In this paper we present a lattice structure optimization approach by leveraging the capabilities of neural networks for implicit geometry representation. We employ the Deep Signed Distance Field (DeepSDF) method, where a continuous and low-dimensional latent space is introduced to encode the geometric information. In contrast to traditional topology optimization methods, this allows the restriction of the design space to specific geometries. In our case, the latent space is used to represent the geometry of different unit cells, that are stacked to form a lattice structure. Moreover, continuously varying the latent vector over the structure allows a functional grading and optimization. Unlike other lattice-structure optimization methods, we neither assume a large separation of scale nor periodicity. Instead, we perform a full-scale finite element analysis at each optimization step. The required mesh is obtained by a differentiable extension of the dual marching cubes algorithm, which enables gradient-based optimization.

With the migration from 2D to 3D geographical information systems (GISs), the amounts of data to manage grow substantially. At the same time, 3D real-time rendering is necessary to provide a convenient user interface. Traditional GIS data management functions are too slow for this purpose, while computer graphics algorithms fail to deal with the sheer amount of data efficiently. In this paper we present LOD-R-trees, a new data structure which elegantly combines R-trees with LODs (levels of detail). Two applications demonstrate the versatility of our approach. With the Vienna Walkthrough System one can virtually walk through Vienna, the capital of Austria. The geometric model consists of about 20,000 blocks of buildings, covering about 75% of Vienna (150 km2 out of 200 km2). With the Styria Flyover System one can virtually fly over Styria, a province of Austria. The digital model covers Styria and parts of its adjoining provinces (30,000 km2); it is based on a digital terrain model (DTM) consisting of more than 23 million triangles and of 50 Mbyte texture data (satellite images). Both applications provide progressive rendering and dynamic performance adjustment. On an SGI 02 they deliver about 10 frames per second. Our approach demonstrates that efficient algorithms make a fast 3D GIS user interface possible without spending a fortune on hardware. Copyright © 2000 John Wiley & Sons, Ltd.

With the Styria Flyover one can virtually fly over Styria, a province of Austria. The countryside is characterized by a mixture of rather flat regions in the south east and mountains up to 3000 m in the north west. The digital model covers Styria and parts of its adjoining provinces (30,000 km/sup 2/); it is based on a DTM consisting of more than 23 million triangles and on 50 Mbyte texture data (satellite images). The framework combines an R-tree data structure with efficient LOD management (automatic mesh refinement), progressive rendering and dynamic performance adjustment. On a SGI O2 it delivers more than 8 frames per second. The authors' approach demonstrates that efficient algorithms make a fast 3D GIS user interface possible without spending a fortune on hardware. The paper focuses on techniques and data structures to maximize the performance of visualization.