2) > 0.1*NM_PER_MIL )
{
step = (s_start-s_end)/(nsteps-1);
for( int i=0; i<nsteps; i++ )
{
double s;
if( i < nsteps-1 )
s = s_start - i*step;
else
s = s_end;
double x = el1.Center.X + el1.xrad*cos(s);
double y = el1.Center.Y + el1.yrad*sin(s);
// if not an arc, use s2 as fractional distance along line
step2 = (s_start2-s_end2)/(nsteps2-1);
for( int i2=0; i2<nsteps2; i2++ )
{
double s2;
if( i2 < nsteps2-1 )
s2 = s_start2 - i2*step2;
else
s2 = s_end2;
double x2, y2;
if( !bArcs )
{
x2 = xi + (xf-xi)*s2;
y2 = yi + (yf-yi)*s2;
}
else
{
x2 = el2.Center.X + el2.xrad*cos(s2);
y2 = el2.Center.Y + el2.yrad*sin(s2);
}
double d = Distance( (int) x, (int) y, (int) x2, (int) y2 );
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if( d < dmin )
{
dmin = d;
xmin = x;
ymin = y;
smin = s;
smin2 = s2;
}
}
}
if( step > step2 )
{
s_start = min(el1.theta1, smin + step);
s_end = max(el1.theta2, smin - step);
step = (s_start - s_end)/nsteps;
}
else
{
s_start2 = min(th1, smin2 + step2);
s_end2 = max(th2, smin2 - step2);
step2 = (s_start2 - s_end2)/nsteps2;
}
}
if( x )
*x = (int) xmin;
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if( y )
*y = (int) ymin;
return max(0, (int)dmin-w1/2-w2/2); // allow for widths
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}
// Get min. distance from (x,y) to line y = a + bx
// if b > DBL_MAX/10, assume vertical line at x = a
// returns closest point on line in xp, yp
//
double GetPointToLineDistance( double a, double b, int x, int y, double * xpp, double * ypp )
{
if( b > DBL_MAX/10 )
{
// vertical line
if( xpp && ypp )
{
*xpp = a;
*ypp = y;
}
return abs(a-x);
}
// find c,d such that (x,y) lies on y = c + dx where d=(-1/b)
double d = -1.0/b;
double c = (double)y-d*x;
// find nearest point to (x,y) on line through (xi,yi) to (xf,yf)
double xp = (a-c)/(d-b);
double yp = a + b*xp;
if( xpp && ypp )
{
*xpp = xp;
*ypp = yp;
}
// find distance
return Distance( x, y, (int) xp, (int) yp );
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}
/***********************************************************************************/
double GetPointToLineSegmentDistance( int x, int y, int xi, int yi, int xf, int yf )
/***********************************************************************************/
/** Function GetPointToLineSegmentDistance
* Get distance between line segment and point
* @param x,y = point
* @param xi,yi and xf,yf = the end-points of the line segment
* @return the distance
*/
{
// test for vertical or horizontal segment
if( xf==xi )
{
// vertical line segment
if( InRange( y, yi, yf ) )
return abs( x - xi );
else
return min( Distance( x, y, xi, yi ), Distance( x, y, xf, yf ) );
}
else if( yf==yi )
{
// horizontal line segment
if( InRange( x, xi, xf ) )
return abs( y - yi );
else
return min( Distance( x, y, xi, yi ), Distance( x, y, xf, yf ) );
}
else
{
// oblique segment
// find a,b such that (xi,yi) and (xf,yf) lie on y = a + bx
double b = (double)(yf-yi)/(xf-xi);
double a = (double)yi-b*xi;
// find c,d such that (x,y) lies on y = c + dx where d=(-1/b)
double d = -1.0/b;
double c = (double)y-d*x;
// find nearest point to (x,y) on line through (xi,yi) to (xf,yf)
double xp = (a-c)/(d-b);
double yp = a + b*xp;
// find distance
if( InRange( xp, xi, xf ) && InRange( yp, yi, yf ) )
return Distance( x, y, (int) xp, (int) yp );
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else
return min( Distance( x, y, xi, yi ), Distance( x, y, xf, yf ) );
}
}
// test for value within range
//
bool InRange( double x, double xi, double xf )
{
if( xf>xi )
{
if( x >= xi && x <= xf )
return true;
}
else
{
if( x >= xf && x <= xi )
return true;
}
return false;
}
// Get distance between 2 points
//
double Distance( int x1, int y1, int x2, int y2 )
{
double d;
d = sqrt( (double)(x1-x2)*(x1-x2) + (double)(y1-y2)*(y1-y2) );
if( d > INT_MAX || d < INT_MIN )
wxASSERT(0);
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return (int)d;
}
// this finds approximate solutions
// note: this works best if el2 is smaller than el1
//
int GetArcIntersections( EllipseKH * el1, EllipseKH * el2,
double * x1, double * y1, double * x2, double * y2 )
