REDUCED DATA FOR CURVE MODELING – APPLICATIONS IN GRAPHICS, COMPUTER VISION AND PHYSICS
Małgorzata Janik 1  
,  
Ryszard Kozera 1, 2  
,  
 
 
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1
Faculty of Mathematics and Information, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
2
Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences – SGGW, Nowoursynowska 159, 02-776 Warsaw, Poland
Publication date: 2013-06-15
 
Adv. Sci. Technol. Res. J. 2013; 7(18):28–35
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ABSTRACT
In this paper we consider the problem of modeling curves in Rn via interpolation without a priori specified interpolation knots. We discuss two approaches to estimate the missing knots for non-parametric data (i.e. collection of points. The first approach (uniform evaluation) is based on blind guess in which knots are chosen uniformly. The second approach (cumulative chord parameterization) incorporates the geometry of the distribution of data points. More precisely, the difference is equal to the Euclidean distance between data points qi+1 and qi. The second method partially compensates for the loss of the information carried by the reduced data. We also present the application of the above schemes for fitting non-parametric data in computer graphics (light-source motion rendering), in computer vision (image segmentation) and in physics (high velocity particles trajectory modeling). Though experiments are conducted for points in R2 and R3 the entire method is equally applicable in Rn.