In industry,the defective point data often make most surface reconstruction methods suffer from inherent problems that some specific aided information is difficult to obtain. To solve the problem,a novel implicit reco...In industry,the defective point data often make most surface reconstruction methods suffer from inherent problems that some specific aided information is difficult to obtain. To solve the problem,a novel implicit reconstruction method without any such information is proposed. This approach extends morphological operations into 3D space and provides an improved procedure to construct off-set gradient functions for indirect approximation. By this method,the dual relative functions guarantee a minimal crust surrounding the point data. They can generate a smooth and watertight resulting surface,filling holes and merging overlapping samples reasonably. Compared with other existing methods,the proposed method is better suited to handle defective point clouds in a convenient and efficient manner. The feasibility and effectiveness of the method are demonstrated through a series of practical examples.展开更多
The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human＇s intuition. We give the maximum order of finite group actions on （R3 E） amon...The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human＇s intuition. We give the maximum order of finite group actions on （R3 E） among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in R3. We also identify the topological types of the bordered surfaces realizing the maximum order, and findsimple representative embeddings for such surfaces.展开更多
基金supported by the National Natural Science Fundation of China (Grant No. 50835004)
文摘In industry,the defective point data often make most surface reconstruction methods suffer from inherent problems that some specific aided information is difficult to obtain. To solve the problem,a novel implicit reconstruction method without any such information is proposed. This approach extends morphological operations into 3D space and provides an improved procedure to construct off-set gradient functions for indirect approximation. By this method,the dual relative functions guarantee a minimal crust surrounding the point data. They can generate a smooth and watertight resulting surface,filling holes and merging overlapping samples reasonably. Compared with other existing methods,the proposed method is better suited to handle defective point clouds in a convenient and efficient manner. The feasibility and effectiveness of the method are demonstrated through a series of practical examples.
基金supported by National Natural Science Foundation of China(Grant Nos.11371034 and 11501239)
文摘The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human＇s intuition. We give the maximum order of finite group actions on （R3 E） among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in R3. We also identify the topological types of the bordered surfaces realizing the maximum order, and findsimple representative embeddings for such surfaces.
