Rao distances and Conformal Mapping
Arni S.R. Srinivasa Rao, Steven G. Krantz
TL;DR
This paper explores Rao distances and conformal mappings on 3D objects, proposing methods to measure point distances and line integrals, with applications in virtual tourism.
Contribution
It introduces new propositions for constructing distances within 3D objects using Rao distances and conformal mappings, linking complex plane integrals to 3D geometry.
Findings
Proposes methods for measuring distances within 3D objects
Connects conformal mappings to virtual tourism applications
Develops propositions for line integrals in complex planes
Abstract
In this article, we have described the Rao distance (due to C.R. Rao) and ideas of conformal mappings on 3D objects with angle preservations. Three propositions help us to construct distances between the points within the 3D objects in \mathbb{R}^{3} and line integrals within complex planes. We highlight the application of these concepts to virtual tourism.
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Taxonomy
Topics3D Shape Modeling and Analysis · Advanced Numerical Analysis Techniques · Computer Graphics and Visualization Techniques