Parabolic-cylindrical moving least squares surfaces - Archive ouverte HAL Access content directly
Journal Articles Computers and Graphics Year : 2015

Parabolic-cylindrical moving least squares surfaces

(1, 2) , (1, 2) , (2, 1) , (2, 3, 1)


Moving least squares (MLS) surface approximation is a popular tool for the processing and reconstruction of non-structured and noisy point clouds. This paper introduces a new variant improving the approximation quality when the underlying surface is assumed to be locally developable, which is often the case in point clouds coming from the acquisition of manufactured objects. Our approach follows Levin's classical MLS procedure: the point cloud is locally approximated by a bivariate quadratic polynomial height-field defined in a local tangent frame. The a priori developability knowledge is introduced by constraining the fitted poly-nomials to have a zero-Gaussian curvature leading to the actual fit of so-called parabolic cylinders. When the local developability assumption cannot be made unambiguously, our fitted parabolic cylinders seamlessly degenerate to linear approximations. We show that our novel MLS kernel reconstructs more locally-developable surfaces than previous MLS methods while being faithful to the data.
Vignette du fichier
graphical_abstract.jpg (166.13 Ko) Télécharger le fichier Fichier principal
Vignette du fichier
main.pdf (19.21 Mo) Télécharger le fichier
Format : Figure, Image
Origin : Files produced by the author(s)
Comment : Graphical abstract
Origin : Files produced by the author(s)

Dates and versions

hal-01169572 , version 1 (29-06-2015)
hal-01169572 , version 2 (15-07-2015)



Brett Ridel, Gael Guennebaud, Patrick Reuter, Xavier Granier. Parabolic-cylindrical moving least squares surfaces. Computers and Graphics, 2015, International Conference Shape Modeling, 51, pp.60-66. ⟨10.1016/j.cag.2015.05.006⟩. ⟨hal-01169572v2⟩
778 View
480 Download



Gmail Facebook Twitter LinkedIn More