To avoid excessive details, thus omitting less important content, of three-dimensional 3D geometric models, this study proposes a fast mesh simplification method based on an energy-operator for 3D geometric models with salient feature-preserving efficiency. The energy-operator can evaluate the smoothness and complexity of the regional mesh in 3D models. Accordingly, it can be directly used to simultaneously reduce the candidate triangle and its three neighboring triangles.

The proposed method can dramatically collapse the excessive details in relatively smooth areas and preserve more important salient features during the simplification process. It can also maintain a trade-off between time efficiency and salient feature-preserving accuracy. The effectiveness and efficiency of the new method are demonstrated by comparing it with OpenMesh, which is considered the most popular mesh operation software and is capable of achieving accurate mesh simplification models.

The new mesh simplification method based on the energy-operator can provide accurate and concise models for interactive 3D rendering, calculating, simulating, and analyzing. Along with the development of high-resolution data acquisition techniques, such as three-dimensional 3D laser scanning, 3D geometric models have become increasingly more complex [ 1 — 4 ].

However, such complex 3D geometric models are not always needed. Due to the limitations in graphics hardware, these models are all difficult to interactively render, calculate, simulate, and analyze [ 235 — 8 ].

In addition to improving the capacity of graphics hardware, it is essential to develop a highly efficient mesh simplification method to avoid excessive details of 3D geometric models [ 79 — 15 ]. Mesh simplification is widely used in many industrial areas, such as engineering applications, 3D printing, and cultural heritage protection [ 31617 ]. For engineering applications, in order to improve the efficiency in dynamically simulating complex CAD models, an efficient mesh simplification method is required.

Meanwhile, to meet the simulation requirements of engineering precision, simplified models should preserve main features of original models. For 3D printing, in order to print models faster, mesh simplification can be used to generate sparse wireframe models from the complex solid models.

For the cultural heritage protection, the volume of cultural heritage models is extremely huge and poses a serious challenge for visualization. Mesh simplification is an important method to reduce the triangle or other geometrical cells numbers. Thus, the highly efficient mesh simplification method is becoming an essential issue for many industrial areas. By studying the related work Section 2 adequately, we propose a faster mesh simplification method for 3D geometric models with salient feature-preserving efficiency.

An energy-operator is used to calculate the complexity of triangles, which is described in Section 3. The energy-operator accounts for the geometrical characters of the neighboring triangles and collapses three edges of a specific triangle in one contraction process. The new method is considered a trade-off for time efficiency and salient feature preservation.

Section 3 introduces the methodology of the new method, which is applied to simplify three popular 3D geometric models in Case Study Section 4. In Section 5we discuss and demonstrate the efficiency and validation of the new simplification method in comparison with OpenMesh. Various methods have been proposed for mesh simplification, and these can be divided into three main categories: vertex decimation, vertex clustering, and iterative edge contraction [ 5 — 818 — 20 ].

Vertex decimation methods involve three major steps: selection of candidate vertexes that satisfy a distance or an angle criterion, removal of loop triangles around the candidate vertexes, and triangulation of the resulting holes [ 91820 — 22 ].

Although these methods are time-efficient, the candidate vertex selection criterion is based on a local error estimate and therefore cannot guarantee the boundary errors.

Moreover, they can only preserve positions, and few salient features are preserved during simplification [ 71922 ]. Vertex clustering methods use grid structures to divide the original model into clusters and then compute a new vertex to represent each cluster [ 23 — 25 ].

These methods are time-efficient and have a high data reduction rate. However, grid size often results in a geometric error bound; as a result, the simplified mesh has very low quality and cannot preserve more salient features [ 619 ].

For the iterative edge contraction methods, the main idea is to collapse edges into new vertexes iteratively [ 626 — 28 ]. The essential difference between these methods lies in how they choose an edge to contract [ 6 ].All Rights Reserved. Registration Log In. Engineering Research. Advanced Engineering Forum. Journal of Biomimetics, Biomaterials and Biomedical Engineering.

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This waifu does not existLimited Collections. Specialized Collections. Retrospective Collection. Home Mesh Simplification. Papers by Keyword: Mesh Simplification. Paper Title Page. On the other hand, 3D model processing technologies has long been researched in computer graphics CG fields. However, few algorithms were designed for the application of machining and manufacturing. In this paper, the current researches about the 3D model processing technologies in the application of freeform surface machining were introduced.

