Shape modeling with point-sampled geometry

By Mark Pauly, Richard Keiser, Leif Kobbelt, Markus H. Gross. 2003

555 citations recorded by the source corpus.

We present a versatile and complete free-form shape modeling framework for point-sampled geometry. By combining unstructured point clouds with the implicit surface definition of the moving least squares approximation, we obtain a hybrid geometry representation that allows us to exploit the advantages of implicit and parametric surface models. Based on this representation we introduce a shape modeling system that enables the designer to perform large constrained deformations as well as boolean operations on arbitrarily shaped objects. Due to minimum consistency requirements, point-sampled surfaces can easily be re-structured on the fly to support extreme geometric deformations during interactive editing. In addition, we show that strict topology control is possible and sharp features can be generated and preserved on point-sampled objects. We demonstrate the effectiveness of our system on a large set of input models, including noisy range scans, irregular point clouds, and sparsely as well as densely sampled models.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

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Citations in the corpus

PCPNet Learning Local Shape Properties from Raw Point Clouds (2017, methodology): “The ﬁrst category includes more robust distance-weighted approaches [PKKG03], methods such as osculating jets [CP03] based on ﬁtting higher-order primitives robustly, the algebraic point set surface approach based on ﬁtting algebraic spheres [GG07], and approaches based on analyzing the…”
An intuitive framework for real-time freeform modeling (2004, methodology): “An alternative approach which mimics boundary constraint modeling is to compute a blending function that propagates the constraints into the interior of the support region [Singh and Fiume 1998; Bendels and Klein 2003; Pauly et al. 2003].”
P2P-NET: Bidirectional Point Displacement Net for Shape Transform (methodology): “Point cloud, as a 3D shape representation, has shown its advantages and applications in geometry modeling [Pauly et al. 2003], rendering [Alexa et al. 2003], and computer animation [Müller et al. 2004].”
A survey of point-based techniques in computer graphics (2004, methodology): “3) [20] The moving least-squares (MLS) surfaces of [21] [22] provide an approximating or interpolating surface for a given set of point samples by local higher order polynomials and have first been applied to point-based methods by Alexa et al. [23] [24].”
Reassembling fractured objects by geometric matching (2006, methodology): “For multi-scale edge extraction we use a modified version of the method presented by [Pauly et al. 2003].”
Neural Unsigned Distance Fields for Implicit Function Learning (2020, background): “Extracting dense point clouds (PC) is necessary for applications such as point based modelling [55, 2], and is a common shape representation for learning [60].”
EC-Net: an Edge-aware Point set Consolidation Network (2018, methodology): “To consolidate a point set in an edge-aware manner, some methods detected/sensed the sharp edges and arranged points deliberatively along edges to preserve their sharpness [16,17,18,19].”
Algebraic point set surfaces (2007, methodology): “The former definition is well suited for resampling, while the latter one is convenient to raytrace the surface [Adamson and Alexa 2003; Wald and Seidel 2005] or to perform Boolean operations [Pauly et al. 2003].”
Voronoi-based variational reconstruction of unoriented point sets (2007, unknown): “Normal estimation from point sets has received a lot of attention in the past few years (see e.g., [ PKKG03 ,MNG04, DLS05,OF05,LP05,HXMP05]).”
Deep Learning for Robust Normal Estimation in Unstructured Point Clouds (2016, background): “Moving least squares [ABCO ∗ 03, PKKG03] and local kernel regression [ÖGG09] estimate normals as the gradient of an implicit surface, preserving sharp features, but requiring reliable normal priors as input.”