// line (or segment) in 3D vs plane
bool vsLine3D(const Line3D& line, const Plane3D& plane, Point3D *rpoint = NULL, bool check = true)
{
// check if line is parallel with plane
if ( abs( line.vector * plane.normal() ) < epsilon )
return false;
Point3D p = line.point, q = line.point + line.vector;
float normalLen = plane.normal().length();
// get dist (and side) from plane for each point
float distP = plane.Evaluate( p ) / normalLen;
float distQ = plane.Evaluate( q ) / normalLen;
// find t
float t;
if ( ( distP < 0.f && distQ < 0.f ) || ( distP > 0.f && distQ > 0.f ) )
{
if ( check ) return false;
t = abs( distP ) < abs( distQ )
? -abs( distP / ( distP - distQ ) )
: abs( ( distP + distQ ) / ( distP - distQ ) );
}
else
{
t = abs( distP ) / ( abs( distP ) + abs( distQ ) );
}
if ( rpoint ) *rpoint = p + t * line.vector;
return true;
}
// Compute angle between two geometric entities (in radians; use acos)
float AngleBetween(const Line3D& line, const Plane3D& plane)
{
Vector3D u = line.vector ^ plane.normal();
Vector3D v = plane.normal() ^ u;
float angle = acos( v * line.vector );
return ( ( angle < 0.f ) ? ( angle + 2.f * M_PI ) : angle );
}
// Determine if two geometric entities are perpendicular.
bool Perpendicular(const Plane3D& plane1, const Plane3D& plane2)
{
return ( plane1.normal() * plane2.normal() <= epsilon );
}
// Determine if two geometric entities are perpendicular.
bool Perpendicular(const Line3D& line, const Plane3D& plane)
{
return ( abs( line.vector * plane.normal() -
line.vector.length() * plane.normal().length() ) <= epsilon );
}
// Determine if two geometric entities are parallel.
bool Parallel(const Plane3D& plane1, const Plane3D& plane2)
{
return ( abs( plane1.normal() * plane2.normal() -
plane1.normal().length() * plane2.normal().length() ) <= epsilon );
}
// Determine if two geometric entities are parallel.
bool Parallel(const Line3D& line, const Plane3D& plane)
{
return ( abs( line.vector * plane.normal() ) <= epsilon );
}
// Compute angle between two geometric entities (in radians; use acos)
float AngleBetween(const Plane3D& plane1, const Plane3D& plane2)
{
return acos( ( plane1.normal() * plane2.normal() ) /
( plane1.normal().length() * plane2.normal().length() ) );
}
// Return the distance from a point to a plane.
float Distance(const Point3D& point, const Plane3D& plane)
{
return abs( plane.Evaluate( point ) / plane.normal().length() );
}