Analysis of Algorithms Generalizing B-Spline Subdivision
نویسندگان
چکیده
منابع مشابه
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
We introduce a new class of subdivision surfaces which generalize uniform tensor product B-spline surfaces of any bi-degree to meshes of arbitrary topology. Surprisingly , this can be done using subdivision rules that involve direct neighbors only. Consequently, our schemes are very easy to implement, regardless of degree. The famous Catmull-Clark scheme is a special case. Similarly we show tha...
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Subdivision surfaces would be useful in a greater number of applications if an arbitrary-degree, non-uniform scheme existed that was a generalisation of NURBS. As a step towards building such a scheme, we investigate non-uniform analogues of the Lane-Riesenfeld ‘refine and smooth’ subdivision paradigm. We show that the assumptions made in constructing such an analogue are critical, and conclude...
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Abstract. We describe and demonstrate an arrow notation for deriving box-spline subdivision schemes. We compare it with the z-transform, matrix, and mask convolution methods of deriving the same. We show how the arrow method provides a useful graphical alternative to the three numerical methods. We demonstrate the properties that can be derived easily using the arrow method: mask, stencils, con...
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The application of spline subdivision schemes to data consisting of convex compact sets with addition replaced by Minkowski sums of sets is investigated These methods generate in the limit set valued functions which can be expressed explicitly in terms of linear com binations of integer shifts of B splines with the initial data as coe cients The subdivision techniques are used to conclude that ...
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Article history: Received 17 March 2011 Received in revised form 24 November 2011 Accepted 29 November 2011 Available online 7 December 2011
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 1998
ISSN: 0036-1429,1095-7170
DOI: 10.1137/s0036142996304346