Developable surface fitting to point clouds

Peternell, Martín

doi:10.1016/j.cagd.2004.07.008

Cited by 56 publications

(43 citation statements)

References 11 publications

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“…In order to find the apex of a generalized cone that approximates a list of rulings, we inspire from the surface reconstruction method from Peternell et al [2004] and compute the best approximating generalized cones using a model based on the Blaschke cylinder 1 , which is particularly well adapted to our setting. This model matches a generalized cone to a one-parameter family of tangent planes computed along the rulings of a curved region.…”

Section: Fitting Generalized Conesmentioning

confidence: 99%

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Nonsmooth Developable Geometry for Interactively Animating Paper Crumpling

et al. 2015

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We present the first method to animate sheets of paper at interactive rates, while automatically generating a plausible set of sharp features when the sheet is crumpled. The key idea is to interleave standard physically-based simulation steps with procedural generation of a piecewise continuous developable surface. The resulting hybrid surface model captures new singular points dynamically appearing during the crumpling process, mimicking the effect of paper fiber fracture. Although the model evolves over time to take these irreversible damages into account, the mesh used for simulation is kept coarse throughout the animation, leading to efficient computations. Meanwhile, the geometric layer ensures that the surface stays almost isometric to its original 2D pattern. We validate our model through measurements and visual comparison with real paper manipulation, and show results on a variety of crumpled paper configurations.

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Section: Fitting Generalized Conesmentioning

confidence: 99%

“…We summarize this model and the way we use it below. See [Peternell 2004] and the references herein for a more detailed description in the context of Laguerre geometry.…”

Section: Fitting Generalized Conesmentioning

confidence: 99%

Nonsmooth Developable Geometry for Interactively Animating Paper Crumpling

et al. 2015

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“…Therefore, relating to our quasidevelopable mesh surface interpolation problem, our objective is to find one "most" developable mesh surface to satisfy the given boundary constraints. This is different from the problem of fitting a point cloud with a single "100 percent" developable torsal surface (cf., [8] and [9]), wherein the objective is to minimize the interpolation error.…”

Section: Background and Previous Workmentioning

confidence: 99%

Quasi-Developable Mesh Surface Interpolation via Mesh Deformation

Tang

Chen

2009

IEEE Trans. Visual. Comput. Graphics

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Abstract-We present a new algorithm for finding a most "developable" smooth mesh surface to interpolate a given set of arbitrary points or space curves. Inspired by the recent progress in mesh editing that employs the concepts of preserving the Laplacian coordinates and handle-based shape editing, we formulate the interpolation problem as a mesh deformation process that transforms an initial developable mesh surface, such as a planar figure, to a final mesh surface that interpolates the given points and/or curves. During the deformation, the developability of the intermediate mesh is maintained by means of preserving the zero-valued Gaussian curvature on the mesh. To treat the high nonlinearity of the geometric constrains owing to the preservation of Gaussian curvature, we linearize those nonlinear constraints using Taylor expansion and eventually construct a sparse and overdetermined linear system that is subsequently solved by a robust least squares solution. By iteratively performing this procedure, the initial mesh is gradually and smoothly "dragged" to the given points and/or curves. The initial experimental tests have shown some promising aspects of the proposed algorithm as a general quasi-developable surface interpolation tool.

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“…Non-planar developable surfaces can be characterized by the fact that exactly one principal curvature vanishes; they have one family of straight principal curvature lines. Recognizing and especially reconstructing developable surfaces from measurement data is not an easy task, as discussed by Peternell (2004). Classical principal curvature lines can hardly be employed for computations where robustness is essential.…”

Section: Principal Curves On Multiple Scalesmentioning

confidence: 99%