A geometric diagram and hybrid scheme for triangle subdivision
نویسندگان
چکیده
We introduce a geometrical diagram to study the improvement in shape of triangles generated by iterative application of triangle subdivision. The four Triangles Longest Edge (4TLE) subdivision pattern and a new hybrid 4T Longest-Edge/Self-Similar (hybrid 4TLE-SS) scheme are investigated in this way. The map diagram provides a convenient way to visualize the evolution and migration of element shapes leading to a better understanding of the improvement process and the effect of recursive subdivision schemes. A complex variable mapping analysis supports the diagram and similarity class specifications. Numerical comparisons confirm the superiority of the new hybrid scheme. © 2006 Elsevier B.V. All rights reserved.
منابع مشابه
Interpolatory quad/triangle subdivision schemes for surface design
Recently the study and construction of quad/triangle subdivision schemes have attracted attention. The quad/triangle subdivision starts with a control net consisting of both quads and triangles and produces finer and finer meshes with quads and triangles. The use of the quad/triangle structure for surface design is motivated by the fact that in CAD modelling, the designers often want to model c...
متن کاملRefinement operators for triangle meshes
Refinement operators for triangular meshes as used in subdivision schemes or remeshing are discussed. A numbering scheme is presented, covering all refinement operators that (topologically) map vertices onto vertices. Using this characterization, some special properties of n-adic and √ 3-subdivision are easy to see.
متن کاملAn Approximating-Interpolatory Subdivision scheme
In the last decade, study and construction of quad/triangle subdivision schemes have attracted attention. The quad/triangle subdivision starts with a control mesh consisting of both quads and triangles and produces finer and finer meshes with quads and triangles (Fig. 1). Designers often want to model certain regions with quad meshes and others with triangle meshes to get better visual quality ...
متن کاملA Hermite interpolatory subdivision scheme for C2-quintics on the Powell-Sabin 12-split
In order to construct a C1-quadratic spline over an arbitrary triangulation, one can split each triangle into 12 subtriangles, resulting in a finer triangulation known as the Powell-Sabin 12-split. It has been shown previously that the corresponding spline surface can be plotted quickly by means of a Hermite subdivision scheme [5]. In this paper we introduce a nodal macroelement on the 12-split...
متن کاملSubdivision Tree Representation of Arbitrary Triangle Meshes
We investigate a new way to represent arbitrary triangle meshes. We prove that a large class of triangle meshes, called normal triangle meshes, can be represented by a subdivision tree, where each subdivision is one of four elementary subdivision types. We also show how to partition an arbitrary triangle mesh into a small set of normal meshes. The subdivision tree representation can be used to ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computer Aided Geometric Design
دوره 24 شماره
صفحات -
تاریخ انتشار 2007