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arXiv · 2304.09440

Fractal Interpolation on the Real Projective Plane

A. Hossain·Md. N. Akhtar·M. A. Navascués
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Abstract

Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then we consider an iterated function system giving rise to a fractal interpolation function of a set of data.

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A. Hossain, Md. N. Akhtar, M. A. Navascués. 2023-04-19. Fractal Interpolation on the Real Projective Plane. https://doi.org/10.1007/s11075-023-01657-z

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