Browsing by Author "Puppo, Enrico"

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    EUROGRAPHICS 2019: Tutorials Frontmatter
    (Eurographics Association, 2019) Jakob, Wenzel; Puppo, Enrico; Jakob, Wenzel and Puppo, Enrico
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    Nearly Smooth Differential Operators on Surface Meshes
    (The Eurographics Association, 2022) Mancinelli, Claudio; Puppo, Enrico; Cabiddu, Daniela; Schneider, Teseo; Allegra, Dario; Catalano, Chiara Eva; Cherchi, Gianmarco; Scateni, Riccardo
    Estimating the differential properties of a signal sampled on a surface is of paramount importance in many fields of applied sciences. In the common practice, the surface is discretized with a polygonal mesh, the signal is sampled at its vertices and extended linearly over the triangles. This means that the polyhedral metric is assumed over the surface; the first derivatives of the signal become discontinuous across edges; and the second derivatives vanish. We present a new method based on surface fitting, which efficiently estimates the metric tensor, and the first and second order Riemannian differential operators at any point on the surface. All our differential operators are smooth within each triangle and continuous across the edges, providing a much better estimate of differential quantities on the - yet unknown - underlying smooth manifold.
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    Practical Computation of the Cut Locus on Discrete Surfaces
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Mancinelli, Claudio; Livesu, Marco; Puppo, Enrico; Digne, Julie and Crane, Keenan
    We present a novel method to compute the cut locus of a distance function encoded on a polygonal mesh. Our method exploits theoretical findings about the cut locus and - with a combination of analytic, geometric and topological tools - it is able to compute a topologically correct and geometrically accurate approximation of it. Our result can be either restricted to the mesh edges, or aligned with the real cut locus. Both outputs may be useful for practical applications. We also provide a convenient tool to optionally prune the weak branches of the cut locus, simplifying its structure. Our approach supersedes prior art, in that it is easier to use and also orders of magnitude faster. In fact, it depends on just one parameter, and it flawlessly operates on meshes with high genus and very high element count at interactive rates. We experiment with different datasets and methods for geodesic distance estimation. We also present applications to local and global surface parameterization.
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    A Scale-space Approach to the Morphological Simplification of Scalar Fields
    (The Eurographics Association, 2023) Rocca, Luigi; Puppo, Enrico; Banterle, Francesco; Caggianese, Giuseppe; Capece, Nicola; Erra, Ugo; Lupinetti, Katia; Manfredi, Gilda
    We present a multi-scale morphological model of scalar fields based on the analysis of the spatial frequencies of the underlying function. Morphological models partition the domain of a function into homogeneous regions. The most popular tool in this field is the Morse-Smale complex, where each region is spanned by all integral lines that join a minimum to a maximum, with the integral lines departing from saddles as region boundaries. Morphological features usually occur at very different scales, from noise and high frequency details up to large trends at the lowest frequencies. Without some form of multi-scale analysis, only the morphology at the finest scale is visible and explicit in such a model. The most popular approach in the literature is the filtration provided by persistent homology, a method that combines the amplitude values of critical points with the topology of the sublevel sets of the function. We propose the adoption of an alternative filtration method, based on the analysis of the deep structure of the linear scale-space of the function. To retrieve an adequately fine-grained ranked sequence of pairs of critical points that vanish through the scales, we adopt a continuous representation of the scale-space that overcomes the limits of discrete scale-space approaches. This sequence provides a progressive simplification of the Morse-Smale complex, resulting in a progressive multi-scale model of the morphology that always refers to the geometry of the original function, which is not changed by our model. We apply our method to digital elevation models, with results providing a multi-scale representation of the network of ridges and valley lines that joins peaks, pits and passes and divide the land into mountains and basins.
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    Straightedge and Compass Constructions on Surfaces
    (The Eurographics Association, 2021) Mancinelli, Claudio; Puppo, Enrico; Frosini, Patrizio and Giorgi, Daniela and Melzi, Simone and RodolĂ , Emanuele
    We discuss how classical straightedge and compass constructions can be ported to manifold surfaces under the geodesic metric. After defining the equivalent tools in the manifold domain, we analyze the most common constructions and show what happens when trying to port them to surfaces. Most such constructions fail, because the geometric properties on which they rely no longer hold under the geodesic metric. We devise some alternative constructions that guarantee at least some of the properties of their Euclidean counterpart; while we show that it is usually impossible to guarantee all properties together. Some constructions remain still unsolved, unless additional tools are used, which violate the constraints of the straightedge and compass framework since they take explicit distance measures. We integrate our constructions in the context of a prototype system that supports the interactive drawing of vector primitives on a surface represented with a high-resolution mesh.