double R3Distance(const R3Point& point, const R3Line& line)
{
// Return distance from point to line (Riddle p. 904)
R3Vector v = line.Vector();
v.Cross(point - line.Point());
return v.Length();
}
double R3Distance(const R3Line& line1, const R3Line& line2)
{
// Return distance from line to line (Riddle p. 905)
R3Vector v = line1.Vector();
v.Cross(line2.Vector());
return v.Dot(line1.Point() - line2.Point());
}
R3Plane::
R3Plane(const R3Point& point, const R3Line& line)
{
// Construct plane through point and line
v = point - line.Point();
v.Cross(line.Vector());
v.Normalize();
d = -(v[0]*point[0] + v[1]*point[1] + v[2]*point[2]);
}
void R3Point::
Project(const R3Line& line)
{
// Move point to closest point on line
const R3Point *p = &(line.Point());
const R3Vector *v = &(line.Vector());
RNScalar denom = v->Dot(*v);
assert(denom != 0);
RNScalar t = (v->X() * (X() - p->X()) + v->Y() *(Y() - p->Y()) + v->Z() * (Z() - p->Z())) / denom;
*this = *p + *v * t;
}
double R3SignedDistance(const R3Plane& plane, const R3Line& line)
{
// Return signed distance from plane to line
if (plane.Normal().Dot(line.Vector()) == 0) {
// Plane and line are parallel
return R3SignedDistance(plane, line.Point());
}
else {
// Plane and line are not parallel
return 0.0;
}
}
void R3Point::
Rotate(const R3Line& axis, RNAngle theta)
{
// Translate axis to origin
R3Vector v = *this - axis.Point();
// Rotate point counterclockwise around axis through origin by radians ???
v.Rotate(axis.Vector(), theta);
// Translate axis back from origin
*this = axis.Point() + v;
}
RNBoolean R3Parallel(const R3Line& line, const R3Ray& ray)
{
// Return whether line and ray are parallel
return R3Parallel(line.Vector(), ray.Vector());
}
RNBoolean R3Parallel(const R3Line& line1, const R3Line& line2)
{
// Return whether line1 and line2 are parallel
return R3Parallel(line1.Vector(), line2.Vector());
}
RNBoolean R3Parallel(const R3Vector& vector, const R3Line& line)
{
// Return whether vector and line are parallel
return R3Parallel(vector, line.Vector());
}
RNBoolean R3Perpendicular(const R3Line& line, const R3Span& span)
{
// Return whether line and span are perpendicular
return R3Perpendicular(line.Vector(), span.Vector());
}
RNBoolean R3Perpendicular(const R3Line& line, const R3Ray& ray)
{
// Return whether line and ray are perpendicular
return R3Perpendicular(line.Vector(), ray.Vector());
}
RNBoolean R3Perpendicular(const R3Line& line1, const R3Line& line2)
{
// Return whether line1 and line2 are perpendicular
return R3Perpendicular(line1.Vector(), line2.Vector());
}
RNBoolean R3Contains(const R3Halfspace& halfspace, const R3Line& line)
{
// Return whether halfspace contains line
return (R3Parallel(halfspace.Plane(), line) &&
R3Contains(halfspace, line.Point()));
}
RNBoolean R3Contains(const R3Plane& plane, const R3Line& line)
{
// Return whether plane contains line
return (R3Parallel(plane, line) &&
R3Contains(plane, line.Point()));
}
RNBoolean R3Contains(const R3Line& line1, const R3Line& line2)
{
// Return whether two lines are equal within tolerance
return (R3Contains(line1.Vector(), line2.Vector()) &&
R3Contains(line1, line2.Point()));
}
RNBoolean R3Parallel(const R3Line& line, const R3Span& span)
{
// Return whether line and span are parallel
return R3Parallel(line.Vector(), span.Vector());
}
RNBoolean R3Parallel(const R3Line& line, const R3Plane& plane)
{
// Return whether line and plane are parallel
return R3Perpendicular(line.Vector(), plane.Normal());
}
RNBoolean R3Perpendicular(const R3Vector& vector, const R3Line& line)
{
// Return whether vector and line are perpendicular
return R3Perpendicular(vector, line.Vector());
}
