Wanted to double check my understanding—why do the derivatives have to be continuous as well? Is it because if the derivative is not continuous, we will still get jerky changes in slope in the interpolation?
michaeltu1
We'll be able to observe jerky changes only as we cross the sample boundaries. (When the derivative jumps to another value) An example used in lecture was to consider when this function is used to approximate the smooth forms of a font. I'm guessing the part of the letter drawn using the smooth linear interpolation between 2 sample points would appear smooth, but as you change between using the linear interpolation between points p0 and p1 to points p1 and p2, at point p1 (the sample boundary) you might see a sharp corner or something.
sheaconlon
Another good example is a camera path— an instantaneous change in the derivative would be an instantaneous change in the velocity of the camera, which would come across as unrealistic.
Wanted to double check my understanding—why do the derivatives have to be continuous as well? Is it because if the derivative is not continuous, we will still get jerky changes in slope in the interpolation?
We'll be able to observe jerky changes only as we cross the sample boundaries. (When the derivative jumps to another value) An example used in lecture was to consider when this function is used to approximate the smooth forms of a font. I'm guessing the part of the letter drawn using the smooth linear interpolation between 2 sample points would appear smooth, but as you change between using the linear interpolation between points p0 and p1 to points p1 and p2, at point p1 (the sample boundary) you might see a sharp corner or something.
Another good example is a camera path— an instantaneous change in the derivative would be an instantaneous change in the velocity of the camera, which would come across as unrealistic.