Points on lines where the two lines are the closest together
- by James Bedford
Hey guys,
I'm trying to find the points on two lines where the two lines are the closest. I've implemented the following method (Points and Vectors are as you'd expect, and a Line consists of a Point on the line and a non-normalized direction Vector from that point):
void CDClosestPointsOnTwoLines(Line line1, Line line2, Point* closestPoints)
{
closestPoints[0] = line1.pointOnLine;
closestPoints[1] = line2.pointOnLine;
Vector d1 = line1.direction;
Vector d2 = line2.direction;
float a = d1.dot(d1);
float b = d1.dot(d2);
float e = d2.dot(d2);
float d = a*e - b*b;
if (d != 0) // If the two lines are not parallel.
{
Vector r = Vector(line1.pointOnLine) - Vector(line2.pointOnLine);
float c = d1.dot(r);
float f = d2.dot(r);
float s = (b*f - c*e) / d;
float t = (a*f - b*c) / d;
closestPoints[0] = line1.positionOnLine(s);
closestPoints[1] = line2.positionOnLine(t);
}
else
{
printf("Lines were parallel.\n");
}
}
I'm using OpenGL to draw three lines that move around the world, the third of which should be the line that most closely connects the other two lines, the two end points of which are calculated using this function.
The problem is that the first point of closestPoints after this function is called will lie on line1, but the second point won't lie on line2, let alone at the closest point on line2! I've checked over the function many times but I can't see where the mistake in my implementation is. I've checked my dot product function, scalar multiplication, subtraction, positionOnLine() etc. etc. So my assumption is that the problem is within this method implementation.
If it helps to find the answer, this is function supposed to be an implementation of section 5.1.8 from 'Real-Time Collision Detection' by Christer Ericson.
Many thanks for any help!
