SGP16: Eurographics Symposium on Geometry Processing (CGF 35-5)

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https://diglib.eg.org/handle/10.2312/2631427

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Browsing SGP16: Eurographics Symposium on Geometry Processing (CGF 35-5) by Subject "I.3.3 [Computer Graphics]"

Now showing 1 - 5 of 5
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    Crawl through Neighbors: A Simple Curve Reconstruction Algorithm
    (The Eurographics Association and John Wiley & Sons Ltd., 2016) Parakkat, Amal Dev; Muthuganapathy, Ramanathan; Maks Ovsjanikov and Daniele Panozzo
    Given a planar point set sampled from an object boundary, the process of approximating the original shape is called curve reconstruction. In this paper, a novel non-parametric curve reconstruction algorithm based on Delaunay triangulation has been proposed and it has been theoretically proved that the proposed method reconstructs the original curve under e-sampling. Starting from an initial Delaunay seed edge, the algorithm proceeds by finding an appropriate neighbouring point and adding an edge between them. Experimental results show that the proposed algorithm is capable of reconstructing curves with different features like sharp corners, outliers, multiple objects, objects with holes, etc. The proposed method also works for open curves. Based on a study by a few users, the paper also discusses an application of the proposed algorithm for reconstructing hand drawn skip stroke sketches, which will be useful in various sketch based interfaces.
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    Curve Reconstruction with Many Fewer Samples
    (The Eurographics Association and John Wiley & Sons Ltd., 2016) Ohrhallinger, Stefan; Mitchell, Scott A.; Wimmer, Michael; Maks Ovsjanikov and Daniele Panozzo
    We consider the problem of sampling points from a collection of smooth curves in the plane, such that the CRUST family of proximity-based reconstruction algorithms can rebuild the curves. Reconstruction requires a dense sampling of local features, i.e., parts of the curve that are close in Euclidean distance but far apart geodesically. We show that e < 0:47-sampling is sufficient for our proposed HNN-CRUST variant, improving upon the state-of-the-art requirement of e < 13 -sampling. Thus we may reconstruct curves with many fewer samples. We also present a new sampling scheme that reduces the required density even further than e < 0:47-sampling. We achieve this by better controlling the spacing between geodesically consecutive points. Our novel sampling condition is based on the reach, the minimum local feature size along intervals between samples. This is mathematically closer to the reconstruction density requirements, particularly near sharp-angled features. We prove lower and upper bounds on reach r-sampling density in terms of lfs e-sampling and demonstrate that we typically reduce the required number of samples for reconstruction by more than half.
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    CustomCut: On-demand Extraction of Customized 3D Parts with 2D Sketches
    (The Eurographics Association and John Wiley & Sons Ltd., 2016) Guo, Xuekun; Lin, Juncong; Xu, Kai; Chaudhuri, Siddhartha; Jin, Xiaogang; Maks Ovsjanikov and Daniele Panozzo
    Several applications in shape modeling and exploration require identification and extraction of a 3D shape part matching a 2D sketch. We present CustomCut, an on-demand part extraction algorithm. Given a sketched query, CustomCut automatically retrieves partially matching shapes from a database, identifies the region optimally matching the query in each shape, and extracts this region to produce a customized part that can be used in various modeling applications. In contrast to earlier work on sketch-based retrieval of predefined parts, our approach can extract arbitrary parts from input shapes and does not rely on a prior segmentation into semantic components. The method is based on a novel data structure for fast retrieval of partial matches: the randomized compound k-NN graph built on multi-view shape projections. We also employ a coarse-to-fine strategy to progressively refine part boundaries down to the level of individual faces. Experimental results indicate that our approach provides an intuitive and easy means to extract customized parts from a shape database, and significantly expands the design space for the user. We demonstrate several applications of our method to shape design and exploration.
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    Interactive Modeling of Mechanical Objects
    (The Eurographics Association and John Wiley & Sons Ltd., 2016) Ureta, Francisca Gil; Tymms, Chelsea; Zorin, Denis; Maks Ovsjanikov and Daniele Panozzo
    Objects with various types of mechanical joints are among the most commonly built. Joints implement a vocabulary of simple constrained motions (kinematic pairs) that can be used to build more complex behaviors. Defining physically correct joint geometry is crucial both for realistic appearance of models during motion, as these are typically the only parts of geometry that stay in contact, and for fabrication. Direct design of joint geometry often requires more effort than the design of the rest of the object geometry, as it requires design of components that stay in precise contact, are aligned with other parts, and allow the desired range of motion. We present an interactive system for creating physically realizable joints with user-controlled appearance. Our system minimizes or, in most cases, completely eliminates the need for the user to manipulate low-level geometry of joints. This is achieved by automatically inferring a small number of plausible combinations of joint dimensions, placement and orientation from part geometry, with the user making the final high-level selection based on object semantic. Through user studies, we demonstrate that functional results with a satisfying appearance can be obtained quickly by users with minimal modeling experience, offering a significant improvement in the time required for joint construction, compared to standard modeling approaches.
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    Splines in the Space of Shells
    (The Eurographics Association and John Wiley & Sons Ltd., 2016) Heeren, Behrend; Rumpf, Martin; Schröder, Peter; Wardetzky, Max; Wirth, Benedikt; Maks Ovsjanikov and Daniele Panozzo
    Cubic splines in Euclidean space minimize the mean squared acceleration among all curves interpolating a given set of data points. We extend this observation to the Riemannian manifold of discrete shells in which the associated metric measures both bending and membrane distortion. Our generalization replaces the acceleration with the covariant derivative of the velocity. We introduce an effective time-discretization for this novel paradigm for navigating shell space. Further transferring this concept to the space of triangular surface descriptors-edge lengths, dihedral angles, and triangle areas-results in a simplified interpolation method with high computational efficiency.