Lecture 7: Intro to Geometry, Splines, and Bezier Curves (22)
yinxudeng
For Cubic Hermite interpolation and Catmull-Rom interpolation, why do we want to use some derivatives as input? Instead of using 2 values and 2 derivates, if we use 4 values, we can still construct a cubic function, but would that cause some problem when we transition from one cubic function to the next one?
Resolved. Yes, if we do not enforce any constraints on the derivatives of endpoints, when we transition from one cubic function to the next, it might not be smooth.
Staffajayjain
Good question and observation @yinxudeng! Bezier curves which appear later in the lecture use 4 control points rather than 2 point values and 2 tangents, but constraints on colinearity of points are needed for smoothness.
For Cubic Hermite interpolation and Catmull-Rom interpolation, why do we want to use some derivatives as input? Instead of using 2 values and 2 derivates, if we use 4 values, we can still construct a cubic function, but would that cause some problem when we transition from one cubic function to the next one?
Resolved. Yes, if we do not enforce any constraints on the derivatives of endpoints, when we transition from one cubic function to the next, it might not be smooth.
Good question and observation @yinxudeng! Bezier curves which appear later in the lecture use 4 control points rather than 2 point values and 2 tangents, but constraints on colinearity of points are needed for smoothness.