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A Novel Mapping with Natural Transition from Linear to Logarithmic Scaling

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The area hyperbolic function ArSinh has the interesting property of performing a linear mapping at arguments close to zero and a quasi-logarithmic mapping for large arguments. Further, it works also with a negative abscissa and at the zero-point. The transition from the linear to the logarithmic range is monotonic, so is the transition to the negative range. This paper demonstrates the use of the ArSinh-function in a range of application examples, such as zooming into the display of transfer-functions, sampling of curves with high density at a specific point and a coarse resolution elsewhere. The paper also reviews the linear and logarithmic mapping and discusses the properties of the new ArSinh-mapping.

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