LOD Generation with Discrete Curvature Error Metric 1 Abstract

retain a good approximation to the original shape and appearance. LOD is generally the representation of a geometric object using different versions having different levels of accuracy and complexity. The data of reconstructed models using range scanning systems can be compressed, simplified, or represented as LOD. LOD can be built easily by the repeated application of any simplification algorithm with different error metrics. Such a simple framework is a straightforward application of the mesh simplification technology. There is more advanced representation, which is called multiresolution. Arbitrary meshes must be remeshed to be converted multiresolution form based on subdivision and wavelet [4]. Though curvature can express characteristics of polyhedral surface, it is difficult to use curvature as simplification criterion [6, 17] or adapt it to other applications since it is not easy to estimate curvature accurately. Discrete curvature is useful to enhance the shape description of triangular surface and results from a geometric reasoning without requiring any smooth approximation. Therefore, discrete curvature is a good criterion of simplification that can preserve an original model’s shape well. Error metric is the difference between two polygonal models. Two models that have small error metric are very similar with each other [5]. Error metric is usually defined as the distance between original and simplified models. Some error metrics combine other attributes – color, normal, and texture coordinator – but it is complex to represent altogether. In some simplification methods, LOD is generated by a simplification ratio. But we suggest that LOD should be generated by an error metric, because level of detail means the degree of closeness between original and
2.1 Error Metric
Error metrics can be classified by the method of estimating error between original and simplified models [15] - global or local, and geometry only or geometry with attributes. Local error metric estimates error using local geometric information. Most decimation methods use this metric [17, 14]. Global error metric gives error bound that applies globally. Simplification envelope [3] makes two offset surfaces from the given model, and samples triangles that exist between them. Clustering [16] and superface [13] also use global error metric. Many simplification methods use geometric information for their error metric. QEM[8] uses Euclidean distance between a face and a point as an error metric. Error metrics of geometric optimization [10], mesh reduction with error control [14], and data reduction scheme [9] also include this kind of error metrics. Some error metrics combine attributes and geometric information together. QEM[7] combines geometric coordinator and attribute coordinator, and estimates error in the high dimension space. New QEM[11] also includes attribute, but 3 estimates in R space. Approximated curvature has been used as simplification criteria. In retiling [18], curvature approximates the radius of the largest sphere that is placed on the more curved side of the surface. In data reduction scheme [9], the absolute curvature is used, which is the absolute value of principal curvature. In static polyhedron simplification [19], the Gaussian curvature is also used and error zone is defined with a sphere as error bound at each vertex. Like above, although curvature is useful for describing characteristics of polygonal model, it is not usually used in simplification because of its difficulty of computation and estimation. This paper proposes to use discrete curvature as error metric to generate LOD. Discrete curvature doesn’t require any smooth approximation, but is computed by geometric reasoning [6]. It characterizes surface on the basis of geometric attributes assigned to edges and triangles, therefore it can describe the surface shape. LOD generation with discrete curvature error metric is useful to preserve the shape of the original surface.
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LOD Generation with Discrete Curvature Error Metric
S. J. Kim, W. K. Jeong, and C. H. Kim1 Dept. of Computer Science & Engineering Korea University
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Abstract
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Introduction