B\'ezier curves that are close to elastica

We study the problem of identifying those cubic B\'ezier curves that are close in the L2 norm to planar elastic curves. The problem arises in design situations where the manufacturing process produces elastic curves; these are difficult to work with in a digital environment. We seek a sub-class of special B\'ezier curves as a proxy. We identify an easily computable quantity, which we call the lambda-residual, that accurately predicts a small L2 distance. We then identify geometric criteria on the control polygon that guarantee that a B\'ezier curve has lambda-residual below 0.4, which effectively implies that the curve is within 1 percent of its arc-length to an elastic curve in the L2 norm. Finally we give two projection algorithms that take an input B\'ezier curve and adjust its length and shape, whilst keeping the end-points and end-tangent angles fixed, until it is close to an elastic curve.Comment: 13 pages, 15 figure

MODELING OF BOND YIELD CURVE USING CUBIC BEZIER CURVE

Investors attracted to Bond have to analyze the Bond yield curve. In this study, the bond yield curve is modeled using a cubic bezier curve. The cubic bezier curve is flexible, precise, and simple to use and evaluate. The bonds used in this study are Surat Berharga Negara (Government Paper) Fix Rate type dated August, 2nd–6th 2021. Bond data is obtained from the Indonesia Stock Exchange https://www.idx.co.id. The results show that the bond yield curve that is formed varies because bond yields change every time following market developments. The cubic bezier curve is able to model the bond yield curve well. Cubic bezier curves have 4 control values ​​that help guide the curve well. The MSE value obtained by the bezier curve is small in general. The MSE values of the cubic bezier curve for the Bond yield data, sequentially from the least to the greatest, are 0,098 on August 4th, 2021; 0,1719 on August 5th, 2021; 0,2161 on August 3rd, 2021; 0,2498 on August 6th, 2021; and 0,2906 on August 2nd, 2021