Computing the distance between two convex polygons is often a basic step to the algorithms of collision detection and path planning. Now, the lowest time complexity algorithm takes O(logm+logn) time to compute the minimum distance between two disjoint convex polygons P and Q, where n and m are the number of the polygons’ edges respectively. This paper discusses the location relations of outer Voronoi diagrams of two disjoint convex polygons P and Q, and presents a new O(logm+logn) algo- rithm to compute the minimum distance between P and Q. The algorithm is simple and easy to implement, and does not need any preprocessing and extra data structures.
YANG Cheng-leiQI MengMENG Xiang-xuLI Xue-qingWANG Jia-ye
We propose a novel technique to extract features from a range image and use them to produce a 3D pen-and-ink style portrait similar to a traditional artistic drawing. Unlike most previous template-based, component-based or example-based face sketching methods, which work from a frontal photograph as input, our system uses a range image as input. Our method runs in real-time for models of moderate complexity, allowing the pose and drawing style to be modified interactively. Portrait drawing in our system makes use of occluding contours and suggestive contours as the most important shape cues. However, current 3D feature line detection methods require a smooth mesh and cannot be reliably applied directly to noisy range images. We thus present an improved silhouette line detection algorithm. Feature edges related to the significant parts of a face are extracted from the range image, connected, and smoothed, allowing us to construct chains of line paths which can then be rendered as desired. We also incorporate various portrait-drawing principles to provide several simple yet effective non- photorealistic portrait renderers such as a pen-and-ink shader, a hatch shader and a sketch shader. These are able to generate various life-like impressions in different styles from a user-chosen viewpoint. To obtain satisfactory results, we refine rendered output by smoothing changes in line thickness and opacity. We are careful to provide appropriate visual cues to enhance the viewer＇s comprehension of the human face. Our experimental results demonstrate the robustness and effectiveness of our approach, and further suggest that our approach can be extended to other 3D geometric objects.
HUANG YueZhuMARTIN Ralph R.ROSIN Paul L.MENG XiangXuYANG ChengLei
