I think it's very clever how the de Casteljau algorithm extends to 3D! Creating multiple Bezier curves, then creating a Bezier curve in the third dimension along the Bezier curves seems like it's very good for maintaining smoothness across our object of interest in the third dimension.
myxamediyar
I found it fascinating just how easily de Casreljau's algorithm extends to 3D. Looking at other mathematical constructions of the Bezier curves, I could've imagined that it would be a nightmare to intuit about them in higher dimensions, but the parametrization of multiple Bezier curves is very generalizable.
jacky-p
I also believed that de Casteljau's application to surfaces would involve lots of complicated math but was amazed on how this algorithm built on itself. It's interesting how one can find the Bezier surface point by essentially "eliminating" a dimension at a time in order to reach a final point. As in evaluating all point u in u space and then using those to evaluate in v space to come to a final point.
mananb77
The 1D separability of the algorithm is highly clever and efficient, since we can have several curves in vector u, and create a moving curve from vector v which results in a full surface point is a very unique way to establish the evaluation of the point. Great work, Casteljau.
angelinelykk
This slide was initially confusing to me as I thought the 1D referred to a bezier curve of order 1 but that did not make sense. The 1D in this case refers to 1 dimensional so like a single line across the control points.
angelajyzhang
de Casteljau's algorithm makes the transferral from Bezier curves to finding the surface position of a Bezier surface very easy to follow. It is very intuitive how to apply 1D de Casteljau first on separate curves and then use those points as the new control points to find the surface point.
I think it's very clever how the de Casteljau algorithm extends to 3D! Creating multiple Bezier curves, then creating a Bezier curve in the third dimension along the Bezier curves seems like it's very good for maintaining smoothness across our object of interest in the third dimension.
I found it fascinating just how easily de Casreljau's algorithm extends to 3D. Looking at other mathematical constructions of the Bezier curves, I could've imagined that it would be a nightmare to intuit about them in higher dimensions, but the parametrization of multiple Bezier curves is very generalizable.
I also believed that de Casteljau's application to surfaces would involve lots of complicated math but was amazed on how this algorithm built on itself. It's interesting how one can find the Bezier surface point by essentially "eliminating" a dimension at a time in order to reach a final point. As in evaluating all point u in u space and then using those to evaluate in v space to come to a final point.
The 1D separability of the algorithm is highly clever and efficient, since we can have several curves in vector u, and create a moving curve from vector v which results in a full surface point is a very unique way to establish the evaluation of the point. Great work, Casteljau.
This slide was initially confusing to me as I thought the 1D referred to a bezier curve of order 1 but that did not make sense. The 1D in this case refers to 1 dimensional so like a single line across the control points.
de Casteljau's algorithm makes the transferral from Bezier curves to finding the surface position of a Bezier surface very easy to follow. It is very intuitive how to apply 1D de Casteljau first on separate curves and then use those points as the new control points to find the surface point.