Simple and Robust Boolean Operations for Triangulated Surfaces

Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two stages: (1) We firstly find out candidate intersected-triangles pairs based on Octree and then compute the inter-section lines for all pairs of triangles with parallel algorithm; (2) We form closed or open intersection-loops, sub-surfaces and sub-blocks quite robustly only according to the cleared and updated topology of meshes while without coordinate computations for geometric enti-ties. A novel technique instead of inside/outside classification is also proposed to distinguish the resulting union, subtraction and intersection. Several examples have been given to illus-trate the effectiveness of our approach.Comment: Novel method for determining Union, Subtraction and Intersectio

Modular matrices from universal wave function overlaps in Gutzwiller-projected parton wave functions

We implement the universal wave function overlap (UWFO) method to extract modular $S$ and $T$ matrices for topological orders in Gutzwiller-projected parton wave functions (GPWFs). The modular $S$ and $T$ matrices generate a projective representation of $SL(2,\mathbb{Z})$ on the degenerate-ground-state Hilbert space on a torus and may fully characterize the 2+1D topological orders, i.e. the quasi-particle statistics and chiral central charge (up to $E_8$ bosonic quantum Hall states). We used the variational Monte Carlo method to computed the $S$ and $T$ matrices of the chiral spin liquid (CSL) constructed by the GPWF on the square lattice, and confirm that the CSL carries the same topological order as the $\nu=\frac{1}{2}$ bosonic Laughlin state. We find that the non-universal exponents in UWFO can be small and direct numerical computation is able to be applied on relatively large systems. We also discuss the UWFO method for GPWFs on other Bravais lattices in two and three dimensions by using the Monte Carlo method. UWFO may be a powerful method to calculate the topological order in GPWFs.Comment: 5 pages with 3 figure

Thermodynamics of the Schwarzschild-AdS black hole with a minimal length

Using the mass-smeared scheme of black holes, we study the thermodynamics of black holes. Two interesting models are considered. One is the self-regular Schwarzschild-AdS black hole whose mass density is given by the analogue to probability densities of quantum hydrogen atoms. The other model is the same black hole but whose mass density is chosen to be a rational fractional function of radial coordinates. Both mass densities are in fact analytic expressions of the ${\delta}$-function. We analyze the phase structures of the two models by investigating the heat capacity at constant pressure and the Gibbs free energy in an isothermal-isobaric ensemble. Both models fail to decay into the pure thermal radiation even with the positive Gibbs free energy due to the existence of a minimal length. Furthermore, we extend our analysis to a general mass-smeared form that is also associated with the ${\delta}$-function, and indicate the similar thermodynamic properties for various possible mass-smeared forms based on the ${\delta}$-function.Comment: v1: 25 pages, 14 figures; v2: 26 pages, 15 figures; v3: minor revisions, final version to appear in Adv. High Energy Phy

Discrete Surface Modeling Based on Google Earth: A Case Study

Google Earth (GE) has become a powerful tool for geological, geophysical and geographical modeling; yet GE can be accepted to acquire elevation data of terrain. In this paper, we present a real study case of building the discrete surface model (DSM) at Haut-Barr Castle in France based on the elevation data of terrain points extracted from GE using the COM API. We first locate the position of Haut-Barr Castle and determine the region of the study area, then extract elevation data of terrain at Haut-Barr, and thirdly create a planar triangular mesh that covers the study area and finally generate the desired DSM by calculating the elevation of vertices in the planar mesh via interpolating with Universal Kriging (UK) and Inverse Distance Weighting (IDW). The generated DSM can reflect the features of the ground surface at Haut-Barr well, and can be used for constructingthe Sealed Engineering Geological Model (SEGM) in further step.Comment: Proceedings of IEEE Conference, ICCSNT 2012, in Pres