I don't know a spline off the top of my head that inherently has the property you want, but you can split Bezier curves to form what you want: https://pomax.git

I don't know a spline off the top of my head that inherently has the property you want, but you can split Bezier curves to form what you want: https://pomax.github.io/bezierinfo/#splitting https://pomax.github.io/bezierinfo/#splitting . You can also drop earlier control points from any spline once you get to the next curve in the piecewise formula. Also, I suspect you might want to know that you can construct cubic Bezier curves as a pair of (point + derivative at point)s instead of using four control points, and you can also easily get the derivative at any point along the curve. You can use this to change your mind about where an animation is headed halfway through but still always get a smooth result.