# Shortest distance from point to Catmull-Rom spline

Lantz
If I have a point P, how do I project it onto a Catmull-Rom spline (ie. get the point on the spline closest to P)?

This is how I calculate the spline, t goes from 0 to 1 (C++):
Code:
float t2 = t * t;
float t3 = t2 * t;
out.x = 0.5f * ( ( 2.0f * p1.x ) +
( -p0.x + p2.x ) * t +
( 2.0f * p0.x - 5.0f * p1.x + 4 * p2.x - p3.x ) * t2 +
( -p0.x + 3.0f * p1.x - 3.0f * p2.x + p3.x ) * t3 );
out.y = 0.5f * ( ( 2.0f * p1.y ) +
( -p0.y + p2.y ) * t +
( 2.0f * p0.y - 5.0f * p1.y + 4 * p2.y - p3.y ) * t2 +
( -p0.y + 3.0f * p1.y - 3.0f * p2.y + p3.y ) * t3 );
out.z = 0.5f * ( ( 2.0f * p1.z ) +
( -p0.z + p2.z ) * t +
( 2.0f * p0.z - 5.0f * p1.z + 4 * p2.z - p3.z ) * t2 +
( -p0.z + 3.0f * p1.z - 3.0f * p2.z + p3.z ) * t3 );

Which I derived from the forumla on this page. Should I use the, whats it called, the smallest square solution or something? My math skills does not go beyond one variable calculus and linear algebra so I have no clue whatsoever.

Regards,
Lantz