Treffer: Hermite Interpolation of Scalar Fields in Computer Graphics.

Scalar valued functions, such as height- and signed distance fields, are essential in real-time computer graphics. Depending on dimensionality, these are represented by function sample values stored on a regular grid that are bi- or trilinearly filtered, resulting in C0 approximations. First, we propose to store the partial derivatives of the scalar valued function with the function values and use Hermite interpolation between the samples. This guarantees a globally C¹ -continuous result. For rendering applications, the surface normal vectors are often part of the discrete field of samples, as such, our technique does not necessarily require extra storage, merely a different basis to store the same data. The exact normals of the reconstructed cubic Hermite surface can be used as shading normals, resulting in a storage efficient replacement for normal mapping with richer visual appearance. We show that our method generalizes to arbitrary orders and dimensions. Moreover, we derive an approximation for mixed partial derivatives for three dimensional first order fields, akin to Adini’s method for parametric surface patches. We demonstrate the applicability of Hermite interpolation in height field and signed distance field rendering. [ABSTRACT FROM AUTHOR]

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