/* 0: lines don't intersect, 1:lines intersect, 2:lines are colinear */
int linesintersect(int x1,int y1,int x2,int y2,int x3,int y3,int x4,int y4,
double *x,double *y)
{
int a1,a2,b1,b2,c1,c2;
int r1,r2,r3,r4;
int denom,num;
a1=y2-y1; b1=x1-x2; c1=x2*y1-x1*y2;
r3=a1*x3+b1*y3+c1;
r4=a1*x4+b1*y4+c1;
if(r3!=0 && r4!=0 && SAME_SIGNS(r3,r4)) return 0;
a2=y4-y3;
b2=x3-x4;
c2=x4*y3-x3*y4;
r1=a2*x1+b2*y1+c2;
r2=a2*x2+b2*y2+c2;
if(r1!=0 && r2!=0 && SAME_SIGNS(r1,r2)) return 0;
denom=a1*b2-a2*b1;
if(denom==0) return 2;
num=b1*c2-b2*c1;
*x=(double)num/denom;
num=a2*c1-a1*c2;
*y=(double)num/denom;
return 1;
}
int intersection_test(point A, point B, point C, point D,
point *INTERSECTION)
{
long a1, b1, c1;
long a2, b2, c2;
long r1, r2, r3, r4;
long denom, offset, num;
/* Compute a1, b1, c1, where line joining points 1 and 2
* is "a1 x + b1 y + c1 = 0".
*/
a1 = B.y - A.y;
b1 = A.x - B.x;
c1 = B.x * A.y - A.x * B.y;
/* Compute r3 and r4.
*/
r3 = a1 * C.x + b1 * C.y + c1;
r4 = a1 * D.x + b1 * D.y + c1;
/* Check signs of r3 and r4. If both point 3 and point 4 lie on
* same side of line 1, the line segments do not intersect.
*/
if ( r3 != 0 &&
r4 != 0 &&
SAME_SIGNS( r3, r4 ))
return 0;
/* Compute a2, b2, c2 */
a2 = D.y - C.y;
b2 = C.x - D.x;
c2 = D.x * C.y - C.x * D.y;
/* Compute r1 and r2 */
r1 = a2 * A.x + b2 * A.y + c2;
r2 = a2 * B.x + b2 * B.y + c2;
/* Check signs of r1 and r2. If both point 1 and point 2 lie
* on same side of second line segment, the line segments do
* not intersect.
*/
if ( r1 != 0 &&
r2 != 0 &&
SAME_SIGNS( r1, r2 ))
return 0;
/* Line segments intersect: compute intersection point.
*/
denom = a1 * b2 - a2 * b1;
if ( denom == 0 )
return 0;
offset = denom < 0 ? - denom / 2 : denom / 2;
/* The denom/2 is to get rounding instead of truncating. It
* is added or subtracted to the numerator, depending upon the
* sign of the numerator.
*/
num = b1 * c2 - b2 * c1;
INTERSECTION->x = ( num < 0 ? num - offset : num + offset ) / denom;
num = a2 * c1 - a1 * c2;
INTERSECTION->y = ( num < 0 ? num - offset : num + offset ) / denom;
return 1;
}
/*!
\brief Line intersect
Author: Mukesh Prasad
Modified for floating point: Bill Brown
This function computes whether two line segments,
respectively joining the input points (x1,y1) -- (x2,y2)
and the input points (x3,y3) -- (x4,y4) intersect.
If the lines intersect, the output variables x, y are
set to coordinates of the point of intersection.
\param x1,y1,x2,y2 coordinates of endpoints of one segment
\param x3,y3,x4,y4 coordinates of endpoints of other segment
\param[out] x,y coordinates of intersection point
\return 0 no intersection
\return 1 intersect
\return 2 collinear
*/
int segs_intersect(float x1, float y1, float x2, float y2, float x3, float y3,
float x4, float y4, float *x, float *y)
{
float a1, a2, b1, b2, c1, c2; /* Coefficients of line eqns. */
float r1, r2, r3, r4; /* 'Sign' values */
float denom, offset, num; /* Intermediate values */
/* Compute a1, b1, c1, where line joining points 1 and 2
* is "a1 x + b1 y + c1 = 0".
*/
a1 = y2 - y1;
b1 = x1 - x2;
c1 = x2 * y1 - x1 * y2;
/* Compute r3 and r4.
