This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Adjustable Speed Surface Subdivision K. Karciauskas and J. Peters Department of Mathematics and Informatics, Vilnius University Dept C.I.S.E., University of Florida Abstract We introduce a nonuniform subdivision algorithm that partitions the neighborhood of an extraordinary point in the ratio : 1 , where (0 , 1) . We call the speed of the nonuniform subdivision and verify C 1 continuity of the limit surface. For = 1 / 2 , the CatmullClark limit surface is recovered. Other speeds are useful to vary the relative width of the polynomial spline rings generated from extraordinary nodes. Key words: nonuniform, subdivision, adjustable speed, = 1 2 = 3 4 = 7 8 = 1 2 = 3 4 = 7 8 Fig. 1. ( left ) Input with gap and ( right three columns) fillings with ( top ) one, respectively ( bottom ) two adjustable speed subdivision steps. Email address: jorg@cise.ufl.edu,kestutis.karciauskas@mif.vu.lt (K. Karciauskas and J. Peters). URL: http://www.cise.ufl.edu/ jorg (K. Karciauskas and J. Peters). Preprint submitted to Dec 2007 1 Introduction To be able to control and adjust, possibly repeatedly, the relative width of the poly nomial surface rings generated by a CatmullClarklike subdivision algorithm (see Figure 1), we derive rules for a new class of nonuniform surface subdivision al gorithms. The resulting family of algorithms has properties akin to CatmullClark subdivision and can in particular generate the limit surface of CatmullClark sub division. Figure 8 shows an application where fast filling of a nsided surface hole is advantageous. In general, the fill speed must depend on the application since the surface quality deteriorates for more rapid fills. We have also used the characteristic rings of adjustable speed subdivision as concentric tessellation map of guided sub division surfaces [KP07b], where the speed controls the parameterization rather than the shape (see Figure 9). The theory is advanced by the paper in that it ex plores a nontraditional approach that allows analyzing the resulting nonuniform subdivision surface. Figure 2 illustrates adjustable speed subdivision in one vari = 1 2 = 2 3 Fig. 2. Univariate localized subdivision near a (central) point, ( left ) in the standard setting and ( right ) adjustable speed subdivision (local truncated geometric progression per half space) with speed = 2 / 3 . ( top two) control point refinement, ( bottom ) knot spacing. able. Instead of subdividing uniformly, we locally subdivide in a ratio : where (0 , 1) and := 1 . We call the speed of the nonuniform subdivision. Since splines are invariant when scaling all knots uniformly or when translating the knot sequence, only the knot spacing is in the following of interest....
View
Full
Document
This note was uploaded on 01/20/2012 for the course CIS 4914 taught by Professor Desimone during the Spring '08 term at University of Florida.
 Spring '08
 Desimone

Click to edit the document details