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This paper presents novel probabilistic nodes combination (PNC) method of curve interpolation.
The proposed method of curve interpolation provides an important alternative solution in curve-based subdivision surface design.
These five steps can be treated as the algorithm of PNC method of curve modeling and interpolation (1).
This method requires only the area above an experimental curve, thus is simpler than the conventional method of curve fitting.
Considering about the disadvantage of measured settlement data treatment methods on tanks in current standards, an optimization method of curve fitting on the measured settlement data is presented.
The variables investigated are, shear displacement/number of measurements, method of curve fitting the loci, shear velocity and depth of the powder sample.
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The following additional information are available with the online version of this paper: Additional file 1 which contains supplementary results and their discussion regarding complementary analysis of the impact of the minimum required number of nearest neighbours for the RDN algorithm, and complementary methods of curve similarity assessment.
Also, there exist several well-established methods of curve modeling, for example shape-preserving techniques [22], subdivision algorithms [23] and others [24] to overcome the difficulties of polynomial interpolation, but probabilistic interpolation with nodes combination seems to be quite novel in the area of shape modeling.
As a new method of representing curves, Q-Bézier curves not only exhibit the beneficial properties of Bézier curves but also allow effective shape adjustment by changing multiple shape parameters.
The proposed method, called probabilistic nodes combination (PNC), is the method of 2D curve interpolation and modeling using the set of key points (knots or nodes).
In the present paper we propose a method of constrained curve drawing using certain C1-quadratic trigonometric splines having shape parameters, which have been recently introduced in [Han X. Quadratic trigonometric polynomial curves with a shape parameter. Computer Aided Geometric Design 2002 19 503 12].
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