What's the relationship between catmull-rom and hermite interpolation? And is there any relationship between catmull-rom and Bezier curves? I'm kind of confused on how all these things we're learning about interact with each other.
i could be wrong, but this is my understanding of it. we use catmull-rom to find the tangent line on point y1. This tangent line is the same as the slope of the line from the adjacent points(y0, y2). you can do the same for the tangent line on y2. With these tangent lines you can find a curve with hermite interpolation.
What is an example of a time in the real world where we know the value but not the derivative? (mentioned in lecture as a reason why Catmull-Rom might be useful)
I found this paper, and they talk about a few reasons why they might be useful in the beginning https://people.engr.tamu.edu/schaefer/research/cr_cad.pdf
Seems that one of the reasons is that since they interpolate their control points, we can have direct control over some of the points on the curve.