These researches take the advantage of 3D model processing technology, and focus on the application of machining and manufacturing. Abstract: In order to implement progressive mesh representation of 3D model, improve the computing method of collapse cost in mesh simplification. Firstly, obtains model data from smf data file, and rapidly establishes the 3D model in the memory, and redesigns weight computing method of Garland QEM algorithm. Using the square of the largest deviation of triangular plane normal adjacent to the vertex as the importance degree of vertex, and brings it into error metric formula, progressive mesh is generated by simplifying.

The following experiment shows that the algorithm is succinct, and the generating speed of mesh and the contour information of model are well preserved. A Short Review on Mesh Simplification. Abstract: Mesh simplification plays an important role in the process of 3D models, such as storage, transmission and real-time rendering.

By analyzing the basic techniques and algorithms of mesh simplification, the paper describes the the typical methods in detail and analyzes the major characters of these methods. The future work of mesh simplification is discussed in the end. Abstract: Mesh simplification should not only emphasize high compression ratio, but also maximize retention of a mesh representation which is another objective of mesh compression.This utility application claims the benefit of U.

Provisional Patent Application No. The present invention relates generally to computer graphics processing. More particularly, the present invention relates to systems and methods for performing real-time polygonal mesh simplification. Massive polygonal datasets have become widely available, particularly because of advances in data acquisition.

However, interactive rendering of such massive geometry in computer games or other applications can be impractical due to the performance penalty for vertex throughput and the associated large memory storage requirements. As a result, mesh simplification has been an active area of research. In general, mesh simplification entails transforming an input mesh containing a number of triangles into a simplified mesh having fewer triangles that approximates well the original mesh.

Various mesh simplification algorithms have been devised to decimate a triangle mesh. Some algorithms employ vertex clustering, which involves placing an input mesh into a bounding box, and dividing the box into a grid. In a simplest case, the result is a rectilinear lattice of cubes, with all vertices in a given cube or cell being replaced with a single representative vertex i. Faces that become degenerate are removed from the resulting simplified mesh.

Other mesh simplification algorithms take an iterative approach, in which a series of primitive simplification operations are applied to an input mesh through intermediate simplification stages. Usually, the choice of operations attempts to minimize the incremental error incurred by the operations.

Simplification of massive datasets demands computational efficiency and effective use of available memory. Traditionally, methods developed for mesh simplification and decimation are designed with the CPU architecture and programming model in mind. Consequently, mesh simplification has been a slow, CPU-limited operation performed as a non-interactive process on static meshes.

In one aspect, the invention features a method of mesh simplification comprising decimating, by a graphics-processing unit, a dataset for an input mesh that describes a three-dimensional graphics object to produce a simplified mesh that describes the three-dimensional graphics object in less detail than the input mesh.

In another aspect, the invention features a graphics-processing unit comprising a vertex shader receiving a dataset for an input mesh that describes a three-dimensional graphics object.

The vertex shader is configured to generate from the dataset vertices for primitives that make up the input mesh. A geometry shader receives the vertices from the vertex shader and is programmed to generate from the received vertices a simplified mesh that describes the three-dimensional graphics object in less detail than the input mesh.

In still another aspect, the invention features computer-useable medium storing computer-readable instructions, wherein the computer-readable instructions when executed on a computer causes a graphics-processing unit of the computer to decimate a data set for an input mesh that describes a three dimensional object to produce a simplified mesh that describes the three-dimensional graphics object in less detail than the input mesh.

The above and further advantages of this invention may be better understood by referring to the following description in conjunction with the accompanying drawings, in which like numerals indicate like structural elements and features in the various figures. The drawings are not meant to limit the scope of the invention. For clarity, not every element may be labeled in every figure.

## Real-time mesh simplification using the GPU

The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. Traditionally, mesh simplification or mesh decimation has been a non-interactive process performed by algorithms restricted to execution on the central processing unit CPU.

The present invention recognizes that the large-scale parallelism of the streaming architecture of current graphics-processing units GPUs and the introduction of a geometry shader to GPU pipelines make the traditionally non-interactive process of mesh simplification amenable to practical, real-time interactive execution on a GPU.

Graphics systems embodying the present invention have a programmable GPU that performs real-time mesh simplification. During the performance of mesh simplification, the GPU takes advantage of a geometry shader stage to use a vertex clustering method. In addition, the use of non-linear warping functions enables a user to preserve details of select portions of the object.Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly.

DOI: Recent advances in real-time rendering have allowed the GPU implementation of traditionally CPU-restricted algorithms, often with performance increases of an order of magnitude or greater. Such gains are achieved by leveraging the large-scale parallelism of the GPU towards applications that are well-suited for these streaming architectures. By contrast, mesh simplification has traditionally been viewed as a non-interactive process not readily amenable to GPU acceleration.

