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SMOOTHING OF FREE-FORM SURFACES WITH BEZIER PATCHES

computer AIDED GEOMETRIC DESIGN 1995年第3期12卷 231-249页

作者： MA, LZ PENG, QS State Key Lab. of CAD & Computer Graphics Zhejiang University Hangzhou 310027 People's Republic of China

In this paper, a unified method for smoothing free-form surfaces with Bezier patches is presented. A non-smooth surface consisting of bicubic patches is turned into a G(1) surface by the following process. Trim each patch along user-defined parameter lines using subdivision. Attach eight patches (one to each edge and one to each vertex) to each trimmed patch to blend between it and its neighbor patches. Using this method, solid objects bounded with bicubic Bezier patches can be G(1) smoothed with bicubic patches. The operation is local. It provides designers with the facility to adjust the shape of a smoothed object interactively. The method can also be used for constructing smooth closed surfaces whose modeling is important for cad/CG (cf. (Barnhill, 1985)).

关键词： COMPUTATIONAL GEOMETRY AND OBJECT MODELING, CURVE, SURFACE, SOLID, AND OBJECT REPRESENTATIONS cad/CG CAGD BEZIER SURFACES SMOOTHING GEOMETRIC CONTINUITY TRANSITION SURFACES

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Optimal constrained multi-degree reduction of Bézier curves with explicit expressions based on divide and conquer

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第4期10卷 577-582页

作者： Lian ZHOU Guo-jin WANG Institute of Computer Graphics and Image Processing State Key Lab of CAD & CG Zhejiang University Hangzhou 310027 China

We decompose the problem of the optimal multi-degree reduction of Bézier curves with corners constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree reduction, and doing optimal degree reduction without making high order interpolations at the two endpoints. Further, we convert the second subproblem into multi-degree reduction of Jacobi polynomials. Then, we can easily derive the optimal solution using orthonormality of Jacobi polynomials and the least square method of unequally accurate measurement. This method of 'divide and conquer' has several advantages including maintaining high continuity at the two endpoints of the curve, doing multi-degree reduction only once, using explicit approximation expressions, estimating error in advance, low time cost, and high precision. More importantly, it is not only deduced simply and directly, but also can be easily extended to the degree reduction of surfaces. Finally, we present two examples to demonstrate the effectiveness of our algorithm.

关键词： Bezier curves Multi-degree reduction Divide and conquer

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A new method in highway route design:joining circular arcs by a single C-Bézier curve with shape parameter

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第4期10卷 562-569页

作者： Hua-hui CAI Guo-jin WANG Institute of Computer Graphics and Image Processing State Key Lab of CAD & CG Zhejiang University Hangzhou 310027 China

We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages：（1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is availab.e; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.

关键词： Transition curve C-Bezier curve Monotone curvature Shape parameter

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Optimal approximate merging of a pair of Bézier curves with G^2-continuity

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第4期10卷 554-561页

作者： Ping ZHU Guo-zhao WANG Institute of Computer Graphics and lmage Processing State Key Lab of CAD & CG Zhejiang University Hangzhou 310027 China

We present a novel approach for dealing with optimal approximate merging of two adjacent Bezier eurves with G^2-continuity. Instead of moving the control points, we minimize the distance between the original curves and the merged curve by taking advantage of matrix representation of Bezier curve＇s discrete structure, where the approximation error is measured by L2-norm. We use geometric information about the curves to generate the merged curve, and the approximation error is smaller. We can obtain control points of the merged curve regardless of the degrees of the two original curves. We also discuss the merged curve with point constraints. Numerical examples are provided to demonstrate the effectiveness of our algorithms.

关键词： Approximate merging Gl-continuity G^2-continuity Discrete subdivision Point constraints

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Adaptive foreground and shadow segmentation using hidden conditional random fields

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第4期8卷 586-592页

作者： CHU Yi-ping YE Xiu-zi QIAN Jiang ZHANG Yin ZHANG San-yuan School of Computer Science State Key Lab. of CAD ＆ CG Zhejiang University Hangzhou 310027 China

Video object segmentation is important for video surveillance, object tracking, video object recognition and video editing. An adaptive video segmentation algorithm based on hidden conditional random fields (HCRFs) is proposed, which models spatio-temporal constraints of video sequence. In order to improve the segmentation quality, the weights of spatio-temporal con- straints are adaptively updated by on-line learning for HCRFs. Shadows are the factors affecting segmentation quality. To separate foreground objects from the shadows they cast, linear transform for Gaussian distribution of the background is adopted to model the shadow. The experimental results demonstrated that the error ratio of our algorithm is reduced by 23% and 19% respectively, compared with the Gaussian mixture model (GMM) and spatio-temporal Markov random fields (MRFs).

