Italian Chapter Conference 2018 - Smart Tools and Apps in computer Graphics

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https://diglib.eg.org/handle/10.2312/2632667

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Browsing Italian Chapter Conference 2018 - Smart Tools and Apps in computer Graphics by Subject "Mathematics of computing"

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    Gradient Field Estimation on Triangle Meshes
    (The Eurographics Association, 2018) Mancinelli, C.; Livesu, M.; Puppo, E.; Livesu, Marco and Pintore, Gianni and Signoroni, Alberto
    The estimation of the differential properties of a function sampled at the vertices of a discrete domain is at the basis of many applied sciences. In this paper, we focus on the computation of function gradients on triangle meshes. We study one face-based method (the standard the facto), plus three vertex based methods. Comparisons regard accuracy, ability to perform on different domain discretizations, and efficiency. We performed extensive tests and provide an in-depth analysis of our results. Besides some behaviour that is common to all methods, in our study we found that, considering both accuracy and efficiency, some methods are preferable to others. This directly translates to useful suggestions for the implementation of gradient estimators in research and industrial code.
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    Indicators Basis for Functional Shape Analysis
    (The Eurographics Association, 2018) Melzi, S.; Livesu, Marco and Pintore, Gianni and Signoroni, Alberto
    Step functions are widely used in several applications from geometry processing and shape analysis. Shape segmentation, partial matching and self similarity detection just to name a few. The standard signal processing tools do not allow us to fully handle this class of functions. The classical Fourier series, for instance, does not give a good representation for these non smooth functions. In this paper we define a new basis for the approximation and transfer of the step functions between shapes. Our definition is fully spectral, allowing for a concise representation and an efficient computation. Furthermore our basis is specifically built in order to enhance its use in combination with the functional maps framework. The functional approach also enable us to handle shape deformations. Thanks to that our basis achieves a large improvement not only in the approximation of step functions but also in the transfer, exploiting the functional maps framework. We perform a large set of experiments showing the improvement achieved by the proposed basis in the approximation and transfer of step functions and its stability with respect to non isometric deformations.