View on ACM. Open Access. Save to Library. Create Alert. Launch Research Feed. Share This Paper. Figures, Tables, and Topics from this paper. Figures and Tables. Citations Publications citing this paper. Forum References Publications referenced by this paper. Adaptive vertex clustering using octrees. Surface simplification using quadric error metrics Michael GarlandPaul S.

Decimation of triangle meshes William J. SchroederJonathan A. ZargeWilliam E. Related Papers. By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy PolicyTerms of Serviceand Dataset License.Surface mesh simplification is the process of reducing the number of faces used in a surface mesh while keeping the overall shape, volume and boundaries preserved as much as possible.

It is the opposite of subdivision. The algorithm presented here can simplify any oriented 2-manifold surfacewith any number of connected components, with or without boundaries border or holes and handles arbitrary genususing a method known as edge collapse. Roughly speaking, the method consists of iteratively replacing an edge with a single vertex, removing 2 triangles per collapse.

93 honda accord wiring diagramEdges are collapsed according to a priority given by a user-supplied cost function, and the coordinates of the replacing vertex are determined by another user-supplied placement function. The algorithm terminates when a user-supplied stop predicate is met, such as reaching the desired number of edges.

The algorithm implemented here is generic in the sense that it does not require the surface mesh to be of a particular type but to be a model of the MutableFaceGraph and HalfedgeListGraph concepts. Each policy object specifies a particular aspect of the algorithm, such as how edges are selected and where the replacement vertex is placed. All policies have a sensible default. Furthermore, the API uses the so-called named-parameters technique which allows you to pass only the relevant parameters, in any order, omitting those parameters whose default is appropriate.

The free function that implements the simplification algorithm takes not only the surface mesh and the desired stop predicate but a number of additional parameters which control and monitor the simplification process. This section briefly describes the process in order to set the background for the discussion of the parameters to the algorithm.

There are two slightly different "edge" collapse operations. One is known as edge-collapse while the other is known as halfedge-collapse.

Twilight french bulldogsGiven an edge e joining vertices w and vthe edge-collapse operation replaces ew and v for a new vertex rwhile the halfedge-collapse operation pulls v into weliminating e and leaving w in place. In both cases the operation removes the edge e along with the 2 triangles adjacent to it.

This package uses the halfedge-collapse operation, which is implemented by removing, additionally, 1 vertex v and 2 edges, one per adjacent triangle.

## Papers by Keyword: Mesh Simplification

It optionally moves the remaining vertex w into a new position, called placementin which case the net effect is the same as in the edge-collapse operation.

Naturally, the surface mesh that results from an edge collapse deviates from the initial surface mesh by some amount, and since the goal of simplification is to reduce the number of triangles while retaining the overall look of the surface mesh as much as possible, it is necessary to measure such a deviation. Some methods attempt to measure the total deviation from the initial surface mesh to the completely simplified surface mesh, for example, by tracking an accumulated error while keeping a history of the simplification changes.

Other methods, like the one implemented in this package, attempt to measure only the cost of each individual edge collapse the local deviation introduced by a single simplification step and plan the entire process as a sequence of steps of increasing cost. Global error tracking methods produce highly accurate simplifications but take up a lot of additional space. Cost-driven methods, like the one in this package, produce slightly less accurate simplifications but take up much less additional space, even none in some cases.

The cost-driven method implemented in this package is mainly based on [4][5]with contributions from [3][2] and [1]. The algorithm proceeds in two stages. In the first stage, called collection stagean initial collapse cost is assigned to each and every edge in the surface mesh.

Then in the second stage, called collapsing stageedges are processed in order of increasing cost. Some processed edges are collapsed while some are just discarded.

Collapsed edges are replaced by a vertex and the collapse cost of all the edges now incident on the replacement vertex is recalculated, affecting the order of the remaining unprocessed edges. Not all edges selected for processing are collapsed. A processed edge can be discarded right away, without being collapsed, if it does not satisfy certain topological and geometric conditions.

The algorithm presented in [2] contracts collapses arbitrary vertex pairs and not only edges by considering certain vertex pairs as forming a pseudo-edge and proceeding to collapse both edges and pseudo-edges in the same way as in [4][5] which is the algorithm implemented here.

However, contracting an arbitrary vertex-pair may result in a non-manifold surface mesh, but the current state of this package can only deal with manifold surface meshes, thus, it can only collapse edges. That is, this package cannot be used as a framework for vertex contraction. The specific way in which the collapse cost and vertex placement is calculated is called the cost strategy.

