Simplification envelopes

Abstract

We propose the idea of simplification envelopes for generating a hierarchy of level-of-detail approximations for a given polygonal model. Our approach guarantees that all points of an approximation are within a user-specifiable distance from the original model and that all points of the original model are within a distance from the approximation. Simplification envelopes provide a general framework within which a large collection of existing simplification algorithms can run. We demonstrate this technique in conjunction with two algorithms, one local, the other global. The local algorithm provides a fast method for generating approximations to large input meshes (at least hundreds of thousands of triangles). The global algorithm provides the opportunity to avoid local "minima" and possibly achieve better simplifications as a result.Each approximation attempts to minimize the total number of polygons required to satisfy the above constraint. The key advantages of our approach are:General technique providing guaranteed error bounds for genus-preserving simplification Automation of both the simplification process and the selection of appropriate viewing distances Prevention of self-intersection Preservation of sharp features Allows variation of approximation distance across different portions of a model

Using Polyhedral Models to Automatically Sketch Idealized Geometry for Structural Analysis

“…a two-manifold model) without topological changes. Among this set of techniques, those which allow the restoration of the initial geometry according to a geometric criterion (references [12], [13] for example) can be distinguished from those which do not explicitly use such a criterion (references [14], [15], [16], [17], [18] for example). Previous works have also led us to develop a simplification approach [19], [20] with specific shape preservation criteria.…”

“…Such simplified models are not useful for structural [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] analysis where the topology of a model can be critical with respect to the mechanical behavior modeled. For visualization purposes, the use of these models often significantly alters the realism of the graphic scene.…”

Adaptive real-time level-of-detail based rendering for polygonal models

“…Turk [35] and Hamann [21] have proposed curvature-guided adaptive simplification with lesser simplification in the areas of higher surface curvature. In [10], [36], adaptive surface approximation is proposed with different amounts of approximation over different regions of the object. Guéziec [20] proposes adaptive approximation by changing the tolerance volume in different regions of the object.…”

“…Recent research on graphics acceleration for the navigation of such three-dimensional environments has been motivated by attempts to bridge the gap between the desired and the actual hardware performance, through algorithmic and software techniques. This research has involved reducing the geometric and rendering complexities of the scene by usinḡ statically computed level-of-detail hierarchies [10], [14], [22], [25], [31], [32], [35], visibility-based culling that is statically computed [1], [34] and dynamically computed [17], [18], [27], various levels of complexity in shading and illumination models [4], texture mapping [5], [6], and image-based rendering [7], [8], [13], [29], [33]. In this paper we will focus on reducing the geometric complexity of a three-dimensional environment by using dynamically computed level-of-detail hierarchies.…”

“…Some of the local approaches have been -vertex deletion by Schroeder et al [32], vertex collapsing by Rossignac and Borrel [31], edge collapsing by Hoppe et al [26] and Guéziec [20], triangle collapsing by Hamann [21], and polygon merging by Hinker and Hansen [24]. Some of the global approaches have been -redistributing vertices over the surface by Turk [35], minimizing global energy functions by Hoppe et al [26], using simplification envelopes by Varshney [36] and Cohen et al [10], and wavelets by DeRose et al [14]. The issue of preservation or simplification of the genus of the object is independent of whether an algorithm uses local rules, or global rules, or both, to simplify.…”