Inclusion test for general polyhedra

doi:10.1016/S0097-8493(96)00067-2

Computers & Graphics

Volume 21, Issue 1, January–February 1997, Pages 23-30

https://doi.org/10.1016/S0097-8493(96)00067-2 Get rights and content

Abstract

This paper presents a new algorithm which tests the inclusion of a point in a general polyhedron, manifold and non-manifold, without solving any equation system and without using trigonometric functions. The algorithm is simple and robust, and easy to apply in every case.

References (8)

J. Lane et al.
An efficient point in polyhedron algorithm
Computer Vision, Graphics and Image Processing
(1984)
W. Horn et al.
A theorem to determine the spatial containment of a point in a planar polyhedron
Computer Vision, Graphics and Image Processing
(1989)
F. Feito et al.
Orientation, simplicity and inclusion test for planar polygons
Computers & Graphics
(1995)
F.P. Preparata et al.

There are more references available in the full text version of this article.

Cited by (81)

Voxel-based point kernel method for dose rate assessment of non-uniform activity and self-shielding sources in nuclear facility decommissioning
2019, Radiation Physics and Chemistry
Decommissioning task in nuclear facilities results in a number of radioactive components with non-uniform activity and self-shielding sources. Previous applications of virtual reality technology in the literature did not consider self-shielding sources and the activity distribution of sources is always considered homogeneous (uniform). In order to calculate the ambient dose equivalent rate of non-uniform activity and self-shielding source after cutting and removal operations in nuclear facility decommissioning, this paper proposes a hybrid of voxelization algorithm and point-kernel method for advanced gamma dose rate assessment for cutting simulation in a radioactive environment. The initial 3D scene model was designed using 3dsMax modeling and imported as a 3DS format file. The source solid models of arbitrary shape are automatically converted to voxelized models according to the voxelization algorithm. The cutting paths of the voxelized models are imported by the G-Code programming language. After the cutting and removing operations, the voxelized source models are compressed. Ultimately, considering the non-uniform distribution of the activity and self-shielding of sources, the gamma dose rate distribution is obtained by voxel-based point-kernel calculation. Simulation results are compared with dose rate calculated with MCNP, which show that the proposed method can produce a fast and accurate simulation of the cutting and removal operations of radioactive components and effectively calculate the ambient dose equivalent rate of non-uniform activity and self-shielding sources.
A gamma-ray dose rate assessment method for arbitrary shape geometries based on voxelization algorithm
2019, Radiation Physics and Chemistry
Citation Excerpt :
It is based on a decomposition of the polyhedron into a set of tetrahedral with a common origin and its scan-conversion into a special 3D presence buffer. The theoretical basis for the solid model voxelization algorithm used in this paper is the point-in-tetrahedron inclusion test of Feito and Torres (1997). In this paper, the following definition expresses the inclusion in a more useful way (Ogáyar et al., 2007):
A gamma-ray dose rate assessment method for arbitrary shape sources and arbitrary shape shields is proposed in this paper. The method is based on voxelization algorithm and Point-Kernel method. Using the modeling capabilities of 3dsMax software, the method can visually perform geometric modeling for arbitrary shape three-dimensional (3D) geometries without writing the textual description. The 3D geometry is imported as a 3DS format file. Using the voxelization-based modeling method, the arbitrary shape solid models are automatically converted to voxel models. In the point-kernel calculation process, source voxels are used as point kernels, and shielding voxels are used to calculate mean free paths (mfp). The effectiveness and flexibility of the proposed method were verified by simulating arbitrary shape geometries, and the accuracy was proved by comparing with MCNP code. The proposed method is suitable for calculating dose rate of arbitrary shape geometries after cutting and demolition operations during the decommissioning of nuclear facilities.
GPU inclusion test for triangular meshes
2018, Journal of Parallel and Distributed Computing
Citation Excerpt :
Several recent studies address this problem, but either the overall solution is inefficient [2] or not all the situations that present special cases can be managed [12]. One of the most cited point-in-polyhedron algorithms is the one presented by Feito and Torres in [5]. This algorithm was further simplified for triangular meshes in [25].