The user can choose different strategies in the form of policies and related parameters, passed to the algorithm. The current version of the package provides a set of policies implementing two strategies: the Lindstrom-Turk strategy, which is the default, and a strategy consisting of an edge-length cost with an optional midpoint placement much faster but less accurate.

The main characteristic of the strategy presented in [4][5] is that the simplified surface mesh is not compared at each step with the original surface mesh or the surface mesh at a previous step so there is no need to keep extra information, such as the original surface mesh or a history of the local changes.Jump to navigation.

These models are usually built as a collection of vertices connected together to form a polygon mesh. Complex models can contain tens of millions of polygons.

As you can imagine, managing large polygonal models within an application presents numerous challenges for developers-the most pressing of which is how quickly the mesh can be rendered. Interactive applications need to render at least 30 frames a second.

A number of clever approaches like view culling, point-based rendering, and geometry caching have been designed to help with this. Another example involves global illumination algorithms like radiosity. The speed of these algorithms depends in large part on the size of the polygon mesh they take as input. Reducing the mesh's size can produce significant speed-ups in the algorithm. This article describes a collection of mesh simplification algorithms. Mesh simplification reduces the number of polygons in the mesh-often dramatically-while remaining faithful to the topology that is, the shape of the original mesh.

You can apply this in any situation where smaller models would help, for example, to improve character models in a game for better rendering speeds, or to simplify a complicated terrain model so it can be held entirely in memory. Any differences between the original and the simplified mesh are called geometric error. You use geometric error to control a simplification algorithm. One option is to define an error threshold, then ask the algorithm to reduce the number of polygons as much as possible without producing geometric error above the set threshold.

Another approach is to pick a desired polygon count, then ask the algorithm to reduce the mesh to this size while minimizing the amount of geometric error being produced. Different algorithms reduce the number of polygons in a mesh in different ways. Two common simplification operations are the edge collapse and vertex collapse.

An edge collapse see Figure 1 takes an edge v 1, v 2 in the mesh and collapses it to a single vertex v new.

**Progressive meshes (SIGGRAPH 1996)**

The edge and any triangles that use the edge are removed. A vertex collapse see Figure 2 combines two vertices v 1, v 2 into a single vertex v new. Unlike an edge collapse, v 1 and v 2 do not need to be connected.

Triangles connected to either v 1 or v 2 are updated to connect to v new. You can place v new somewhere along the line connecting v 1 and v 1, or in any other position that does not introduce inconsistency like the mesh folding over or polygons interpenetrating one another.

Notice that an edge collapse is a special case of a vertex collapse. It's a vertex collapse where v 1 and v2 are connected and vnew is somewhere along the edge between v 1 and v2. Edge collapses seem like a promising way to reduce a mesh's size.Skip to Main Content.

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Use of this web site signifies your agreement to the terms and conditions. Personal Sign In. For IEEE to continue sending you helpful information on our products and services, please consent to our updated Privacy Policy. Email Address. Sign In. Access provided by: anon Sign Out. However, immersive quality of experience in such VR applications is constrained mainly by the large data size and the hardware limitations to handle it.

The depth data captured by RGB-D cameras provide a dense sampling of the surface, resulting in a high-poly mesh, which is difficult to be rendered on handheld VR devices due to their limited processing power. To improve the immersive VR experience, a sparse approximation of the depth data is needed.

### RELATED APPLICATION

Traditional mesh and point cloud simplification methods are iterative and so are unsuitable for real-time applications. In this paper, we introduce a depth-imagebased approach that is capable of generating a good quality sparse mesh for visualization in real time. We propose a curvaturesensitive surface simplification-CS 3 operator that assigns an importance measure to each point in the depth image, based on the local curvature.

Further, it applies an importance-order-based restrictive sampling to generate a sparse representation that retains the overall shape as well as the finer features of the object.

We also modify the 2-D sweep-line-based constrained Delaunay triangulation to generate 3-D meshes from the sparse point sampling obtained using CS 3. In addition, the proposed approach preserves key surface properties, such as texture coordinates and materials. We used three different datasets containing dense 3-D models with and without texture, which are scanned using various sensors to validate and compare the robustness, real-time performance, and accuracy of the proposed method over existing approaches.

Based on the experimental results, we show that the proposed CS 3 operator and modified 2-D sweep-line-based triangulation generate sparse meshes from depth image in real time, performing significantly faster than current state-of-the-art methods while maintaining similar visual quality.

Article :. Date of Publication: 02 November DOI: Need Help?

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