Why can't we do this with quadratic Bezier curves? It seems like only the degrees of freedom increases, while the # of constraints stays the same, meaning DOF > # of constraints so we can find a satisfying assignment of control points.
nsp
The DoF decreases, because we are moving from cubic Bezier (3rd order curve made by weighting 4 basis functions) to quadratic (2nd order curve made by weighting 3 basis functions)
spartace98
What does u refer to in this slide?
nsp
u is simply a parameter that varies from 0 at the first control point to 1 at the second control point. For animations, it may be time. However, for a spline represented based on control points in space, it does not have a specific meaning. In particular, changes in u do not match changes in arclength of the curve, so we cannot even use it directly to break up the curve into identical arclength segments.
Why can't we do this with quadratic Bezier curves? It seems like only the degrees of freedom increases, while the # of constraints stays the same, meaning DOF > # of constraints so we can find a satisfying assignment of control points.
The DoF decreases, because we are moving from cubic Bezier (3rd order curve made by weighting 4 basis functions) to quadratic (2nd order curve made by weighting 3 basis functions)
What does u refer to in this slide?
u is simply a parameter that varies from 0 at the first control point to 1 at the second control point. For animations, it may be time. However, for a spline represented based on control points in space, it does not have a specific meaning. In particular, changes in u do not match changes in arclength of the curve, so we cannot even use it directly to break up the curve into identical arclength segments.