Curvature based sampling of curves and surfaces

Abstract

Efficient sampling methods enable the reconstruction of a generic surface with a limited amount of points. The reconstructed surface can therefore be used for inspection purpose. In this paper a sampling method that enables the reconstruction of a curve or surface is proposed. The input of the proposed algorithm is the number of required samples. The method takes into account two factors: the regularity of the sampling and the complexity of the object. A higher density of samples is assigned where there are some significant features, described by the curvature. The analysed curves and surfaces are described through the B-splines spaces. The sampling of surfaces generated by two or more curves is also discussed.

Efficient Adaptive Sampling Methods Based on Deviation Analysis of Piecewise Cubic Spline Interpolation

“…The curve sampling methods used for comparison are ISD, USP , uniform sampling of arc length (USL) [4], uniform sampling of arc length and accumulative curvature (USLC) [2], EISD-7, EISD-L2(3,3), and EISD-L3 (3,3,3). The methods were compared on three NURBS curves having different geometrical complexities.…”

“…• , where denotes the number of inspection points in the direction, and denotes the number of inspection points in direction. The comparison surface sampling methods are as follows: S-EISD, USP, uniform sampling of accumulative marginal areas (USE) [2], and uniform sampling of accumulative marginal areas and mean curvature (USEC) [2]. The maximum deviations of the four sampling methods are shown in Fig.…”

“…The geometry-guided sampling methods usually analyze geometrical features, such as knot vectors, curvature, arclength, and inflection points, and combine multiple factors by conferring different weights. These methods enable the inspection points to reach the characteristic distribution [2,3,[7][8][9][10]. The error-guided sampling methods analyze the machine error, reconstruction error, reconstruction uncertainty, and other errors and utilize the error analysis results to determine critical points.…”

“…Blind sampling methods use a fixed pattern without considering features such as shape and complexity of geometry. These methods are easy to understand and implement and include various methods, such as uniform sampling of parametric value, arclength, or surface area [2][3][4]. To increase the discrepancy between points, Hammersley sampling and Halton sampling have been proposed [5,6].…”

NurbsNet: A Nurbs approach for 3d object recognition

“…There are some studies [24] and [25] that investigate this topic in order to choose the proper parameters that generate the points that better represent the surface.…”