These slope calculations confuse me. Can anyone help explain 1) is b supposed to be a specific x,y,z? 2) why we don't normalize by something like x (slope is traditionally (y2-y1)/(x2-x1)?

1. b(t) is the function to evaluate the bezier curve. 2) the "slope" in this case is w.r.t the parameter t. It is a vector that points in the tangent direction. I'm not sure where the constant of 3 comes from, I think its related to the algebra of the bernstein polynomial somehow.