This paper presents a new GPU-based rasterization algorithm for Boolean operations that handles arbitary closed polygons. We construct an efficient data structure for interoperation of CPU and GPU and propose a fast GPU-based contour extraction method to ensure the performance of our algorithm. We then design a novel traversing strategy to achieve an error-free calculation of intersection point for correct Boolean operations. We finally give a detail evaluation and the results show that our algorithm has a higher performance than exsiting algorithms on processing polygons with large amount of vertices.

This letter proposes a Light Space Partitioned Shadow Maps (LSPSMs) algorithm which implements shadow rendering based on a novel partitioning scheme in light space. In stead of splitting the view frustum like traditional Z-partitioning methods, we split partitions from the projection of refined view frustum in light space. The partitioning scheme is performed dual-directionally while limiting the wasted space. Partitions are created in dynamic number corresponding to the light and view directions. Experiments demonstrate that high quality shadows can be rendered in high efficiency with our algorithm.

A simple and efficient semi-supervised classification method is presented. An unsupervised spectral mapping method is extended to a semi-supervised situation with multiplicative modulation of similarities between data. Our proposed algorithm is derived by linearization of this nonlinear semi-supervised mapping method. Experiments using the proposed method for some public benchmark data and color image data reveal that our method outperforms a supervised algorithm using the linear discriminant analysis and a previous semi-supervised classification method.

A semi-supervised classification method is presented. A robust unsupervised spectral mapping method is extended to a semi-supervised situation. Our proposed algorithm is derived by linearization of this nonlinear semi-supervised mapping method. Experiments using the proposed method for some public benchmark data reveal that our method outperforms a supervised algorithm using the linear discriminant analysis for the iris and wine data and is also more accurate than a semi-supervised algorithm of the logistic GRF for the ionosphere dataset.

Vector data differs in the rasterized height field by data type. It is difficult to render dynamic vectors on height field because their shapes and locations may change at any time. This letter proposes a novel method: View-dependent Projective Atlases (VdPAs). As an intermediate data source, VdPAs act as rendering targets which enable height field and vectors to be rasterized at the same resolution. Then, VdPAs can be viewed as super-tiles. State of art height field rendering algorithms can be used for scenario rendering. Experimental results demonstrate that atlases are able to make dynamic vectors to be rendered on height field with real-time performance and high quality.

We extend a graph spectral method for extracting clusters from graphs representing pairwise similarity between data to hypergraph data with hyperedges denoting higher order similarity between data. Our method is robust to noisy outlier data and the number of clusters can be easily determined. The unsupervised method extracts clusters sequentially in the order of the majority of clusters. We derive from the unsupervised algorithm a semi-supervised one which can extract any cluster irrespective of its majority. The performance of those methods is exemplified with synthetic toy data and real image data.