A theorem to determine the spatial containment of a point in a planar polyhedron
Computer Vision, Graphics, and Image Processing
Solid representation and operation using extended octrees
ACM Transactions on Graphics (TOG)
Visibility-ordering meshed polyhedra
ACM Transactions on Graphics (TOG)
Dynamic Perfect Hashing: Upper and Lower Bounds
SIAM Journal on Computing
Computer graphics (2nd ed. in C): principles and practice
Computer graphics (2nd ed. in C): principles and practice
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Michael Abrash's Graphics Programming Black Book, with CD: The Complete Works of Graphics Master, Michael Abrash
Front-to-Back Display of BSP Trees
IEEE Computer Graphics and Applications
Distance Field Manipulation of Surface Models
IEEE Computer Graphics and Applications
Signed Distance Computation Using the Angle Weighted Pseudonormal
IEEE Transactions on Visualization and Computer Graphics
Signed Distance Transform Using Graphics Hardware
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Technical section: 2D point-in-polygon test by classifying edges into layers
Computers and Graphics
Technical section: Point in solid strategies
Computers and Graphics
A new point containment test algorithm based on preprocessing and determining triangles
Computer-Aided Design
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This paper presents the layer-based representation of polyhedrons and its use for point-in-polyhedron tests. In the representation, the facets and edges of a polyhedron are sequentially arranged, and so the binary search algorithm is efficiently used to speed up inclusion tests. In comparison with conventional representation for polyhedrons, the layer-based representation we propose greatly reduces the storage requirement because it represents much information implicitly, though it still has a storage complexity O(n). It is simple to implement, and robust for inclusion tests because many singularities are erased in constructing the layer-based representation. Incorporating an octree structure for organizing polyhedrons, our approach can run at a speed comparable with BSP-based inclusion tests, and at the same time greatly reduce storage and preprocessing time in treating large polyhedrons. We have developed an efficient solution for point-in-polyhedron tests with the time complexity varying between O(n) and O(log n), depending on the polyhedron shape and the constructed representation, and less than O(log^3 n) in most cases. The time complexity of preprocess is between O(n) and O(n^2), varying with polyhedrons, where n is the edge number of a polyhedron.