I wondered why cubic Beziers appeared to be the highest-order Bezier curve in common use, and found that interestingly, online font formats use a maximum of third order Beziers. This is because in terms of interpolation, there is no clear benefit to using higher degree curves above cubic. Also, some useful properties of cubic and quadratic Beziers do not even apply to higher degree curves, making them potentially harder to work. Higher degree curves also get more and more computationally taxing; since these curves can be simulated by joining multiple lower degree curves together for a lower cost, there are few upsides to using higher degree Beziers after a certain point.
kujjwal
Specifically, what is the performance tradeoff when using higher degree Bezier curves as opposed to second or third order Beziers? Are there cases in which only higher order Bezier curves would work to approximate certain curves, and are there generally any guidelines for when to use a certain degree of Bezier curves to approximate complex curves in images?
myxamediyar
I found this algorithm to be really cool! At first it doesn’t seem like it would draw out a continuous smooth curve, but after attending discussion it becomes more clear. I also wonder if we use an infinite number of lines, would it just draw out a line?
etam1
I found this calculation really cool, how you can take the linear interpolations multiple times to find a point in the curve. A question I do have now is how calculating the bezier curve affect the computational complexity and are there cases where specific curves might make the complexity longer.
andrewn3672
De Casteljau's algorithm didn't make much sense to me originally, but after implementing the project and practicing by hand, it is actually very intuitive and quite simple to understand. I find it very cool how such a simple algorithm can essentially make any curve you want. I do understand why relying on Bezier curves is not ideal as it does take many calculations to render an image.
I wondered why cubic Beziers appeared to be the highest-order Bezier curve in common use, and found that interestingly, online font formats use a maximum of third order Beziers. This is because in terms of interpolation, there is no clear benefit to using higher degree curves above cubic. Also, some useful properties of cubic and quadratic Beziers do not even apply to higher degree curves, making them potentially harder to work. Higher degree curves also get more and more computationally taxing; since these curves can be simulated by joining multiple lower degree curves together for a lower cost, there are few upsides to using higher degree Beziers after a certain point.
Specifically, what is the performance tradeoff when using higher degree Bezier curves as opposed to second or third order Beziers? Are there cases in which only higher order Bezier curves would work to approximate certain curves, and are there generally any guidelines for when to use a certain degree of Bezier curves to approximate complex curves in images?
I found this algorithm to be really cool! At first it doesn’t seem like it would draw out a continuous smooth curve, but after attending discussion it becomes more clear. I also wonder if we use an infinite number of lines, would it just draw out a line?
I found this calculation really cool, how you can take the linear interpolations multiple times to find a point in the curve. A question I do have now is how calculating the bezier curve affect the computational complexity and are there cases where specific curves might make the complexity longer.
De Casteljau's algorithm didn't make much sense to me originally, but after implementing the project and practicing by hand, it is actually very intuitive and quite simple to understand. I find it very cool how such a simple algorithm can essentially make any curve you want. I do understand why relying on Bezier curves is not ideal as it does take many calculations to render an image.