Abstract
Polygonal meshes and particularly triangular meshes are the most used structure for 3D modelling. The ‘direct edges’ data structure is the most efficient way to represent them and subdivision surfaces is an appropriate method to generate them. From a review of subdivision surfaces we chose the ‘√3 subdivision’ method for mesh generation. Our main challenge was to take advantage of the direct edges data structure and to find the right formulas for an efficient implementation. We decided to use files in the 3DS file format and convert them to the direct edges data structures for use in our application. We tested our algorithm with arbitrary mesh topologies and calculated efficiency. Our implementation will be used in the creation of a virtual dog head.
Highlights
We needed an adequate method to represent the surface of a 3D virtual dog skull that will be part of a bigger project [1]
Parametric representations are better for evaluation and modification, implicit representations are better for query [2]
Coarse meshes may bring distorted triangles and edges (i.e. “nonmanifold meshes are problematic for most algorithms, since around non-manifold configurations there exist no well-defined local geodesic neighbourhood”), [2, p.19]
Summary
We needed an adequate method to represent the surface of a 3D virtual dog skull that will be part of a bigger project [1]. Complex shapes require piecewise representations and are split in sub-regions each one of which is defined by an individual function. These representations are just approximations of the surface and it can be demonstrated from the Taylor theorem that the approximation error in an interval h of the surface by a polynomial of degree p is O(h p+1). Operations required by surfaces include evaluation, query and modification. Parametric representations are defined by a vector valued parameterization function (1). Implicit or volumetric representations are defined by a zero set of a scalar valued function (2) [2]. Parametric representations are better for evaluation and modification, implicit representations are better for query [2]
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