Tensor Product Surface Splines

2000 ◽  
pp. 193-209
Author(s):  
Gary D. Knott
Keyword(s):  
Tensor Product ◽  
Surface Splines ◽  
Product Surface ◽  
Tensor Product Surface

scholarly journals Tensor-product surface patches with Pythagorean-hodograph isoparametric curves

2015 ◽  
Vol 36 (3) ◽  
pp. 1389-1409 ◽  
Author(s):  
Rida T. Farouki ◽  
Francesca Pelosi ◽  
Maria Lucia Sampoli ◽  
Alessandra Sestini
Keyword(s):  
Tensor Product ◽  
Surface Patches ◽  
Pythagorean Hodograph ◽  
Product Surface ◽  
Tensor Product Surface

scholarly journals A Family of Binary Approximating Subdivision Schemes based on Binomial Distribution

2019 ◽  
Vol 38 (4) ◽  
pp. 1087-1100 ◽  
Author(s):  
Muhammad Asghar ◽  
Ghulam Mustafa
Keyword(s):  
Tensor Product ◽  
Binomial Distribution ◽  
Probability Generating Function ◽  
Visual Performance ◽  
Complete Analysis ◽  
Subdivision Schemes ◽  
B Splines ◽  
Surface Subdivision ◽  
Product Surface ◽  
Tensor Product Surface

A simplest way is introduced to generate a generalized algorithm of univariate and bivariate subdivision schemes. This generalized algorithm is based on the symbol of uniform B-splines subdivision schemes and probability generating function of Binomial distribution. We present a family of binary approximating subdivision schemes which has maximum continuity and less support size. Our proposed family members P4, P5, P6, and P7, have C7, C9, C11 and C13 continuities respectively. In fact, we use Binomial probability distribution to increase the continuity of uniform B-splines subdivision schemes up to more than double. We present the complete analysis of one family member of proposed schemes and give a visual performance to check smoothness graphically. In our analysis, we present continuity, Holder regularity, degree of generation, degree of reproduction and limit stencils analysis of proposed family of subdivision schemes. We also present a survey of high continuity subdivision schemes. Comparison shows that our proposed family of subdivision schemes gives high continuity of subdivision schemes comparative to existing subdivision schemes. We have found that as complexity increases the continuity also increases. In the last, we give the general formula for tensor product surface subdivision schemes and also present the visual performance of proposed tensor product surface subdivision schemes.

scholarly journals Accurate and Efficient Evaluation of Chebyshev Tensor Product Surface

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Keshan He ◽  
Peibing Du ◽  
Hao Jiang ◽  
Chongwen Duan ◽  
Hongxia Wang ◽  
...  
Keyword(s):  
Image Analysis ◽  
Error Analysis ◽  
Tensor Product ◽  
Condition Number ◽  
Numerical Experiments ◽  
Numerical Approximation ◽  
Classical Approach ◽  
Accurate Evaluation ◽  
Product Surface ◽  
Tensor Product Surface

A Chebyshev tensor product surface is widely used in image analysis and numerical approximation. This article illustrates an accurate evaluation for the surface in form of Chebyshev tensor product. This algorithm is based on the application of error-free transformations to improve the traditional Clenshaw Chebyshev tensor product algorithm. Our error analysis shows that the error bound is u+Ou2×condP,x,y in contrast to classic scheme u×cond(P,x,y), where u is working precision and condP,x,y is a condition number of bivariate polynomial P(x,y), which means that the accuracy of the computed result is similar to that produced by classical approach with twice working precision. Numerical experiments verify that the proposed algorithm is stable and efficient.

scholarly journals Implicitization of tensor product surfaces in the presence of a generic set of basepoints

2017 ◽  
Vol 16 (10) ◽  
pp. 1750189
Author(s):  
Eliana Duarte
Keyword(s):  
Tensor Product ◽  
Geometric Modeling ◽  
Vector Subspace ◽  
Rational Map ◽  
Implicit Equation ◽  
Generic Position ◽  
Finite Set ◽  
Product Surface ◽  
Proof Techniques ◽  
Generic Set

Given a [Formula: see text]-dimensional vector subspace [Formula: see text] of [Formula: see text], a tensor product surface, denoted by [Formula: see text], is the closure of the image of the rational map [Formula: see text] determined by [Formula: see text]. These surfaces arise in geometric modeling and in this context it is useful to know the implicit equation of [Formula: see text] in [Formula: see text]. In this paper, we show that if [Formula: see text] has a finite set of [Formula: see text] basepoints in generic position, then the implicit equation of [Formula: see text] is determined by two syzygies of [Formula: see text] in bidegrees [Formula: see text] and [Formula: see text]. This result is proved by understanding the geometry of the basepoints of [Formula: see text] in [Formula: see text]. The proof techniques for the main theorem also apply when [Formula: see text] is basepoint free.

Reference Signal Based Tensor Product Expansion for EOG-Related Artifact Separation in EEG

2017 ◽  
Vol E100.A (11) ◽  
pp. 2230-2237
Author(s):  
Akitoshi ITAI ◽  
Arao FUNASE ◽  
Andrzej CICHOCKI ◽  
Hiroshi YASUKAWA
Keyword(s):  
Tensor Product ◽  
Reference Signal

On degeneracy problem of NFSRs via semi-tensor product

2020 ◽  
Author(s):  
Xinyu Zhao ◽  
Biao Wang ◽  
Shuqian Zhu ◽  
Jun-e Feng
Keyword(s):  
Tensor Product ◽  
Degeneracy Problem

On the Buchstaber Subring in MSp∗

1998 ◽  
Vol 5 (5) ◽  
pp. 401-414
Author(s):  
M. Bakuradze
Keyword(s):  
Tensor Product ◽  
Characteristic Classes ◽  
Generalized Quaternion ◽  
Symplectic Cobordisms

Abstract A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups.

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