A New Mesh Simplification Algorithm Based on Triangle Collapses

In this paper a new mesh simplification algorithm based on triangle collapses is presented. The algorithm can provide efficient error management and simplify the original mesh greatly. Progressive meshes may be constructed with triangle collapsing operation. To make continuous transition between level of detail (LOD) models possible, a method for interpolating is also presented. Examples illustrate the efficiency of the algorithm.

Feature Preserving Mesh Simplification Using Feature Sensitive Metric

We present a new method for feature preserving mesh simplification based on feature sensitive （FS） metric. Previous quadric error based approach is extended to a high-dimensional FS space so as to measure the geometric distance together with normal deviation. As the normal direction of a surface point is uniquely determined by the position in Euclidian space, we employ a two-step linear optimization scheme to efficiently derive the constrained optimal target point. We demonstrate that our algorithm can preserve features more precisely under the global geometric properties, and can naturally retain more triangular patches on the feature regions without special feature detection procedure during the simplification process. Taking the advantage of the blow-up phenomenon in FS space, we design an error weight that can produce more suitable results. We also show that Hausdorff distance is markedly reduced during FS simplification.

Mesh simplification algorithm based on edge curvature metrics and local optimization

Aiming at the problem that the mesh simplification algorithm loses the geometric features of the model in large-scale simplification,an improved half-edge collapse mesh simplification algorithm is proposed.The concept of approximate measurement of edge curvature is introduced,and the edge curvature is added to the error measure,so that the order of half-edge collapse of the mesh is changed,and the simplified details of the mesh model can be preserved accurately.At the same time,by analyzing the quality of simplified triangular mesh,optimizing triangular mesh locally,reducing the amount of narrow triangles,the quality of the simplified model is improved.The proposed algorithm was tested on Cow model,Car model and Bunny model,and compared with another three algorithms,one of them is a classical mesh simplification algorithm based on edge collapse,the other is an improved algorithm of the classical one.The experimental results show that the improved algorithm can better retain the detail features of the original model at the same reduction ratio,and has reasonable mesh allocation,fast execution speed and small error.

Laplacian-based 3D mesh simplification with feature preservation

We propose a novel Laplacian-based algorithm that simplifies triangle surface meshes and can provide different preservation ratios of geometric features.Our efficient and fast algorithm uses a 3D mesh model as input and initially detects geometric features by using a Laplacian-based shape descriptor(L-descriptor).The algorithm further performs an optimized clustering approach that combines a Laplacian operator with K-means clustering algorithm to perform vertex classification.Moreover,we introduce a Laplacian weighted cost function based on L-descriptor to perform feature weighting and error statistics comparison,which are further used to change the deletion order of the model elements and preserve the saliency features.Our algorithm can provide different preservation ratios of geometric features and may be extended to handle arbitrary mesh topologies.Our experiments on a variety of 3D surface meshes demonstrate the advantages of our algorithm in terms of improving accuracy and applicability,and preserving saliency geometric features.

Complex Model Simplification Algorithm with Improved Error Evaluation

Given the framework of incremental mesh simplification based on edgecollapse, the paper proposes a mesh simplification algorithm using an improved approach formeasuring simplification error. The algorithm uses edge collapse to simplify the trianglemesh andmaintains surface error approximations using c-error for the faces which have changed after edgecollapse and d-crror for the faces which become degenerated after edge collapse. Also, we reportsome results using a variety of computer graphics models, which can show that the algorithm canachieve the desired simplification effect.

3D Engineering Model Retrieval Based on Enhanced Shape Distributions

To reuse and share the valuable knowledge embedded in repositories of engineering models for accelerating the design process, improving product quality, and reducing costs, it is crucial to devise search engines capable of matching 3D models efficiently and effectively. In this paper, an enhanced shape distributions-based technique of using geometrical and topological information to search 3D engineering models represented by polygonal meshes was presented. A simplification method of polygonal meshes was used to simplify engineering model as the pretreatment for generation of sample points. The method of sampling points was improved and a pair of functions that was more sensitive to shape was employed to construct a 2D shape distribution. Experiments were conducted to evaluate the proposed algorithm utilizing the Engineering Shape Benchmark (ESB) database. The experiential results suggest that the search effectiveness is significantly improved by enforcing the simplification and enhanced shape distributions to engineering model retrieval.

Method of Direct Texture Synthesis on Arbitrary Surfaces

A direct texture synthesis method on arbitrary surfaces is proposed in thispaper. The idea is to recursively map triangles on surface to texture space until the surface iscompletely mapped. First, the surface is simplified and a tangential vector field is created overthe simplified mesh. Then, mapping process searches for the most optimal texture coordinates intexture sample for each triangle, and the textures of neighboring triangles are blended on the mesh.All synthesized texture triangles are compressed to an atlas. Finally, the simplified mesh issubdivided to approach the initial surface. The algorithm has several advantages over formermethods: it synthesizes texture on surface without local parameterization; it does not needpartitioning surface to patches; and it does not need a particular texture sample. The resultsdemonstrate that the new algorithm is applicable to a wide variety of texture samples and anytriangulated surfaces.

Automatic Cage Building with Quadric Error Metrics

Modern computer graphics applications usually require high resolution object models for realistic rendering. However, it is expensive and difficult to deform such models in real time. In order to reduce the computational cost during deformations, a dense model is often manipulated through a simplified structure, called cage, which envelops the model. However, cages are usually built interactively by users, which is tedious and time-consuming. In this paper, we introduce a novel method that can build cages automatically for both 2D polygons and 3D triangular meshes. The method consists of two steps： 1） simplifying the input model with quadric error metrics and quadratic programming to build a coarse cage; 2） removing the self-intersections of the coarse cage with Delaunay partitions. With this new method, a user can build a cage to envelop an input model either entirely or partially with the approximate vertex number the user specifies. Experimental results show that, compared to other cage building methods with the same number of vertex, cages built by our method are more similar to the input models. Thus, the dense models can be manipulated with higher accuracy through our cages.

An Algorithm for LOD by Merging Near Coplanar Faces Based on Gauss Sphere

LOD (Level of Detail) models are widely used recently to accelerate the rendering of 3D scenes. An algorithm that creates multiple levels of detail for 3D scene by merging near-coplanar faces is presented in this paper. First a Gauss sphere is defined for the model of scene and it is divided into meshes near-uniformly. Then, the faces of objects are attached to the respective spherical meshes according to their normal direction. If faces attached to the same mesh are connected with each other, they are merged to form a near coplanar patch (Superface). Isolated vertices inside the patch are removed and the patch is retriangulated. To further improve the simplification, vicinity vertices on the boundary of the surface patch are merged. In the algorithm, a planar separate rule planar-enneatree is adopted to set up a hierarchical structure of the Gauss sphere, which is used to support the hierarchical model of the scene (LOD). The experimental result shows that the algorithm can achieve desired simplification effects.