Querying the relative position of a point regarding a solid defined by a triangular mesh is a fundamental algorithm in geometric modelling. This algorithm has many applications in fields like Computer Graphics or Computer Aided Design and is the basis of many other basic algorithms in these areas. In this paper we present an efficient implementation of one of the classic algorithms for solving this problem, the point-in-solid test of Feito and Torres based on simplicial coverings. This algorithm is simple, robust and valid for non-manifold solids. Our implementation resolves the test, including all the special cases, needing no conditional branches. This fact allows us to obtain a parallel and very efficient GPU implementation of the algorithm. We have coded the algorithm in CUDA and the results showed that this GPU implementation achieved a speedup of up to 142 $\times$ with respect to a CPU single-thread implementation of the same optimized algorithm. Against a multi-thread implementation in CPU, our CUDA algorithm obtains a speedup of up to 38 $\times$ . We have also compared our algorithm to a previous GPU implementation in CUDA of the inclusion test of Feito and Torres. Against this GPU implementation, our algorithm achieved a speedup of up to 11.8 $\times$ .
A fast boundary integral equation method for point location problem
2018, Engineering Analysis with Boundary Elements
A numerical method based on the boundary integral equation is proposed for the point location problem. For a bounded domain, the integral value is close to 1.0 if a point is inside the domain, and is close to 0.0 when the point is outside the domain. For convenience of integration, the boundary of the domain can be discretized into boundary integral cells. The idea of isogeometric analysis can be easily coupled with the proposed method, i.e., using the parametric functions in geometric modeling to create the integral cells, which results in a mesh-free procedure for which the geometry can be exactly produced at all stages. Thus, the method can be applied to arbitrary shapes and easily embedded in computer-aided design (CAD) packages. The method is time-consuming if implemented directly; a fast multipole method is coupled with the proposed method to accelerate the integral procedure. Some examples of 2D and 3D cases are tested to show the accuracy and efficiency of the proposed method.
Dynamic modeling of traffic noise in both indoor and outdoor environments by using a ray tracing method
2017, Building and Environment
The complexity of the urban environment and traffic characteristics give the dynamic simulation of traffic noise practical significances. A new dynamic modeling of traffic noise in both indoor and outdoor environments was proposed. First, considering multiple reflections and diffractions, 3D ray tracing method subordinated to space partitioning was used to simulate sound propagations. Then, microscopic traffic simulation which provided time-variant parameters for the vehicle emission model, was used to gain spatial and temporal outputs. Space partitioning improved the computational efficiency by transforming the global search into a local one in complex sound propagation simulation. A case was validated the accuracy, as the indoor and outdoor average errors of equivalent sound levels ( $L_{e q}$ ) were respectively 1.68 dB and 1.65 dB. Moreover, less than 1.5 dB errors of statistical indicators ( $L_{90}$ , $L_{50}$ and $L_{10}$ ) and well coincidence of statistical distributions of the instantaneous sound pressure levels ( $L_{e q, 1 s}$ ) illustrated a good performance on dynamic simulation. Finally, the effects of vehicle speed, proportion of heavy vehicles and signal phase on traffic noise were discussed. The results showed that 1) Indoor/outdoor $L_{e q}$ had logarithmic relationships with vehicle speed. 2) It presented quadratic polynomial relationships between $L_{e q}$ and proportion of heavy vehicles. 3) Dynamic results showed that noise variations were consistent with the changes of the signal period, and it revealed different noise distributions with various vehicle statuses; upstream average $L_{e q}$ was 3.3 dB louder than the downstream one with vehicle acceleration; average $L_{e q, 1 s}$ during the red light was 20 dB softer than it during the green light.
Fast and robust GPU-based point-in-polyhedron determination
2017, CAD Computer Aided Design
This paper presents a fast and robust GPU-based point-in-polyhedron determination method. The method partitions the bounding box of the polyhedron into a grid with $O (N)$ cells, where $N$ is the number of polyhedron faces, and predetermines the inclusion property of the grid cells’ center points. Then, a line segment is generated from the query point to the center point of its related grid cell to determine the inclusion property of the query point by counting the faces intersected by the line segment. Such a localization treatment is further exploited to optimize the visiting pattern in using GPUs, by which a high increase in the testing speed is achieved. We also provide a unified solution to all singular cases, especially those caused by localization, to guarantee the efficiency and robustness for point-in-polyhedron tests. The results show that our proposed method can be faster than both state-of-the-art serial and parallel methods by several orders of magnitude, with only a slight increase in storage requirement.

View all citing articles on Scopus

View full text

Inclusion test for general polyhedra

Abstract

Computer Vision, Graphics and Image Processing

Computer Vision, Graphics and Image Processing

Computers & Graphics