Warren, JoeWeimer, Henrik2017-08-022017-08-022000-02-14Warren, Joe and Weimer, Henrik. "Subdivision Schemes for Variational Splines." (2000) https://hdl.handle.net/1911/96273.https://hdl.handle.net/1911/96273The original theory of splines grew out of the study of simple variational problems. A spline was a function that minimized some notion of energy subject to a set of interpolation constraints. A more recent method for creating splines is subdivision. In this framework, a spline is the limit of a sequence of functions, each related by some simple averaging rule. This paper shows that the two ideas are intrinsically related. Specifically, the solution space to a wide range of variational problems can be captured as spline spaces defined through subdivision.30 ppengYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, but this permission is only for a period of forty-five (45) days from the most recent time that you verified that this technical report is still available from the Computer Science Department of Rice University under terms that include this permission. All other rights are reserved by the author(s).Technical reportTR00-354