How does tension relate to cubic spline interpolation? I am referring to this article for cubic spline interpolation. The tension factor t=0 is for the first and t=1 for the last knot point. But where can we substitute the other tension values, like 0.1, 0.2, etc., in the cubic spline? Can anyone direct me to any helpful references?
Cubic spline has no tension values, we calculate the first derivative and 2nd derivative to ensure continuity. Bezier curve (and tension spline) has tension value, tension determines "how sharply does the curve bend". Graphic designers on Photoshop are already playing with tensions when using bezier tool
Best place to start is Wikipedia's spline and run though some calculation with pen and paper (reading it mechanically wont help much with understanding). Start with cubic spline as they are usually introduced to 3rd yr math student.
This page on "Hermite Splines" claims "mathematical background of hermite curves will help you to understand the entire family of splines".