Inverse solutions to interpolation techniques in computer graphics may increase the accuracy of the rendered frames. An example is the use of an arbitrary time stamp in time interpolation to evaluate the t-parameter, which in turn can be used for time-variant spatial interpolation. In this paper, an analytic inverse is presented for a shape-preserving piecewise cubic Hermite interpolant, used i...

Polynomial geometric interpolation by parametric curves became one of the standard techniques for interpolation of geometric data. An obvious generalization leads to rational geometric interpolation schemes, which are a much less investigated research topic. The aim of this paper is to present a general framework for Hermite geometric interpolation by rational Bézier spatial curves. In particul...

Smoothness is a desirable characteristic of interpolated zero curves; not only is it intuitively appealing, but there is some evidence that it provides more accurate pricing of securities. This paper outlines the mathematics necessary to understand the smooth interpolation of zero curves, and describes two useful methods: cubic-spline interpolation—which guarantees the smoothest interpolation o...

In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters w...

This study investigates the effects of the number of interpolation points on the prediction accuracy of segment angle trajectory during lifting. Ten participants performed various lifting tasks while a motion tracking system recorded their movements. Two-point through ten-point equal time-spaced segment angles extracted from major segment trajectory data captured by the motion tracking system w...

The interpolation task plays a key role in the reconstruction of high-resolution image quality in superresolution algorithms. In fact, the foremost shortcoming encountered in the classical interpolation algorithms, is that they often work poorly when used to eliminate blur and noise in the input image. In this sense, the aim of this work is to develop an interpolation scheme for the purpose of ...

Image magnification algorithms directly affect the quality of image magnification. In this paper, based on the image interpolation algorithm principle, features of the nearest neighbor interpolation, bilinear interpolation, bicubic interpolation and cubic B spline interpolation were analyzed. At the same time, their advantages and disadvantages were compared. In the experiment, image magnificat...

This paper deals with the shape preserving interpolation problem for visualization of 3D positive data. A required display of 3D data looks smooth and pleasant. A rational bi-cubic function involving six shape parameters is presented for this objective which is an extension of piecewise rational function in the form of cubic/quadratic involving three shape parameters. Simple data dependent cons...