# Geometry

 Outward facing normal vector from points p0,p1,p2 transform normal from space A to B with transform matrix M transform a normal formed from cross prodect from space A to B Distance from point q to line v, u = q-p, p = point on line Alternate distance formula Time parameters for distance between to parameteric lines at points Distance obtained from the above time parameters between two parametric lines Distance between two lines if they are parallel (determinant = 0) implicit plane representation, n is the normal to the plane, d = distance from plane to origin distance d from point p to plane f Reflection of point p through normalized plane f Reflection matrix through plane f Intersection point of a line L(t) = p + tv with plane f Intersection point of 3 planes (divisor is scalar triple product) Intersection point of two planes, Transformation of plane f in space A to space B with transform mat H Plucker coords rep of a line, v = direction, and p1,p2 are any points on the line (called 'moment') Plucker coords rep of a 4D point vector with w component Distance between two lines in Plucker rep

 Line transform from mat H, M = upper 3x3 matrix from H, t = last column (translation) of H