Justin Bisceglio

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Given a nonsingular compact two-manifold F without boundary, we present methods for establishing a family of surfaces which can approximate F so that each approximant is ambient isotopic to F: The methods presented here offer broad theoretical guidance for a rich class of ambient isotopic approximations, for applications in graphics, animation and surface(More)
We report new techniques and theory in computational topology for reconstructing surfaces with boundary. This complements and extends known techniques for surfaces without boundary. Our approach is motivated by differential geometry and differential topology. We have also conducted significant experimental work to test our resultant implementations. We(More)
The Boolean algebra of regular closed sets is prominent in topol-ogy, particularly as a dual for the Stone-ˇ Cech compactification. This algebra is also central for the theory of geometric computation, as a representation for combinatorial operations on geometric sets. However, the issue of computational approximation introduces unresolved subtleties that(More)
An example is presented of a cubic Bézier curve that is the unknot (a knot with no crossings), but whose control polygon is knotted. It is also shown that there is no upper bound on the number of crossings in the control polygon for an unknotted Bézier curve. These examples complement known upper bounds on the number of subdivisions sufficient for a control(More)
Given a nonsingular compact 2-manifold ¦ without boundary, we present methods for establishing a family of surfaces which can approximate ¦ so that each approximant is ambient isotopic to ¦. The methods presented here offer broad theoretical guidance for a rich class of ambient isotopic approximations, for applications in graphics, animation and surface(More)
This paper presents computational topology techniques for reconstruction of surfaces with boundary, where all manifolds considered are assumed to be embedded in R 3. The focus here is upon examples and applications, with the theoretical basis being presented in a companion paper. As a step towards these results, we consider any C 2 compact 2-manifold M with(More)
Meshes with T-joints (T-meshes) and related high-order surfaces have many advantages in situations where flexible local refinement is needed. At the same time, designing subdivision rules and bases for T-meshes is much more difficult, and fewer options are available. For common geometric modeling tasks it is desirable to retain the simplicity and(More)
This paper presents new mathematical foundations for topologically correct surface reconstruction techniques that are applicable to 2-manifolds with boundary, where provable techniques previously had been limited to surfaces without boundary. This is done by an intermediate construction of the envelope (as defined herein) of the original surface. For any(More)
In <i>Epic</i> (2013), crowds are integral to the narrative and form a character as a whole. This required a new type of crowd at Blue Sky Studios, one that permits dynamic interaction between crowd characters and the environments around them in addition to supporting the high-resolution geometry with fur, deformation rigs, and material complexities needed(More)
New computational topology techniques are presented for surface reconstruction of 2-manifolds with boundary, while rigorous proofs have previously been limited to surfaces without boundary. This is done by an intermediate construction of the envelope (as defined herein) of the original surface. For any compact C 2 manifold M embedded in R 3 , it is shown(More)