I'm having trouble understanding why two Bezier curves is better than using one in this particular case. I feel like the technique described in slide 65 could have been useful here in finding one Bezier curve that fits all of these points since these points don't seem to create an absurd shape like in slide 73. I guess I'm interested in knowing what criteria calls for needing more than one Bezier curve?
MichaelYu15
From my understanding, a Bezier curve only touches the endpoints and not any of the intermediary control points. So applying the technique described in slide 65 would create a curve that does not touch the middle gray point in this example, but only approach it. However, a second bezier curve allows us to continue or add onto the previous curve to reach a new endpoint.
ninjab3381
From this picture, one can see how 2 Bézier curves can make a semicircle. It turns out that 4 Bézier curves are commonly used to make a circle.
you can also choose specific points to draw a circle by choosing (1,0) and (0,1) as the first 2 points and then (1, 0.55), (0.55, 1) where the 0.55 was chosen to match the derivatives of the circle at the top.
I'm having trouble understanding why two Bezier curves is better than using one in this particular case. I feel like the technique described in slide 65 could have been useful here in finding one Bezier curve that fits all of these points since these points don't seem to create an absurd shape like in slide 73. I guess I'm interested in knowing what criteria calls for needing more than one Bezier curve?
From my understanding, a Bezier curve only touches the endpoints and not any of the intermediary control points. So applying the technique described in slide 65 would create a curve that does not touch the middle gray point in this example, but only approach it. However, a second bezier curve allows us to continue or add onto the previous curve to reach a new endpoint.
From this picture, one can see how 2 Bézier curves can make a semicircle. It turns out that 4 Bézier curves are commonly used to make a circle.
you can also choose specific points to draw a circle by choosing (1,0) and (0,1) as the first 2 points and then (1, 0.55), (0.55, 1) where the 0.55 was chosen to match the derivatives of the circle at the top.