关键词： Video segmentation Shadow elimination Hidden conditional random fields (HCRFs) On-line learning

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Line clipping against polygonal window algorithm based on the multiple virtual boxes rejecting

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第B08期6卷 100-107页

作者：王进陆国栋彭群生吴煊晖 State Key Lab. of CAD&CG Zhejiang University Department of Electrical and Computer Engineering National University of Singapore

This paper presents a new algorithm for line clipping against a polygonal window by exploiting the local relationship between each line segment and the polygon. Firstly, a minimal enclosing box （MEB） of the polygon is adopted to reject the invisible line segments located outside the MEB. Secondly, a 45° rotated box is used to encode the endpoint of the line segment, and then reject a portion of the invisible segments crossing polygon comers. Finally, instead of encoding the endpoints of all line segments with respect to the polygonal window, each vertex of the polygon is encoded, taking the line segment to be clipped as reference. For efficient encoding of the polygon vertices, a new concept, termed with slope adaptive virtual box, is introduced regarding each line segment. Such a box can not only conveniently reject all totally invisible lines lying outside the MEB conveniently, but also precisely identify the edges of the polygon with which the line segment potentially intersects. With the summation of the vertex codes, it can be verified whether the line segment is separated from or potentially intersects the polygon window. Based on the product of the codes of adjacent vertices, singular cases of intersection can be solved accurately. Experimental results demonstrate the efficiency and stability of the new algorithm.

关键词： Polygon vertex encoding Adaptive virtual box Line segment rejection Line segment intersection Line clipping

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Interactive browsing of large images on multi-projector display wall system

Interactive browsing of large images on multi-projector disp...

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12th International Conference on Human-computer Interaction, HCI International 2007

作者： Zhongding, Jiang Xuan, Luo Yandong, Mao Binyu, Zang Hai, Lin Hujun, Bao Computer Graphics Lab. Software School Fudan University Shanghai China State Key Lab. of CAD and CG Zhejiang University Hangzhou China

ISBN: (纸本)9783540731061

With the precision of data acquisition increases, large images that may occupy terabytes, become common in research and industry fields. Since multi-projector display wall systems can provide higher resolution, they becomes paramount to display the large images. In this paper, we present one large image viewing system designed for display wall system. Our system need not totally downloading the whole image data to each rendering node. It enables users to browse the out-of-core images in real time using data streaming techniques. In the system, the original out-of-core raw image is compressed and represented using one hierarchical structure in multi-resolution manner. We design one proxy architecture that interactive streams data from remote data server to all rendering nodes. Our system allows users to interactively pan, and zoom the large images with versatile graphical user interface. © Springer-Verlag Berlin Heidelberg 2007.

关键词： Image retrieval

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Opacity volume based halo generation for enhancing depth perception

Opacity volume based halo generation for enhancing depth per...

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12th International Conference on computer-Aided Design and computer graphics, cad/graphics 2011

作者： Tao, Yubo Lin, Hai Dong, Feng Clapworthy, Gordon State Key Lab. of CAD and CG Zhejiang University China Centre for Computer Graphics and Visualisation University of Bedfordshire United Kingdom

ISBN: (纸本)9780769544977

Halos are usually used to enhance depth perception and display spatial relationships in illustrative visualization. In this paper, we present a simple and effective method to create volumetric halo illustration. In the pre-processing stage, we generate a view-independent halo intensity volume, which contains all potential halos around the boundaries of features, based on the opacity volume on graphic hardware. During halo rendering, the halo intensity volume is used to extract halos only around the contours of structures for the current viewpoint. The performance of our approach is significantly faster than previous halo illustration methods, which perform both halo generation and rendering during volume rendering. Experimental results demonstrate volumetric halo effects and the efficiency of the proposed approach. © 2011 IEEE.

关键词： Volume rendering

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Interactive mesh deformation with pseudo material effects

Interactive mesh deformation with pseudo material effects

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作者： Huang, Jin Zhang, Hongxin Shi, Xiaohan Liu, Xinguo Bao, Hujun State Key Lab. of CAD and CG Zhejiang University China State Key Lab. of CAD and CG Computer Science School Zhejiang University State Key Laboratory of CAD and CG Zhejiang University

This paper presents a novel interactive mesh deformation method that can achieve various dynamic material effects, including elastic membrane and cloth effects. In our framework, a mesh is encoded by some differential quantities based on edge length and dihedral angle;and the deformation is formulated as a least square problem for preserving the edge length and dihedral angle via the differential quantities. In order to obtain anisotropic material effects, we further propose an edge-weighting scheme based on a user-specified vector field. To avoid specifying the local transformations, we set up an iterative scheme for solving the deformation. At last, several examples are presented to show that our approach can interactively generate visually pleasing deformations. Copyright © 2006 John Wiley & Sons, Ltd.

关键词： Interactive computer graphics

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As-consistent-as-possible compositing of virtual objects and video sequences

As-consistent-as-possible compositing of virtual objects and...

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作者： Zhang, Guofeng Qin, Xueying An, Xiaobo Chen, Wei Bao, Hujun State Key Lab. of CAD and CG Zhejiang University China State Key Lab. of CAD and CG College of Computer Science Zhejiang University Zhejiang University Department of Computer Science Zhejiang Univ. State Key Lab. of CAD and CG Zhejiang University

We present an efficient approach that merges the virtual objects into video sequences taken by a freely moving camera in a realistic manner. The composition is visually and geometrically consistent through three main steps. First, a robust camera tracking algorithm based on key frames is proposed, which precisely recovers the focal length with a novel multi-frame strategy. Next, the concerned 3D models of the real scenes are reconstructed by means of an extended multi-baseline algorithm. Finally, the virtual objects in the form of 3D models are integrated into the real scenes, with special cares on the interaction consistency including shadow casting, occlusions, and object animation. A variety of experiments have been implemented, which demonstrate the robustness and efficiency of our approach. Copyright © 2006 John Wiley & Sons, Ltd.

关键词： Virtual reality

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