double angleBetween(const LineSegment& one, const LineSegment& two) // will return angle in radians measured from line one to line two -- negative if one has greater slope than two
{
// assume both lines pass through the origin -- find the angles each form with the x axis using the slope
// atan returns -pi/2 to +pi/2
double angle1 = atan(one.slope());
double angle2 = atan(two.slope());
double ret = 0.0;
// If the slopes of the lines have the same, they are in the same quadrent
if( (one.slope() >= 0 && two.slope() >= 0) ||
(one.slope() < 0 && two.slope() < 0)) {
// simply return the difference between the angles of the two lines
ret = angle1 - angle2;
}
else { // lines fall in different quadrents
// Add the absolute values of the two lines, then set the sign based on which slope has the greater absolute value
ret = fabs(angle1) + fabs(angle2);
// if line one has a slope > 0, then sign of difference is negative
if(one.slope() > 0)
{
ret = -1*ret;
}
}
return ret;
}
Coord findIntersection(LineSegment& one, LineSegment& two, bool extrapolate)
{
Coord foundCoord = noCoord; // return variable, defaults to noCoord if cannot find
// get point-slope information for each line
// point-slope: form Y-y1 = m(X-x1)
one.normalize(); two.normalize();
double m1 = one.slope();
double m2 = two.slope();
Coord pt1 = one.A;
Coord pt2 = two.A;
// check for same-slope ... if so, then must do something else
if(m1 == m2)
{
// check to see if the lines have overlapping endpoints - if so, choose one of those endpoints
if( one.onSegment(two.A) )
foundCoord = two.A;
if( one.onSegment(two.B) )
foundCoord = two.B;
if( two.onSegment(one.A) )
foundCoord = one.A;
if( two.onSegment(one.B) )
foundCoord = one.B;
}
else // if lines have different slopes, derive coordinates of intersection from intersection of point-slope formulas
{
// edge case: check for infinite slope on either one
if(isinf<double>(m1)) {
// TODO
}
if(isinf<double>(m2)) {
// TODO
}
foundCoord.x = (pt2.y - pt1.y + m1*pt1.x - m2*pt2.x) / (m1 - m2);
foundCoord.y = m1*(foundCoord.x - pt1.x) + pt1.y;
// if we are constraining this to the actual points within the segments, need to make sure it exists on both segments
if(!extrapolate) {
if( !one.onSegment(foundCoord) || !two.onSegment(foundCoord) ) {
foundCoord = noCoord; // cannot find this point on both segments
}
}
}
return foundCoord;
}
Coord findIntersection(LineSegment& one, LineSegment& two, double extrapolatePercentage)
{
// extrapolate both lines out by making new segments that are larger
one.normalize(); two.normalize(); // A < B
// line one
double ext1 = extrapolatePercentage*one.length();
Coord A1 (one.A.x-ext1, one.A.y-ext1*one.slope());
Coord B1 (one.B.x+ext1, one.B.y+ext1*one.slope());
LineSegment L1 (A1, B1);
// line one
double ext2 = extrapolatePercentage*two.length();
Coord A2 (two.A.x-ext2, two.A.y-ext2*two.slope());
Coord B2 (two.B.x+ext2, two.B.y+ext2*two.slope());
LineSegment L2 (A2, B2);
// lines are now ready for intersection check
return findIntersection(L1, L2, false);
}
bool LineSegment::colinear(const LineSegment& l) const // lines are colinear if their slopes are the same AND if there is a point they both pass through
{
if(l.slope() != slope()) return false;
// assert: lines are the same slope
LineSegment buffer1(l); // to preserve const
LineSegment buffer2(*this);
if( findIntersection(buffer1, buffer2, true) == noCoord) // check for a point lying on both lines
return false;
// assert: we found a point that lies on both lines
return true;
}