In this paper we present a novel method for dividing and clustering large volumetric scalar out-of-core datasets. This work is based on the Ordered Cluster Binary Tree (OCBT) structure created using a top-down or divi...In this paper we present a novel method for dividing and clustering large volumetric scalar out-of-core datasets. This work is based on the Ordered Cluster Binary Tree (OCBT) structure created using a top-down or divisive clustering method. The OCBT structure allows fast and efficient sub volume queries to be made in combination with level of detail (LOD) queries of the tree. The initial partitioning of the large out-of-core dataset is done by using non-axis aligned planes calculated using Principal Component Analysis (PCA). A hybrid OCBT structure is also proposed where an in-core cluster binary tree is combined with a large out-of-core file.展开更多
We first investigate the translative containment measure for convex domain K0 to contain, or to be contained in, the homothetic copy of another convex domain K1, i.e., given two convex domains K0, K1 of areas A0, A1, ...We first investigate the translative containment measure for convex domain K0 to contain, or to be contained in, the homothetic copy of another convex domain K1, i.e., given two convex domains K0, K1 of areas A0, A1, respectively, in the Euclidean plane R2, is there a translation T so that t(T K1) K0 or t(T K1) ? K0 for t > 0? Via the translative kinematic formulas of Poincar′e and Blaschke in integral geometry,we estimate the symmetric mixed isohomothetic deficit σ2(K0, K1) ≡ A201- A0A1, where A01 is the mixed area of K0 and K1. We obtain a sufficient condition for K0 to contain, or to be contained in, t(T K1). We obtain some Bonnesen-style symmetric mixed isohomothetic inequalities and reverse Bonnesen-style symmetric mixed isohomothetic inequalities. These symmetric mixed isohomothetic inequalities obtained are known as Bonnesen-style isopermetric inequalities and reverse Bonnesen-style isopermetric inequalities if one of domains is a disc. As direct consequences, we obtain some inequalities that strengthen the known Minkowski inequality for mixed areas and the Bonnesen-Blaschke-Flanders inequality.展开更多
文摘In this paper we present a novel method for dividing and clustering large volumetric scalar out-of-core datasets. This work is based on the Ordered Cluster Binary Tree (OCBT) structure created using a top-down or divisive clustering method. The OCBT structure allows fast and efficient sub volume queries to be made in combination with level of detail (LOD) queries of the tree. The initial partitioning of the large out-of-core dataset is done by using non-axis aligned planes calculated using Principal Component Analysis (PCA). A hybrid OCBT structure is also proposed where an in-core cluster binary tree is combined with a large out-of-core file.
基金supported by National Natural Science Foundation of China(Grant Nos.1127130211161007 and 11401486)+1 种基金the Ph.D.Program of Higher Education Research Fund(Grant No.2012182110020)Guizhou Foundation for Science and Technology(Grant No.LKS[2011]6)
文摘We first investigate the translative containment measure for convex domain K0 to contain, or to be contained in, the homothetic copy of another convex domain K1, i.e., given two convex domains K0, K1 of areas A0, A1, respectively, in the Euclidean plane R2, is there a translation T so that t(T K1) K0 or t(T K1) ? K0 for t > 0? Via the translative kinematic formulas of Poincar′e and Blaschke in integral geometry,we estimate the symmetric mixed isohomothetic deficit σ2(K0, K1) ≡ A201- A0A1, where A01 is the mixed area of K0 and K1. We obtain a sufficient condition for K0 to contain, or to be contained in, t(T K1). We obtain some Bonnesen-style symmetric mixed isohomothetic inequalities and reverse Bonnesen-style symmetric mixed isohomothetic inequalities. These symmetric mixed isohomothetic inequalities obtained are known as Bonnesen-style isopermetric inequalities and reverse Bonnesen-style isopermetric inequalities if one of domains is a disc. As direct consequences, we obtain some inequalities that strengthen the known Minkowski inequality for mixed areas and the Bonnesen-Blaschke-Flanders inequality.
