I always remember the point-to-line formula in vector-land by thinking of a point A and line through points B and C. The norm of AB x AC is twice the area of the triangle ABC. Twice the area of the triangle is also base times height; base is the norm of BC, and height is what you want. So the distance is norm(AB x AC) / norm(BC).
I forget what the answer is for the Ax + By + ... = Z form; I should really look it up. I missed that day in 6th grade or something. Point-to-ray distance is either the distance to the corresponding line, or the distance to the endpoint -- depends on whether the point in question lies on the right "side" of that endpoint. You'd have to define what you mean by point-to-vector. If you mean distance to a line segment, it's the same argument as for rays but with two endpoints to think about. On Fri, Oct 14, 2011 at 7:42 AM, Lance Norskog <[email protected]> wrote: > Is there an n-dimensional point-to-line or point-to-vector or point-to-ray > distance method somewhere? > > Is this the easiest to do? > http://mathforum.org/kb/message.jspa?messageID=1072518&tstart=0 > > For the truly obsessed: N-dimensional CGI artifacts such as normals, > bounding boxes, etc. > http://www.cs.indiana.edu/pub/hanson/Siggraph01QuatCourse/ggndgeom.pdf >