*/
r3 = a1 * x3 + b1 * y3 + c1;
r4 = a1 * x4 + b1 * y4 + c1;
/* Check signs of r3 and r4. If both point 3 and point 4 lie on
* same side of line 1, the line segments do not intersect.
*/
if (!EQUAL(r3, 0.0) && !EQUAL(r4, 0.0) && SAME_SIGNS(r3, r4)) {
return (DONT_INTERSECT);
}
/* Compute a2, b2, c2 */
a2 = y4 - y3;
b2 = x3 - x4;
c2 = x4 * y3 - x3 * y4;
/* Compute r1 and r2 */
r1 = a2 * x1 + b2 * y1 + c2;
r2 = a2 * x2 + b2 * y2 + c2;
/* Check signs of r1 and r2. If both point 1 and point 2 lie
* on same side of second line segment, the line segments do
* not intersect.
*/
if (!EQUAL(r1, 0.0) && !EQUAL(r2, 0.0) && SAME_SIGNS(r1, r2)) {
return (DONT_INTERSECT);
}
/* Line segments intersect: compute intersection point.
*/
denom = a1 * b2 - a2 * b1;
if (denom == 0) {
return (COLLINEAR);
}
offset = denom < 0 ? -denom / 2 : denom / 2;
/* The denom/2 is to get rounding instead of truncating. It
* is added or subtracted to the numerator, depending upon the
* sign of the numerator.
*/
num = b1 * c2 - b2 * c1;
*x = num / denom;
num = a2 * c1 - a1 * c2;
*y = num / denom;
return (DO_INTERSECT);
}
int lines_intersect(
CPoint one, CPoint two, /* First line segment */
CPoint three, CPoint four, /* Second line segment */
CPoint &result)
{
long a1, a2, b1, b2, c1, c2; /* Coefficients of line eqns. */
long r1, r2, r3, r4; /* 'Sign' values */
long denom, offset, num; /* Intermediate values */
/* Compute a1, b1, c1, where line joining points 1 and 2
* is "a1 x + b1 y + c1 = 0".
*/
a1 = two.y - one.y; //y2 - y1;
b1 = one.x - two.x; //x1 - x2;
c1 = two.x * one.y - one.x * two.y; //x2 * y1 - x1 * y2;
/* Compute r3 and r4.
*/
r3 = a1 * three.x + b1 * three.y + c1; //a1 * x3 + b1 * y3 + c1;
r4 = a1 * four.x + b1 * four.y + c1; //a1 * x4 + b1 * y4 + c1;
/* Check signs of r3 and r4. If both point 3 and point 4 lie on
* same side of line 1, the line segments do not intersect.
*/
if ( r3 != 0 &&
r4 != 0 &&
SAME_SIGNS( r3, r4 ))
return ( DONT_INTERSECT );
/* Compute a2, b2, c2 */
a2 = four.y - three.y; //y4 - y3;
b2 = three.x - four.x; //x3 - x4;
c2 = four.x * three.y - three.x * four.y; //x4 * y3 - x3 * y4;
/* Compute r1 and r2 */
r1 = a2 * one.x + b2 * one.y + c2; //a2 * x1 + b2 * y1 + c2;
r2 = a2 * two.x + b2 * two.y + c2; //a2 * x2 + b2 * y2 + c2;
/* Check signs of r1 and r2. If both point 1 and point 2 lie
* on same side of second line segment, the line segments do
* not intersect.
*/
if ( r1 != 0 &&
r2 != 0 &&
SAME_SIGNS( r1, r2 ))
return ( DONT_INTERSECT );
/* Line segments intersect: compute intersection point.
*/
denom = a1 * b2 - a2 * b1;
if ( denom == 0 )
return ( COLLINEAR );
offset = denom < 0 ? - denom / 2 : denom / 2;
/* The denom/2 is to get rounding instead of truncating. It
* is added or subtracted to the numerator, depending upon the
* sign of the numerator.
*/
num = b1 * c2 - b2 * c1;
result.x = ( num < 0 ? num - offset : num + offset ) / denom;
num = a2 * c1 - a1 * c2;
result.y = ( num < 0 ? num - offset : num + offset ) / denom;
return ( DO_INTERSECT );
} /* lines_intersect */