public clsLine3d Cross(clsLine3d l1)
{
double x = 0;
double y = 0;
double z = 0;
x = DY() * l1.DZ() - DZ() * l1.DY();
y = -(DX() * l1.DZ() - DZ() * l1.DX());
z = DX() * l1.DY() - DY() * l1.DX();
return(new clsLine3d(0, 0, 0, x, y, z));
}
public clsPoint3d ClosestPointToLine(clsLine3d l2)
{
clsPoint3d v1;
clsPoint3d v2;
clsPoint3d M;
double m2;
clsPoint3d R;
clsPoint3d P21;
double t1;
clsPoint3d Q1;
//Find the actual point on this line where the perpendicular distance hits.
v1 = new clsPoint3d(DX(), DY(), DZ());
v1.Normalise();
v2 = new clsPoint3d(l2.DX(), l2.DY(), l2.DZ());
v2.Normalise();
M = v2.Cross(v1);
m2 = M.Dot(M);
if (m2 < mdlGeometry.myTol)
{
return(l2.P1);
}
//Parallel
P21 = new clsPoint3d(l2.X1 - X1, l2.Y1 - Y1, l2.Z1 - Z1);
R = P21.Cross(M);
R.Scale(1 / m2);
t1 = R.Dot(v2);
Q1 = P1 + t1 * v1;
return(Q1);
}
public clsPoint3d DistanceAlongLine(double d)
{
clsLine3d l1 = default(clsLine3d);
l1 = Copy();
l1.Normalise();
return(new clsPoint3d(X1 + d * l1.DX(), Y1 + d * l1.DY(), Z1 + d * l1.DZ()));
}
public double DistanceToLine(clsLine3d l2)
{
//Perpendicular distance between 3d lines. Limited to the line segments.
double myNormalDist;
clsPoint3d v1;
clsPoint3d v2;
clsPoint3d M;
double m2;
clsPoint3d R;
clsPoint3d P21;
double t1;
double t2;
clsPoint3d Q1;
clsPoint3d Q2;
//Find the actual point on this line where the perpendicular distance hits. If it is off the line, then find the minimum distance between the end points
v1 = new clsPoint3d(DX(), DY(), DZ());
v1.Normalise();
v2 = new clsPoint3d(l2.DX(), l2.DY(), l2.DZ());
v2.Normalise();
P21 = new clsPoint3d(l2.X1 - X1, l2.X1 - X1, l2.X1 - X1);
M = v2.Cross(v1);
m2 = M.Dot(M);
if (m2 < mdlGeometry.myTol)
{
return(DistanceToPoint(l2.P1));
}
//Parallel
myNormalDist = Abs(P21.Dot(M)) / Sqrt(m2);
//Perpendicular distance
R = P21.Cross(M);
R.Scale(1 / m2);
t1 = R.Dot(v2);
Q1 = P1 + t1 * v1;
if (t1 < 0)
{
Q1 = P1;
}
if (t1 > Length)
{
Q1 = P2;
}
t2 = R.Dot(v1);
Q2 = l2.P1 + t2 * v2;
if (t2 < 0)
{
Q2 = l2.P1;
}
if (t2 > l2.Length)
{
Q2 = l2.P2;
}
return(Q1.Dist(Q2));
}
public void RotateAboutLine(clsLine3d l1, double theta)
{
clsPoint3d p1 = default(clsPoint3d);
clsPoint3d p2 = default(clsPoint3d);
clsPoint3d p2a = default(clsPoint3d);
clsPoint3d p2b = default(clsPoint3d);
clsPoint3d p3 = default(clsPoint3d);
clsLine3d l2 = default(clsLine3d);
if (l1.IsOnLine(this))
{
return;
}
//Setup a coordinate system with X running along l1 and the origin at l1.p2
l2 = new clsLine3d(l1.P2.Copy(), Copy());
p1 = new clsPoint3d(l1.DX(), l1.DY(), l1.DZ());
p1.Length = 1;
p2 = new clsPoint3d(l2.DX(), l2.DY(), l2.DZ());
p2a = new clsPoint3d(l2.DX(), l2.DY(), l2.DZ());
p2.Length = 1;
p3 = p1.Cross(p2);
p3.Length = 1;
p2 = p1.Cross(p3);
p2.Length = 1;
if (p2.Dot(p2a) < 0)
{
p2.Scale(-1);
}
p2b = new clsPoint3d(p1.Dot(p2a), p2.Dot(p2a), p3.Dot(p2a));
p2b.RotateAboutX(theta);
myX = l1.X2 + p2b.x * p1.x + p2b.y * p2.x + p2b.z * p3.x;
myY = l1.Y2 + p2b.x * p1.y + p2b.y * p2.y + p2b.z * p3.y;
myZ = l1.Z2 + p2b.x * p1.z + p2b.y * p2.z + p2b.z * p3.z;
}