Approximating Bézier Rectangular Surface Using Degree Elevation

2011 ◽  
Author(s):  
Pathom Mangkang ◽  
Natasha Dejdumrong
Keyword(s):  
Degree Elevation

Degree Operations on Periodic Surfaces

2007 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Surface Model ◽  
Implicit Surface ◽  
Periodic Surface ◽  
Degree Elevation ◽  
Periodic Surfaces ◽  
Computer Aided ◽  
Particle Aggregates

In previous work, a periodic surface model for computer-aided nano-design (CAND) was developed. This implicit surface model can construct Euclidean and hyperbolic nano geometries parametrically and represent morphologies of particle aggregates and polymers. In this paper, we study the characteristics of degree elevation and reduction based on a generalized periodic surface model. Methods of degree elevation and reduction operations are developed in order to support multi-resolution representation and model exchange.

On degree elevation of T-splines

2016 ◽  
Vol 46 ◽  
pp. 16-29 ◽  
Author(s):  
Jingjing Zhang ◽  
Xin Li
Keyword(s):  
Degree Elevation

Degree elevation for -sided surfaces

2001 ◽  
Vol 18 (2) ◽  
pp. 135-147 ◽  
Author(s):  
A.A. Ball ◽  
J.J. Zheng
Keyword(s):  
Degree Elevation

scholarly journals Generalized Shifted Chebyshev Koornwinder’s Type Polynomials: Basis Transformations

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 692 ◽  
Author(s):  
Mohammad AlQudah ◽  
Maalee AlMheidat
Keyword(s):  
Explicit Formula ◽  
Bernstein Polynomial ◽  
Continuous Functions ◽  
The Other ◽  
Numerical Techniques ◽  
Bernstein Basis ◽  
Fixed Degree ◽  
Explicit Formulas ◽  
Degree Elevation ◽  
Polynomial Bases

Approximating continuous functions by polynomials is vital to scientific computing and numerous numerical techniques. On the other hand, polynomials can be characterized in several ways using different bases, where every form of basis has its advantages and power. By a proper choice of basis, several problems will be removed; for instance, stability and efficiency can be improved, and numerous complications can be resolved. In this paper, we provide an explicit formula of the generalized shifted Chebyshev Koornwinder’s type polynomial of the first kind, T r * ( K 0 , K 1 ) ( x ) , using the Bernstein basis of fixed degree. Moreover, a Bézier’s degree elevation was used to rewrite T r * ( K 0 , K 1 ) ( x ) in terms of a higher degree Bernstein basis without altering the shapes. In addition, explicit formulas of conversion matrices between generalized shifted Chebyshev Koornwinder’s type polynomials and Bernstein polynomial bases were given.

Comparison of noise and tone azimuth tuning of neurons in cat primary auditory cortex and medical geniculate body

1995 ◽  
Vol 74 (3) ◽  
pp. 961-980 ◽  
Author(s):  
J. C. Clarey ◽  
P. Barone ◽  
W. A. Irons ◽  
F. K. Samson ◽  
T. J. Imig
Keyword(s):  
Auditory Cortex ◽  
Medial Geniculate Body ◽  
Primary Auditory Cortex ◽  
Broadband Noise ◽  
Statistical Analyses ◽  
Data Set ◽  
Degree Elevation ◽  
Level Data ◽  
Medial Geniculate ◽  
Ventral Nucleus

1. A comparison of the azimuth tuning of single neurons to broadband noise and to best frequency (BF) tone bursts was made in primary auditory cortex (AI: n = 173) and the medial geniculate body (MGB: n = 52) of barbiturate-anesthetized cats. Observations were largely restricted to cells located within the tonotopically organized divisions of the MGB (i.e., the ventral nucleus and the lateral division of the posterior nuclear group) and the middle layers of AI. All cells studied had BFs > or = 4 kHz. 2. The responses of each cell to sounds presented from seven frontal azimuthal locations (-90 to +90 degrees in 30 degrees steps; 0 degree elevation) and at five sound pressure levels (SPLs: 0-80 dB or 5-85 dB in 20-dB steps) provided an azimuth-level data set. Responses were averaged over SPL to obtain an azimuth function, and a number of features of this function were used to describe azimuth tuning to noise and to tone stimulation. Azimuth function modulation was used to assess azimuth sensitivity, and cells were categorized as sensitive or insensitive depending on whether modulation was > or = 75% or < 75% of maximum, respectively. The majority (88%) of cells in the sample were azimuth sensitive to noise stimulation, and statistical analyses were restricted to these cells, which are presumably best suited to encode sound source azimuth. Azimuth selectivity was assessed by a preferred azimuth range (PAR) over which azimuth function values exceeded 75% (PAR75) or 50% of maximum response. Cells were categorized according to the location and extent of their noise PARs. Unbounded cells had laterally located PARs that extended to the lateral pole (+/- 90 degrees); bounded cells had PARs that were contained entirely within the frontal hemifield, and a subset of these had PARs centered on the midline (+/- 15 degrees). A final group of cells exhibited multipeaked azimuth functions to noise stimulation. 3. Azimuth functions to noise were generally more selective and/or more sensitive than those to tones. Statistical analyses showed that these differences were significant for cells in each azimuth function category, and for the thalamic and cortical samples. With the exception of multipeaked cells, responsiveness to noise was significantly lower than that to tones in all categories, and for the thalamic and cortical samples.(ABSTRACT TRUNCATED AT 400 WORDS)

A blossoming approach to accuracy of the degree elevation process

1996 ◽  
Vol 13 (2) ◽  
pp. 265-306 ◽  
Author(s):  
J. -C. Fiorot ◽  
P. Jeannin
Keyword(s):  
Degree Elevation
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