Subdivision is a powerful technique that has many useful applications. The fundamental concept is the splitting of a curve or surface into smaller pieces whose union is identical to the original curve or surface. Standard Bezier subdivision splits the curve at the midpoint of the curve, in parametric space.
This paper generalizes midpoint subdivision to arbitrary subdivision, enabling the subdivision to be performed at any parametric value, not solely at the midpoint. This allows for subdivision that would adapt to regions of varying curvature or correlate with the curve length in geometric space.
After explaining the original development of Bezier curves, the mathematical theory for arbitrary subdivision is developed, and finally an illustration of the subdivision process that shows the recursive procedure in a step-by-step manner is given.
Arbitrary Subdivision of Bezier Curves
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
The Engineering Library
Researchers may make free and open use of the UC Berkeley Library’s digitized public domain materials. However, some materials in our online collections may be protected by U.S. copyright law (Title 17, U.S.C.). Use or reproduction of materials protected by copyright beyond that allowed by fair use (Title 17, U.S.C. § 107) requires permission from the copyright owners. The use or reproduction of some materials may also be restricted by terms of University of California gift or purchase agreements, privacy and publicity rights, or trademark law. Responsibility for determining rights status and permissibility of any use or reproduction rests exclusively with the researcher. To learn more or make inquiries, please see our permissions policies (https://www.lib.berkeley.edu/about/permissions-policies).