Home of Xiaobin (Eric) Wu

About me:

My research areas are Computer Graphics, Computer Aided Geometric Design and Numerical Algorithms.
I worked in the Graphics Lab in University of Florida. My advisor is Dr. Jorg Peters.

I graduated in Aug. 2005 with a Ph.D. degree and now I am working in Solidworks Research.

Office: Room E325, CSE building, Gainesville, FL 32611.
tel: (352)392-1255
Email: xwu @ cise.ufl.edu.


On the Local Linear Independence of Generalized Subdivision Functions
Jorg Peters, Xiaobin Wu SIAM Journal on Numerical Analysis 2006

Abstract: Characterizing the linear and local linear independence of the functions that span a linear space is a key task if the space is to be used computationally. Given the control net, the spanning functions of one spatial coordinate of a generalized subdivision surface are called nodal functions. They are the limit, under subdivision, of associating the value one with one node and zero with all others. No characterization of independence of nodal functions has not been published to date, even for the two most popular generalized subdivision algorithms, Catmull-Clark subdivision and Loop's subdivision. This paper provides a road map for the verification of linear and local linear independence of generalized subdivision functions. It proves the conjectured global independence of the nodal functions of both algorithms; disproves local linear independence (for higher valences); and establishes linear independence on every surface region corresponding to a facet of the control net. Subtle exceptions, even to global independence, underscore the need for a detailed analysis to provide a sound basis for a number of recently developed computational approaches. [pdf]

Two different control polygons
leading to same Catmull-Clark surface.

An Accurate Error Measure for Adaptive Subdivision Surfaces
Xiaobin Wu, Jorg Peters, Shape Modeling International 2005

Abstract: A tight estimate on the maximum distance between a subdivision surface and its linear approximation is introduced to guide adaptive subdivision with guaranteed accuracy. [pdf]

Interference Detection for Subdivision Surfaces
Xiaobin Wu, Jorg Peters, Eurographics 2004

Abstract: Accurate and robust interference detection and ray-tracing of subdivision surfaces requires safe linear approximations. Due to the exponential growth of the number of facets, approximation by the subdivided polyhedron can be both costly and inaccurate. This paper shows how a standard intersection hierarchy, such as an OBB tree, can be made safe and efficient for subdivision surface interference detection. The key is to construct, on the fly, optimally placed triangles, whose spherical offsets tightly enclose the limit surface. The offset triangles can be locally subdivided and they can be efficiently intersected based on standard triangle-triangle interference detection. [pdf] Source Code:[zip] [tar.gz]

SLEVEs for planar spline curves
Jorg Peters, Xiaobin Wu, Computer Aided Geometric Design 2004

Abstract: Given a planar spline curve and local tolerances, a matched pair of polygons is computed that encloses the curve and whose width (distance between corresponding break points) is below the tolerances. This is the simplest instance of a subdividable linear efficient variety enclosure, short sleve. We develop general criteria, that certify correctness of a global, polygonal enclosure built from a sequence of individual bounding boxes by extending and intersecting their edges. These criteria prove correctness of the sleve construction. [pdf]

On the optimality of piecewise linear max-norm enclosures based on slefes
Jorg Peters, Xiaobin Wu, proceedings of Curves and Surfaces, St Malo, 2002

Abstract: Subdividable linear efficient function enclosures (Slefes) provide, at low cost, a piecewise linear pair of upper and lower bounds f^+, f^-, that sandwich a function f on a given interval: f^- <= f <= f^+. In practice, these bounds are observed to be very tight. This paper addresses the question just how close to optimal, in the max-norm, the slefe construction actually is. Specifically, we compare the width (f^+)-(f^-) of the slefe to the narrowest possible piecewise linear enclosure of f when f is a univariate cubic polynomial. [pdf]




What is BezierView: BezierView is a light weight viewer that renders Bezier patches, rational Bezier patches and polygonal meshes. It provides a simple tool to analyze surfaces based on curvature plots, curvature needle plots, and highlight line plots.
Last updated: Feb 18th 2007.

Pov-Ray with Subdivision (Pov-Sub)

What is Pov-Sub: This is an expansion of POV-Ray (Persistence of Vision Raytracer), a very popular (and free!) ray-tracing software. We enhanced the POV-Ray rendering kernel with subdivision surfaces (Loop's Scheme). With this expanded version, you can easily create high-quality ray-tracing images using smooth subdivision surfaces.
Last updated: Jan 30th 2005.

Thanks for visiting my website.
Last Updated: Nov 07th, 2006.