A Note on Variable Upper Limit Integral of Bézier Curve

2022

COVID

Self Cite

Facing the worldwide coronavirus disease 2019 (COVID-19) pandemic, a new fitting method (QDF, quasi-distribution fitting) which can be used to analyze the data of COVID-19 is developed based on piecewise quasi-uniform B-spline curves. For any given country or district, it simulates the distribution histogram data which is made from the daily confirmed cases (or the other data including daily recovery cases and daily fatality cases) of COVID-19 with piecewise quasi-uniform B-spline curves. After using the area normalization method, the fitting curves could be regarded as a kind of probability density function (PDF): its mathematical expectation and the variance could be used to analyze the situation of the coronavirus pandemic. Numerical experiments based on the data of certain countries have indicated that the QDF method demonstrates the intrinsic characteristics of COVID-19 data of a given country or district, and because the interval of data used in this paper is over one year (500 days), it reveals the fact that after the multi-wave transmission of the coronavirus, the case fatality rate has obviously declined. These results show that the QDF method is effective and feasible as an appraisal method.

Section: Theoretical Considerationsmentioning

confidence: 99%

Analyzing the Data of COVID-19 with Quasi-Distribution Fitting Based on Piecewise B-Spline Curves

Zhao

2022

COVID

Self Cite

“…In order to get the expression of it, we need the following theorem: The details about the proof of theorem 1 could be found in our previous work [11].…”

Section: A Variable Upper Limit Integral Of Degree N Bézier Curvementioning

confidence: 99%

“…Given a degree n Bézier curve denoted by ( ) The details about the proof of theorem 2 could be found in our previous work [11].…”

Section: A Variable Upper Limit Integral Of Degree N Bézier Curvementioning

confidence: 99%

The construction of sets made by Bézier curves

Xue

2012 International Conference on Systems and Informatics (ICSAI2012)

2012

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“…Nowadays, CAD systems are widely used in all kinds of fields of mechanical engineering and manufacturing industry [1], as we known, the theory of CAD systems was beginning from so called Bézier curve developed by Pierre Bézier [2]. Based on that, there arose many other mathematic theories to construct curves and surfaces, in 1974 Ball, the British mathematician developed a kind of Cubic Ball basis to define his lofting surface program CONSURF at the British Aircraft Corporation [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Partial Said-Ball curves: A new type of generalized Ball curves

2012 IEEE International Conference on Computer Science and Automation Engineering (CSAE)

Lang

Xue

et al. 2012

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Ball basis was introduced for cubic polynomials by Ball, then generalized for polynomials of higher degree by Wang and Said. In this paper we present theorems and algorithms about constructing a new type of generalized Ball curves: Partial Said-Ball curves; investigate the properties and Bézier representation of the new curves; give the transforming matrixes between the basis of new curves and Bernstein basis which constructing Bézier curves. Furthermore, the shape differences between the new curves and the other existent generalized Ball curves are demonstrated through examples.