Abstract Polygon meshes with 3‐valent vertices often occur as the frame of free‐form surfaces in architecture, in which rigid beams are connected in rigid joints. For modelling such meshes, it is desirable to measure the deformation of the joints' shapes. We show that it is natural to represent joint shapes as points in hyperbolic 3‐space. This endows the space of joint shapes with a geometric structure that facilitates computation. We use this structure to optimize meshes towards different constraints, and we believe that it will be useful for other applications as well.

Abstract A discrete Laplace‐Beltrami operator is called perfect if it possesses all the important properties of its smooth counterpart. It is known which triangle meshes admit perfect Laplace operators and how to fix any other mesh by changing the combinatorics. We extend the characterization of meshes that admit perfect Laplacians to general polygon meshes. More importantly, we provide an algorithm that computes a perfect Laplace operator for any polygon mesh without changing the combinatorics, although, possibly changing the embedding. We evaluate this algorithm and demonstrate it at applications.

This paper surveys the field of nonphotorealistic rendering (NPR), focusing on techniques for transforming 2D input (images and video) into artistically stylized renderings. We first present a taxonomy of the 2D NPR algorithms developed over the past two decades, structured according to the design characteristics and behavior of each technique. We then describe a chronology of development from the semiautomatic paint systems of the early nineties, through to the automated painterly rendering systems of the late nineties driven by image gradient analysis. Two complementary trends in the NPR literature are then addressed, with reference to our taxonomy. First, the fusion of higher level computer vision and NPR, illustrating the trends toward scene analysis to drive artistic abstraction and diversity of style. Second, the evolution of local processing approaches toward edge-aware filtering for real-time stylization of images and video. The survey then concludes with a discussion of open challenges for 2D NPR identified in recent NPR symposia, including topics such as user and aesthetic evaluation.

Abstract Virtual 3D city models play an important role in the communication of complex geospatial information in a growing number of applications, such as urban planning, navigation, tourist information, and disaster management. In general, homogeneous graphic styles are used for visualization. For instance, photorealism is suitable for detailed presentations, and non‐photorealism or abstract stylization is used to facilitate guidance of a viewer's gaze to prioritized information. However, to adapt visualization to different contexts and contents and to support saliency‐guided visualization based on user interaction or dynamically changing thematic information, a combination of different graphic styles is necessary. Design and implementation of such combined graphic styles pose a number of challenges, specifically from the perspective of real‐time 3D visualization. In this paper, the authors present a concept and an implementation of a system that enables different presentation styles, their seamless integration within a single view, and parametrized transitions between them, which are defined according to tasks, camera view, and image resolution. The paper outlines potential usage scenarios and application fields together with a performance evaluation of the implementation.

Abstract In this work, we present a non‐photorealistic rendering technique to create stylized abstractions from color images and videos. Our approach is based on adaptive line integral convolution in combination with directional shock filtering. The smoothing process regularizes directional image features while the shock filter provides a sharpening effect. Both operations are guided by a flow field derived from the structure tensor. To obtain a high‐quality flow field, we present a novel smoothing scheme for the structure tensor based on Poisson's equation. Our approach effectively regularizes anisotropic image regions while preserving the overall image structure and achieving a consistent level of abstraction. Moreover, it is suitable for per‐frame filtering of video and can be efficiently implemented to process content in real‐time.

Abstract We present a non‐photorealistic rendering technique to transform color images and videos into painterly abstractions. It is based on a generalization of the Kuwahara filter that is adapted to the local shape of features, derived from the smoothed structure tensor. Contrary to conventional edge‐preserving filters, our filter generates a painting‐like flattening effect along the local feature directions while preserving shape boundaries. As opposed to conventional painting algorithms, it produces temporally coherent video abstraction without extra processing. The GPU implementation of our method processes video in real‐time. The results have the clearness of cartoon illustrations but also exhibit directional information as found in oil paintings.