ISSN:
1572-9125
Keywords:
parametric cubic spline
;
Primary 41A15
;
Secondary 41A25
;
65D05
;
G.1.1
;
G.1.2
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A plane curveC can be approximated by a parametric cubic splineΓ as follows. Points (x i ,y i ) are chosen in order alongC and a monotonically increasing variable τ is assigned values τ i at the points (x i ,y i ): τ i = the cumulative chordal distance from (x 1 ,y 1 ). The points (τ i ,x i ) and (τ i ,y i ) are then fitted separately by cubic splinesx(τ) andy(τ), to obtain Γ: (x(τ),y(τ)). This paper establishes estimates for the errors involved in approximatingC by Γ. It is found that the error in position betweenC and Γ decreases likeh 3, whereh is the maximum length of arc between consecutive knots onC. For first derivatives, the error behaves likeh 2; for second derivatives, likeh.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01933748
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