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A Density-Controlled Planar Area Adaptive Sampling Method
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A self-adaptive sampling, plane technology, applied in the generation of 2D images, instruments, calculations, etc., can solve the problem of not adapting to the density function, has not seen the literature and technical records of adaptive sampling in the plane area, and cannot adaptively add or delete sampling points. and other problems, to achieve the effect of wide adaptability, encryption or simplified sampling set operation, and easy implementation.
Active Publication Date: 2019-04-12
NANJING NORMAL UNIVERSITY
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[0005] None of the above methods can adaptively add or delete sampling points, and the density of sampling points is determined by the nature of the surface or image itself, and is not suitable for any density function.
[0006] At present, there are no literature and related technical records on the adaptive sampling of planar areas controlled by the density function.
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Embodiment 1
[0054] The concrete steps of this embodiment are as follows:
[0055] 1. Input the boundary of the plane area Ω and the sampling density function f(x,y)
[0056] Input the boundary of the plane area Ω, in the present embodiment, the boundary of the input plane area Ω is represented by a hexagon (referring to the attached Figure 5 ), the vertices of the hexagon are (-2,0),(-1,2),(1,2),(2,0),(1,-2),(-1,-2) ;Define the sampling density function f(x,y) on the plane area Ω as:
[0057]
[0058] Where ||·|| is an absolute value symbol, and for any point (x, y) in the plane area Ω, the function f(x, y) can give a density value greater than 0.
[0059] 2. Determine the convex polygon Γ containing the plane area Ω, and generate the initial sampling point set
[0060] Determine a convex polygon Γ covering the plane area Ω on the plane. In this embodiment, the convex polygon Γ is overlapped with the plane area Ω, that is, the convex polygon Γ is also a hexagon, and the vertices ar...
Embodiment 2
[0079] The concrete steps of this embodiment are:
[0080] 1. Input the boundary of the plane area Ω and the sampling density function f(x,y)
[0081] Input the boundary of the plane area Ω, in this embodiment, the boundary of the plane area Ω is represented by a non-convex polygon, and the vertices of the polygon are all in the plane area [-1.5, 1.5] × [-1.5, 1.5] (see the appendix Figure 10 ); define the sampling density function f(x,y) on the plane area Ω as:
[0082] f(x,y)=1.0 / (10·d Ω (x,y)+1.0)
[0083] where d Ω (x, y) is the shortest distance from any point on the plane to the boundary of the plane area Ω. For any point (x, y) in the plane area Ω, the function f(x, y) can give a density value greater than 0.
[0084] 2. Determine the convex polygon Γ containing the plane area Ω, and generate the initial sampling point set
[0085] Determine a convex polygon Γ covering the plane area Ω on the plane. In this embodiment, the convex polygon Γ is taken as a rectangle,...
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Abstract
The invention discloses a density-controlled plane region adaptive sampling method, the main steps of which:inputting plane area Omega and sampling density function f; determining the convex region Gamma covering the plane region Omega and a sampling point set P is generated in the convex region Gamma;determining the dual triangular grids of the V diagram and calculating the average resolution and average density of the grids,adaptively adding, deleting the sampling point operation for the sampling point set P; processing the centralization of gravity to V diagram according to the density function f ;repeating the operation of adding, deleting the sampling point set for the sampling point set P and the processing of centralization of gravity to V diagram, sampling points controlled by the density function f in the convex region Gamma are obtained, and then the sampling point set in the plane region Omega is obtained and taken as the sampling results of the method.The invention can generate a set of adaptive sampling points controlled by density in the plane area,which principle is simple and easy to realize,the generated set of points is randomly distributed on the basis of the density function.
Description
technical field [0001] The invention relates to a density-controlled plane area self-adaptive sampling method, which belongs to the field of computer graphics. Background technique [0002] There are two main methods of sampling: [0003] (1) Sampling method of free-form surface: using discrete sampling points to extract the original shape information of the surface is surface digitization. At present, there are many methods of surface digitalization, such as the shape-based digital sampling method of free-form surfaces (see: Lai Xinmin et al., Digital Adaptive Sampling of Free-form Surfaces with Known Mathematical Models, Journal of Computer-Aided Design and Graphics, 1999, 11( 4): 359-362), this type of method proposes a shape-based sampling method based on the concept of centroid, which can determine a reasonable number of sampling points under the condition of a given sampling accuracy. This technology mainly samples the surface, and the sampling process depends on the...
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