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{
if( el1->theta2 > el1->theta1 )
wxASSERT(0);
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if( el2->theta2 > el2->theta1 )
wxASSERT(0);
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const int NSTEPS = 32;
double xret[2], yret[2];
double xscale = 1.0/el1->xrad;
double yscale = 1.0/el1->yrad;
// now transform params of second ellipse into reference frame
// with origin at center if first ellipse,
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// scaled so the first ellipse is a circle of radius = 1.0
double xo = (el2->Center.X - el1->Center.X)*xscale;
double yo = (el2->Center.Y - el1->Center.Y)*yscale;
double xr = el2->xrad*xscale;
double yr = el2->yrad*yscale;
// now test NSTEPS positions in arc, moving clockwise (ie. decreasing theta)
double step = M_PI/((NSTEPS-1)*2.0);
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double d_prev=0, th_prev;
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double th_interp;
double th1;
int n = 0;
for( int i=0; i<NSTEPS; i++ )
{
double theta;
if( i < NSTEPS-1 )
theta = el2->theta1 - i*step;
else
theta = el2->theta2;
double x = xo + xr*cos(theta);
double y = yo + yr*sin(theta);
double d = 1.0 - sqrt(x*x + y*y);
if( i>0 )
{
bool bInt = false;
if( d >= 0.0 && d_prev <= 0.0 )
{
th_interp = theta + (step*(-d_prev))/(d-d_prev);
bInt = true;
}
else if( d <= 0.0 && d_prev >= 0.0 )
{
th_interp = theta + (step*d_prev)/(d_prev-d);
bInt = true;
}
if( bInt )
{
x = xo + xr*cos(th_interp);
y = yo + yr*sin(th_interp);
th1 = atan2( y, x );
if( th1 <= el1->theta1 && th1 >= el1->theta2 )
{
xret[n] = x*el1->xrad + el1->Center.X;
yret[n] = y*el1->yrad + el1->Center.Y;
n++;
if( n > 2 )
wxASSERT(0);
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}
}
}
d_prev = d;
th_prev = theta;
}
if( x1 )
*x1 = xret[0];
if( y1 )
*y1 = yret[0];
if( x2 )
*x2 = xret[1];
if( y2 )
*y2 = yret[1];
return n;
}
// this finds approximate solution
//
//double GetSegmentClearance( EllipseKH * el1, EllipseKH * el2,
double GetArcClearance( EllipseKH * el1, EllipseKH * el2,
double * x1, double * y1 )
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{
const int NSTEPS = 32;
if( el1->theta2 > el1->theta1 )
wxASSERT(0);
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if( el2->theta2 > el2->theta1 )
wxASSERT(0);
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// test multiple positions in both arcs, moving clockwise (ie. decreasing theta)
double th_start = el1->theta1;
double th_end = el1->theta2;
double th_start2 = el2->theta1;
double th_end2 = el2->theta2;
double dmin = DBL_MAX;
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double xmin=0, ymin=0, thmin=0, thmin2=0;
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int nsteps = NSTEPS;
int nsteps2 = NSTEPS;
double step = (th_start-th_end)/(nsteps-1);
double step2 = (th_start2-th_end2)/(nsteps2-1);
while( (step * max(el1->xrad, el1->yrad)) > 1.0*NM_PER_MIL
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&& (step2 * max(el2->xrad, el2->yrad)) > 1.0*NM_PER_MIL )
{
step = (th_start-th_end)/(nsteps-1);
for( int i=0; i<nsteps; i++ )
{
double theta;
if( i < nsteps-1 )
theta = th_start - i*step;
else
theta = th_end;
double x = el1->Center.X + el1->xrad*cos(theta);
double y = el1->Center.Y + el1->yrad*sin(theta);
step2 = (th_start2-th_end2)/(nsteps2-1);
for( int i2=0; i2<nsteps2; i2++ )
{
double theta2;
if( i2 < nsteps2-1 )
theta2 = th_start2 - i2*step2;
else
theta2 = th_end2;
double x2 = el2->Center.X + el2->xrad*cos(theta2);
double y2 = el2->Center.Y + el2->yrad*sin(theta2);
double d = Distance( (int) x, (int) y, (int) x2, (int) y2 );
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if( d < dmin )
{
dmin = d;
xmin = x;
ymin = y;
thmin = theta;
thmin2 = theta2;
}
}
}
if( step > step2 )
{
th_start = min(el1->theta1, thmin + step);
th_end = max(el1->theta2, thmin - step);
step = (th_start - th_end)/nsteps;
}
else
{
th_start2 = min(el2->theta1, thmin2 + step2);
th_end2 = max(el2->theta2, thmin2 - step2);
step2 = (th_start2 - th_end2)/nsteps2;
}
}
if( x1 )
*x1 = xmin;
if( y1 )
*y1 = ymin;
return dmin;
}