# Quadric error metric simplification problems

Complex and highly detailed polygon meshes have been adopted for model representation in many areas of computer graphics. Existing works mainly focused on the quadric error metric based complex models approximation, which has not taken the retention of important model details into account. This may lead to visual degeneration. Our experiments on various models show that the geometry and topology structure as well as the features of the original models are precisely retained by employing discrete curvature. There are lots of 3D models with complex polygon meshes in computer graphics application, such as virtual reality, computer aided design technology, and geographic information system.

**Quadric error metric simplification problems**

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Mesh simplification based on Willmore energy weighted quadric error metric Abstract: Rendering, storing and transmission of high resolution models composed of large number of triangles primitives represents one of problems that scientific visualization and virtual reality faces. When these models exceed the capacity of the graphics hardware real-time rendering the solution is to simplify the mesh models by eliminating primitives from the original models while trying to keep topological information and main surface characteristics. This paper presents a new approach to the quadric error metric mesh simplification that uses the local surface features to quantify the cost of an edge collapse. We achieve this by using a weight for each quadric error processed that takes into account local Willmore energy. We defined the probability of each vertex to be decimated or not in the simplification process to be the entropy value of the vertex neighborhood Willmore energy values.

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20.7.2021

**In this paper, we improve Garland and Heckberts' quadric error metric based Based on Discrete Curvature", Mathematical Problems in Engineering, vol. .**

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## Quadratic Error Metric Mesh Simplification Algorithm Based on Discrete Curvature

manifold regions. Surface Simpliﬁcation. In recent years, the problem of surface simpliﬁcation, and the more. general problem of.

Existing works mainly focused on the quadric error metric based complex models approximation, Mathematical Problems in Engineering.

edge contraction and quadric error metrics, can rapidly produce problem. Also, to simplify the presentation we have assumed that all planes are uniformly.

the quadric error metric to encompass surfaces with material The problems of surface simplification and multiresolution modeling have re-.

## Mathematical Problems in Engineering

problem of simplifying objects of mixed dimension (e.g., containing both lines and approach is a novel generalization of the well-known quadric error metric [.

Mesh simplification based on Willmore energy weighted quadric error metric of large number of triangles primitives represents one of problems that scientific.

Quadratic Error Metric and Triangle Collapse. GUANGYOU ZHOU1 of the results of the algorithm, proposes the problems to be solved in the.