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**11 - 15**of**15**### Graphics Education

"... The winged- and half- edge data structures are commonly used representations for polyhedron models. Due to the complexity, students in an introductory to computer graphics course usually have difficulty in handling these data structures and developing applications. This paper describes the authors ’ ..."

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The winged- and half- edge data structures are commonly used representations for polyhedron models. Due to the complexity, students in an introductory to computer graphics course usually have difficulty in handling these data structures and developing applications. This paper describes the authors ’ effort in the development of a visualization and animation tool for teaching and learning these data structures. This tool also includes a simple pseudo code-like language for algorithm design. Instructors may employ this tool for presentation and demonstration purposes. Students may use the simple language to develop and experiment with new algorithms before their actual implementation. The visualization and animation system may be used to explore and understand the relationship among mesh elements and algorithm execution.

### Real-time Rendering of Stack-based Terrains

"... Usually, terrain rendering relies on a 2D regular grid of height values, the so called height field. Height fields describe 2.5D surfaces and are not able to present complex 3D terrain features. In contrast, a 3D data representa-tion quickly exceeds the available memory resources. To overcome this p ..."

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Usually, terrain rendering relies on a 2D regular grid of height values, the so called height field. Height fields describe 2.5D surfaces and are not able to present complex 3D terrain features. In contrast, a 3D data representa-tion quickly exceeds the available memory resources. To overcome this problem we apply material stacks. Material stacks combine the simplicity of 2D height fields and the extended modeling capabilities of 3D volumetric data. However, this approach requires expensive rendering and is difficult to realize in real-time. In this paper we present an innovative real-time rendering approach of terrains relying on material stacks. Our approach is based on two major steps: First, a LoD hierarchy for material-stacks is generated. Second, during rendering a multi-staged quadrangulation pipeline extracts terrain surface from the material stacks. As a result, we achieve real-time frame rates at high resolutions.

### Hierarchical mesh segmentation editing through rotation operations

"... Abstract. Hierarchical and multi-resolution models are well known tools used in may application domains for representing an object at varying levels of detail. In the case of segmentations computed on a mesh, a hierarchical model can be structured as a binary tree representing the hierarchy of the r ..."

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Abstract. Hierarchical and multi-resolution models are well known tools used in may application domains for representing an object at varying levels of detail. In the case of segmentations computed on a mesh, a hierarchical model can be structured as a binary tree representing the hierarchy of the region merging operations performed on the original segmentation for reducing its resolution. In this paper, we address the problem of modifying a hierarchical segmentation in order to augment its expressive power. We adapt two well-known operators defined for modifying binary trees, namely left and right rotation, to the case of hierarchical segmentations. Such operators are then applied to modify-ing a given hierarchy based on a user-defined function and based on a user-defined segmentation. 1

### Modified Streaming Format for Direct Access Triangular Data Structures

"... Abstract — We define in this paper an extended solution to improve an Out-of-Core data structure which is the streaming format, by adding new information allowing to reduce file access cost, reducing the neighborhood access delay to constant time. The original streaming format is conceived to manipu ..."

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Abstract — We define in this paper an extended solution to improve an Out-of-Core data structure which is the streaming format, by adding new information allowing to reduce file access cost, reducing the neighborhood access delay to constant time. The original streaming format is conceived to manipulate huge triangular meshes. It assumes that the whole mesh cannot be loaded entirely into the main memory. That's why the authors did not include the neighborhood in the file structure. However, almost all of the applications need the neighborhood information in the triangular structures. Using the original streaming format does not allow us to extract the neighborhood information easily. By adding the neighbor indices to the file in the same way as the original format, we can benefit from the streaming format, and at the same time, guarantee a constant time access to the neighborhood. We have adapted our new structure so that it can allow us to apply our direct access algorithm to different parts of the structure without having to go through the entire file. Index Terms — Triangular data structure, Streaming format, Direct access structure I.

### Weighted Mesh Simplification of 3D . . .

, 2011

"... Representing huge triangular datasets in a real-time rendering environment is a challenge which receives continuous attention. There is a growing complexity of geometric meshes on the one hand and an increasing computational power of graphics hardware on the other hand. Although hardware acceleratio ..."

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Representing huge triangular datasets in a real-time rendering environment is a challenge which receives continuous attention. There is a growing complexity of geometric meshes on the one hand and an increasing computational power of graphics hardware on the other hand. Although hardware acceleration is very powerful, simplification using software is much cheaper and more flexible. Additionally, for a large class of geometric models, simplification can be performed as a preprocessing step where there is no demand for real-time operations. The underlying theory of this diploma thesis is based on mesh simplification using quadric error metrics. This algorithm was first published by Michael Garland and it was implemented into Aardvark, a sophisticated rendering framework. It contains a comprehensive set of libraries dealing with data structures in general and polygonal mesh data structures in particular. The application takes a triangulated mesh as input and iteratively creates an even more simplified approximation by weighting and collapsing suitable mesh areas. Some surface details will be lost, but the overall shape of the model will be preserved. The presented code can handle models by preprocessing static, closed triangular meshes. The iterative computation stops when a user specified percentage of the original mesh size is reached. A further improvement in a later research project will try to add vertex colors, normals and texture coordinates to the simplification method.