How does the degree of a Bézier curve affect its shape and flexibility in representing curves or surfaces?
onionzn
For Bezier curves, the movement of one control point will be cascaded through the remaining points downstream. This is very different from Catmull-Rom interpolation where each control point is only in charge of its own segment of the curve. Is it right to say that Bezier curves are more costly to compute? If so, what are the methods available to speed up the computation?
s3kim2018
Since the number of interpolation steps increases with the number of points used in one bezier curve, do we usually stick with 4 points (b0, b1, b2, b3) in real life use cases? I think it will be much more efficient to use c1, c2 continuity while generating multiple bezier curves in 4 point intervals.
nicolel828
From my understanding, the degree of a bezier curve is related to how many control points are used. Therefore, bezier curves of higher degrees will be more complex, and have the ability to represent a wider range of shapes.
stephanie-fu
As the degree increases, it seems like a major downside is controllability - with a specific goal for the whole curve in mind, it seems harder to assign a specific role to each control point.
How does the degree of a Bézier curve affect its shape and flexibility in representing curves or surfaces?
For Bezier curves, the movement of one control point will be cascaded through the remaining points downstream. This is very different from Catmull-Rom interpolation where each control point is only in charge of its own segment of the curve. Is it right to say that Bezier curves are more costly to compute? If so, what are the methods available to speed up the computation?
Since the number of interpolation steps increases with the number of points used in one bezier curve, do we usually stick with 4 points (b0, b1, b2, b3) in real life use cases? I think it will be much more efficient to use c1, c2 continuity while generating multiple bezier curves in 4 point intervals.
From my understanding, the degree of a bezier curve is related to how many control points are used. Therefore, bezier curves of higher degrees will be more complex, and have the ability to represent a wider range of shapes.
As the degree increases, it seems like a major downside is controllability - with a specific goal for the whole curve in mind, it seems harder to assign a specific role to each control point.