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标题: Simple Quad Domains for Field Aligned Mesh Parametrization [打印本页]

作者: 晃晃 时间: 2011-12-28 08:41
标题: Simple Quad Domains for Field Aligned Mesh Parametrization
Simple Quad Domains for Field Aligned Mesh Parametrization

Marco Tarini 1;2 Enrico Puppo3 Daniele Panozzo3 Nico Pietroni1 Paolo Cignoni1

1ISTI-CNR, Italy 2Universit` a dell’Insubria, Italy 3Universit` a di Genova, Italy

Abstract

We present a method for the global parametrization of meshes that

preserves alignment to a cross ﬁeld in input while obtaining a para-

metric domain made of few coarse axis-aligned rectangular patches,

which form an abstract base complex without T-junctions. The

method is based on the topological simpliﬁcation of the cross ﬁeld

in input, followed by global smoothing.

CR Categories: I.3.5 [Computer graphics]: Computational geom-

etry and object modeling—Curve, surface, solid and object repres.

Keywords: quad mesh, mesh parametrization

becoming increasingly common.

A recent trend is to ﬁrst deﬁne a cross ﬁeld C over M, and then

to ﬁnd f such that its gradient vectors match C as much as pos-

sible. Interestingly, each of the criteria above can be redeﬁned in

terms of desired properties of C. Thus the task is shifted from the

deﬁnition of a good parameterization to the deﬁnition of a good

cross ﬁeld C for a given M. High quality parametrization can be

obtained following this approach [Ray et al. 2006; Bommes et al.

2009]. It is now appearent that the deﬁnition of a good cross ﬁeld

C implies, among other things, the good placing of a few irregular

points (a.k.a. cone singularities). Irregular points tend to be needed,

for example, in places where M exhibits high Gaussian curvature.

In this paper, we focus on an important additional criterion for the

quality of f, which we refer to as the simplicity of domain D (see

below for an informal deﬁnition). Simplicity determines how much

a parametrization f will be effectively useful in most applications,

just as much as the other criteria listed above. As we will show, a

cross ﬁeld C designed to satisfy all the above conventional criteria,

but not simplicity, will usually fail producing an acceptably sim-

ple domain. Still, it is often the case that a slightly modiﬁed cross

ﬁeld C0

exists, which is able to generate a parametrization f with a

dramatically simpler domain, while preserving to a large extent the

other qualities of C. This work presents a way to obtain the cross

ﬁeld C0

, given C.

1.1 Objective: Domain Simplicity

For topologies ofM other than the disk, the domain D must neces-

sarily include discontinuities (a.k.a. cuts, or seams): two inﬁnitesi-

mally close points m0 and m1 of M lying of different sides of the

cut may be mapped by f 1

to arbitrarily distant positions d0 and d1

of D. The values d0 and d1 are often constrained to be reciprocally

associated with a “transition function” associated to that cut.

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