Wavelets based quantitative design of B-spline curves

Wang, Aizeng; Zhao, Gang

doi:10.1016/j.eswa.2014.04.029

Cited by 3 publications

(3 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, because B-spline functions F m and F n are already known, if scale factors m and n are determined, then a (n + 3) 3 (m + 3) inner product matrix ½hF n jF m i could be calculated. Assume that E = ½hF n jF m i and X = Q mn , then equation 9is transformed into the solution of null space, as expressed in equation (10). Here, E is the coefficient matrix of null space…”

Section: Description Of Wavelet Constructionmentioning

confidence: 99%

“…By constructing the length-preserving projection of curves, Wang et al 9 deduced the double-scale subdivision equations of multi-scale functions and multi-scale wavelets, and constructed the multi-wavelets on some smooth plane curves. In order to control the better deformation of the curves and obtain the more accurate modeling, Wang and Zhao 10 initially introduced a new concept of reference index of modeling (RIOM) based on wavelet theory. Compared to traditional algorithms, this one takes RIOM as objective function and objective shape, which can quantitatively evaluate objective function value determined by RIOM and ensure the overall shape of the curve at the same time.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Rapid wavelet construction of multi-resolution fairing for curves and surfaces with any number of control vertices

2020

Advances in Mechanical Engineering

View full text Add to dashboard Cite

In the field of curves and surfaces fairing, arbitrary resolution wavelet fairing algorithm made wavelet fairing technology widely extended to general curves and surfaces, which are determined by any number of control vertices. Unfortunately, accurate wavelet construction algorithm for general curves and surfaces still has not been perfect now. In this article, a concrete algorithm for reconstruction matrix and wavelet construction was emphatically studied, which would be used in the multi-resolution fairing process for curves and surfaces with any number of control vertices. The essence of this algorithm is to generalize wavelet construction into the solution of null space, which could be solved gradually and rapidly by the procedures of decomposition and simplification of coefficient matrix. Certainly, the related compactly supported wavelets could be constructed efficiently and accurately, too. In the last of the article, a complex curve and a complex surface case were provided to verify the stability, high performance, and robustness of this algorithm.

show abstract

Section: Description Of Wavelet Constructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rapid wavelet construction of multi-resolution fairing for curves and surfaces with any number of control vertices

2020

Advances in Mechanical Engineering

View full text Add to dashboard Cite

show abstract

“…This is an advantage over the traditional algorithms [4,6,7] for multi-resolution representation of one surface. So, the new algorithm can be applied in wavelet-based model editing to filter out unwanted frequency noise while preserving the geometric features of the boundaries [19,20].…”

mentioning

confidence: 99%

An algorithm for multi-resolution analysis of NURBS surfaces

Wang

Zhao

2016

Computers & Mathematics with Applications

Self Cite

View full text Add to dashboard Cite

a b s t r a c tA new algorithm is proposed for the multi-resolution representation of NURBS (NonUniform Rational B-Spline) surfaces with boundary consistency constraints. The kernel idea is to employ T-meshes (T-spline control meshes) to construct the multi-resolution representation for surfaces. To this end, the original B-mesh (B-spline control mesh) is first divided into a boundary part and an inner one; then, the multi-resolution representation of the inner part is achieved by wavelet transform; at last, the topology of the boundary part is added onto the obtained multi-resolution meshes to construct the final T-spline based multi-resolution representation result. The boundary shapes keep unchanged in the whole process of the treatment, because the boundary consistency constraints are always contained in the boundary part. This advantage of the new algorithm is demonstrated by three examples.

show abstract

Wavelet based local fairing algorithm for surfaces with data compression

Wang

Zhao

2015

Int. J. Wavelets Multiresolut Inf. Process.

View full text Add to dashboard Cite

By combining the T-spline and wavelet techniques together, this paper proposes a new local fairing algorithm for B-spline surfaces. There are two steps of operations in the new algorithm. The first is to decompose a local region into a scale part and a detail one by wavelet analysis. The second is to reconstruct the surface by removing the detail part and then replacing the local region by the scale one. Because the scale part constitutes a T-spline, the new algorithm can not only realize local fairing, but also simultaneously reduce the control points. The effectiveness of the new approach is verified by three examples, which also demonstrate that the major advantage of the new algorithm over the traditional ones lies in its local fairing capability.

show abstract

Wavelets based quantitative design of B-spline curves

Cited by 3 publications

References 17 publications

Rapid wavelet construction of multi-resolution fairing for curves and surfaces with any number of control vertices

Rapid wavelet construction of multi-resolution fairing for curves and surfaces with any number of control vertices

An algorithm for multi-resolution analysis of NURBS surfaces

Wavelet based local fairing algorithm for surfaces with data compression

Contact Info

Product

Resources

About