Peter Wonka

Gap processing for adaptive maximal poisson-disk sampling

In this article, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or when their radii are changed. We build on the concepts of regular triangulations and the power diagram. Third, we show how our analysis contributes to the state-of-the-art in surface remeshing.

Interactive Coherence-Based Façade Modeling

We propose a novel interactive framework for modeling building façades from images. Our method is based on the notion of coherence‐based editing which allows exploiting partial symmetries across the façade at any level of detail. The proposed workflow mixes manual interaction with automatic splitting and grouping operations based on unsupervised cluster analysis. In contrast to previous work, our approach leads to detailed 3d geometric models with up to several thousand regions per façade. We compare our modeling scheme to others and evaluate our approach in a user study with an experienced user and several novice users.

Design and volume optimization of space structures

We study the design and optimization of statically sound and materially efficient space structures constructed by connected beams. We propose a systematic computational framework for the design of space structures that incorporates static soundness, approximation of reference surfaces, boundary alignment, and geometric regularity. To tackle this challenging problem, we first jointly optimize node positions and connectivity through a nonlinear continuous optimization algorithm. Next, with fixed nodes and connectivity, we formulate the assignment of beam cross sections as a mixed-integer programming problem with a bilinear objective function and quadratic constraints. We solve this problem with a novel and practical alternating direction method based on linear programming relaxation. The capability and efficiency of the algorithms and the computational framework are validated by a variety of examples and comparisons.

A Survey of Blue-Noise Sampling and Its Applications

In this paper, we survey recent approaches to blue-noise sampling and discuss their beneficial applications. We discuss the sampling algorithms that use points as sampling primitives and classify the sampling algorithms based on various aspects, e.g., the sampling domain and the type of algorithm. We demonstrate several well-known applications that can be improved by recent blue-noise sampling techniques, as well as some new applications such as dynamic sampling and blue-noise remeshing.

Urban pattern: layout design by hierarchical domain splitting

We present a framework for generating street networks and parcel layouts. Our goal is the generation of high-quality layouts that can be used for urban planning and virtual environments. We propose a solution based on hierarchical domain splitting using two splitting types: streamline-based splitting, which splits a region along one or multiple streamlines of a cross field, and template-based splitting, which warps pre-designed templates to a region and uses the interior geometry of the template as the splitting lines. We combine these two splitting approaches into a hierarchical framework, providing automatic and interactive tools to explore the design space.

On-the-fly generation and rendering of infinite cities on the GPU

In this paper, we present a new approach for shape‐grammar‐based generation and rendering of huge cities in real‐time on the graphics processing unit (GPU). Traditional approaches rely on evaluating a shape grammar and storing the geometry produced as a preprocessing step. During rendering, the pregenerated data is then streamed to the GPU. By interweaving generation and rendering, we overcome the problems and limitations of streaming pregenerated data. Using our methods of visibility pruning and adaptive level of detail, we are able to dynamically generate only the geometry needed to render the current view in real‐time directly on the GPU. We also present a robust and efficient way to dynamically update a scenes derivation tree and geometry, enabling us to exploit frame‐to‐frame coherence. Our combined generation and rendering is significantly faster than all previous work. For detailed scenes, we are capable of generating geometry more rapidly than even just copying pregenerated data from main memory, enabling us to render cities with thousands of buildings at up to 100 frames per second, even with the camera moving at supersonic speed.

Low-Resolution Remeshing Using the Localized Restricted Voronoi Diagram

A big problem in triangular remeshing is to generate meshes when the triangle size approaches the feature size in the mesh. The main obstacle for Centroidal Voronoi Tessellation (CVT)-based remeshing is to compute a suitable Voronoi diagram. In this paper, we introduce the localized restricted Voronoi diagram (LRVD) on mesh surfaces. The LRVD is an extension of the restricted Voronoi diagram (RVD), but it addresses the problem that the RVD can contain Voronoi regions that consist of multiple disjoint surface patches. Our definition ensures that each Voronoi cell in the LRVD is a single connected region. We show that the LRVD is a useful extension to improve several existing mesh-processing techniques, most importantly surface remeshing with a low number of vertices. While the LRVD and RVD are identical in most simple configurations, the LRVD is essential when sampling a mesh with a small number of points and for sampling surface areas that are in close proximity to other surface areas, e.g., nearby sheets. To compute the LRVD, we combine local discrete clustering with a global exact computation.

Exploring quadrangulations

We present a framework for exploring topologically unique quadrangulations of an input shape. First, the input shape is segmented into surface patches. Second, different topologies are enumerated and explored in each patch. This is realized by an efficient subdivision-based quadrangulation algorithm that can exhaustively enumerate all mesh topologies within a patch. To help users navigate the potentially huge collection of variations, we propose tools to preview and arrange the results. Furthermore, the requirement that all patches need to be jointly quadrangulatable is formulated as a linear integer program. Finally, we apply the framework to shape-space exploration, remeshing, and design to underline the importance of topology exploration.

Non-Obtuse Remeshing with Centroidal Voronoi Tessellation

We present a novel remeshing algorithm that avoids triangles with small (acute) angles and those with large (obtuse) angles. Our solution is based on an extension of Centroidal Voronoi Tesselation (CVT). We augment the original CVT formulation with a penalty term that penalizes short Voronoi edges, while the CVT term helps to avoid small angles. Our results show significant improvements in remeshing quality over the state of the art.

Reconstructing building mass models from UAV images

We present an automatic reconstruction pipeline for large scale urban scenes from aerial images captured by a camera mounted on an unmanned aerial vehicle. Using state-of-the-art Structure from Motion and Multi-View Stereo algorithms, we first generate a dense point cloud from the aerial images. Based on the statistical analysis of the footprint grid of the buildings, the point cloud is classified into different categories (i.e., buildings, ground, trees, and others). Roof structures are extracted for each individual building using Markov random field optimization. Then, a contour refinement algorithm based on pivot point detection is utilized to refine the contour of patches. Finally, polygonal mesh models are extracted from the refined contours. Experiments on various scenes as well as comparisons with state-of-the-art reconstruction methods demonstrate the effectiveness and robustness of the proposed method. Graphical abstractDisplay Omitted HighlightsA novel framework for automatic reconstruction of large scale urban scenes from UAV images.An object level point cloud segmentation algorithm and a roof extraction algorithm based on a regularized Markov random field formulation.An effective contour refinement method based on pivot point detection.