In lecture Kayvon said that the tangent for the endpoints was computed by using the other control points, i.e. use p0 and p1 in the image above to figure out the derivative at p0. Maybe I'm missing something simple, but don't we just need the direction between p0 and p1 to determine that tangent? And if so, doesn't that mean we could draw the same Bezier curve but with p1 closer to p0, and therefore the curve no longer be contained within the control point quadrilateral?
kencheng
These points are now in 2D, so really you have a function f(t): R => R x R. The derivative is thus also 2D, and needs two values to represent it (not just one: direction).
In lecture Kayvon said that the tangent for the endpoints was computed by using the other control points, i.e. use p0 and p1 in the image above to figure out the derivative at p0. Maybe I'm missing something simple, but don't we just need the direction between p0 and p1 to determine that tangent? And if so, doesn't that mean we could draw the same Bezier curve but with p1 closer to p0, and therefore the curve no longer be contained within the control point quadrilateral?
These points are now in 2D, so really you have a function f(t): R => R x R. The derivative is thus also 2D, and needs two values to represent it (not just one: direction).