+// calculate the projection, p, of u along the direction of d.
+void sgProjection(sgVec3 p, const sgVec3 u, const sgVec3 d){
+ double denom = sgScalarProductVec3(d,d);
+ if (denom == 0.) sgCopyVec3(p, u);
+ else sgScaleVec3(p, d, sgScalarProductVec3(u,d) / denom);
+}
+
+// Same thing, except using double precision
+void sgProjection(sgdVec3 p, const sgdVec3 u, const sgdVec3 d){
+ double denom = sgdScalarProductVec3(d,d);
+ if (denom == 0.) sgdCopyVec3(p, u);
+ else sgdScaleVec3(p, d, sgdScalarProductVec3(u,d) / denom);
+}
+
+// Given a point p, and a line through p0 with direction vector d,
+// find the closest point (p1) on the line
+void sgClosestPointToLine( sgVec3 p1, const sgVec3 p, const sgVec3 p0,
+ const sgVec3 d ) {
+
+ sgVec3 u, u1;
+
+ // u = p - p0
+ sgSubVec3(u, p, p0);
+
+ // calculate the projection, u1, of u along d.
+ sgProjection(u1, u, d);
+
+ // calculate the point p1 along the line that is closest to p
+ // p0 = p1 + u1
+ sgAddVec3(p1, p0, u1);
+}
+
+
+// Given a point p, and a line through p0 with direction vector d,
+// find the closest point (p1) on the line
+void sgdClosestPointToLine( sgdVec3 p1, const sgdVec3 p, const sgdVec3 p0,
+ const sgdVec3 d ) {
+
+ sgdVec3 u, u1;
+
+ // u = p - p0
+ sgdSubVec3(u, p, p0);
+
+ // calculate the projection, u1, of u along d.
+ sgProjection(u1, u, d);
+
+ // calculate the point p1 along the line that is closest to p
+ // p0 = p1 + u1
+ sgdAddVec3(p1, p0, u1);
+}
+
+