Free Deformation of Multiresolution B-Splines Curves (original) (raw)
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An ideal spline-wavelet family for curve design and editing
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Subdivision schemes provide the most efficient and effective way to design and render smooth spatial curves. It is well known that among the most popular schemes are the de Rham-Chaikin and Lane-Riesenfeld subdivision schemes, that can be readily formulated by direct applications of the two-scale (or refinement) sequences of the quadratic and cubic cardinal B-splines, respectively. In more recent works, semi-orthogonal and bi-orthogonal spline-wavelets have been integrated to curve subdivision schemes to add such powerful tools as automatic level-of-detail control algorithm for curve editing and rendering, and efficient simulation processing scheme for global graphic illumination and animation. The objective of this paper is to introduce and construct a family of spline-wavelets to overcome the limitations of semi-orthogonal and bi-orthogonal spline-wavelets for these and other applications, by adding flexibility to the enhancement of desirable characters without changing the sweep of the subdivision spline curve, by providing the shortest lowpass and highpass filter pairs without decreasing the discrete vanishing moments, and by assuring robust stability.
Interactive Manipulation of Multiresolution Curves
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A new method for manipulation of curves in several degrees is presented.When a point of curve is moved, it affects a relative local segment, which sizecould depends of the propagation of the point through their lower resolutioncurves. So, for the same displacement of the point, could be generated relativelocal segments of different sizes, only varying a local parameter such stiffnessconstant.
Parameterization Method on B-Spline Curve
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The use of computer graphics in many areas allows a real object to be transformed into a three-dimensional computer model (3D) by developing tools to improve the visualization of two-dimensional (2D) and 3D data from series of data point. The tools involved the ...
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The parameterization method plays a critical role in B-spline interpolation. Some of the well-known parameterizations are the uniform, centripetal, chord length, Foley and universal methods. However, the interpolating results of these methods do not always satisfy all data features. In this study, we propose a new parameterization method which aims to improve the wiggle deviation of the interpolation, especially when interpolating the abrupt data interpolation. This new method is a refined centripetal method. The core of refinement is introducing the osculating circle at each data point. Besides the new parameterization method, we also design a fine wiggle validation method to verify the performance of all methods. In this paper, the proposed method is compared with centripetal, chord length, Foley, uniform and universal methods in both curve and surface cases. As a result, the proposed method has fewer wiggles than the centripetal method and other methods in the cases of abrupt-changing data. In addition, this refined method is stable for all kinds of data types, including free-form data distribution in this paper. The proposed method has fewer drawbacks than other methods, such as wiggles, oscillations, loops, and peaks, among others. More advantage, the proposed method is less influenced by the degree changing.
This paper describes a method of locally editing a B-spline curve via a set of positional constraints which the curve interpolates. Manipulation of a given constraint requires only a small number of neighbouring control points to be updated, providing local shape control. The B-spline curve can have single multiplicity at all internal knots, giving C 2 continuity for cubic curves. Updated control points are computed directly without the need to translate a region of the curve into Bézier form. The local update algorithm can also be used for interactive curve sketching and the insertion and removal of positional constraints. Consideration is given to ensuring that the curve maintains an aesthetically pleasing shape, and has an agreeable " dynamic behaviour " during sketching and editing.
Comparison of Parameterization Methods Used for B-Spline Curve Interpolation
European Journal of Technic, 2017
In this work we deal with the enterpolation of B-spline curves to fiven data points. B-spline curves are generated and compared with the given data points by various parameterization methods. To perform B-spline curve interpolation on the input data, the parameterization and the node vector must be generated using the input data. For parameterization purposes, uniform, chord length, centripetal, Foley, universal and similar methods have been developed. The uniform method gives good results if the data points are regular. Chord-to-beam parameterization can produce undesirable oscillations in long chords. Therefore, the centripetal method has been developed which operates according to the square root of the chord distance. In this study, these methods were compared with different data sets.
Multiresolution surface reconstruction for hierarchical B-splines
Graphics Interface, 1998
This paper presents a method for automatically generating a hierarchical B-spline surface from an initial set of control points. Given an existing mesh of control points , a mesh with half the resolution , is constructed by simultaneously approximating the finer mesh while minimizing a smoothness constraint using weighted least squares. Curvature measures of are used to identify features that need only be represented in the finer mesh. The resulting hierarchical surface accurately and economically reproduces the original mesh, is free from excessive undulations in the intermediate levels and produces a multiresolution representation suitable for animation and interactive modelling.
A QUICK GLANCE OF SPLINE WAVELETS AND ITS APPLICATIONS
Polynomial spline wavelets have played a momentous role in the enlargement of wavelet theory. Due to their attractive properties compact support, good smoothness property, interpolation property, they are now provide powerful tools for many scientific and practical problems. As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation. This paper is a summary of spline wavelet which started with splines and ends with the applications of spline wavelets. The paper is divided into four sections. The first section contains a brief introduction of splines and the second section is devoted to the discussion of spline wavelet construction via multiresolution analysis (MRA) with emphasis on B-spline wavelet. The underlying scaling functions are B-splines, which are shortest and most regular scaling function. In the third section, some remarkable properties of spline wavelets are discussed. The orthogonality and finite support properties make the spline wavelets useful for numerical applications and also have the best approximation properties among all the known wavelets. And the last section enclose a brief discussion of application of spline wavelets.