Modelling with implicit surfaces that interpolate

By Greg Turk, James F. O'Brien. TOGS, 2002

382 citations recorded by the source corpus.

We introduce new techniques for modelling with interpolating implicit surfaces. This form of implicit surface was first used for problems of surface reconstruction and shape transformation, but the emphasis of our work is on model creation. These implicit surfaces are described by specifying locations in 3D through which the surface should pass, and also identifying locations that are interior or exterior to the surface. A 3D implicit function is created from these constraints using a variational scattered data interpolation approach, and the iso-surface of this function describes a surface. Like other implicit surface descriptions, these surfaces can be used for CSG and interference detection, may be interactively manipulated, are readily approximated by polygonal tilings, and are easy to ray trace. A key strength for model creation is that interpolating implicit surfaces allow the direct specification of both the location of points on the surface and the surface normals. These are two important manipulation techniques that are difficult to achieve using other implicit surface representations such as sums of spherical or ellipsoidal Gaussian functions ("blobbies"). We show that these properties make this form of implicit surface particularly attractive for interactive sculpting using the particle sampling technique introduced by Witkin and Heckbert. Our formulation also yields a simple method for converting a polygonal model to a smooth implicit model, as well as a new way to form blends between objects.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/525e83b0b0c996c22b713e04ed0b0b01b58c7ce9

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

In Computer Vision and Pattern Recognition

Citations in the corpus

Multi-level partition of unity implicits (2003, methodology): “Because of its local nature, the MPU method is more sensitive to the quality of input data, especially the field of normals, to compare with the approximation and interpolation techniques based on globally-supported RBFs [Carr et al. 2001; Turk and O’Brien 2002].”
Kernel techniques: From machine learning to meshless methods (2006, positive): “For example, this has been successfully demonstrated in various papers (Carr, Beatson, Cherrie, Mitchell, Fright, McCallum and Evans 2001, Turk and O’Brien 2002, Ohtake, Belyaev, Alexa, Turk and Seidel 2003a, Ohtake, Belyaev and Seidel 2003b) and is already well established in industry.3”
Interpolating and approximating implicit surfaces from polygon soup (2004, methodology): “, 2001], and [Turk and O’Brien, 2002] the function is represented using globally supported radial splines.”
A geometry projection method for shape optimization (2004, background): “Specifically, is identified with the zero-level set of a scalar function f , such that = {x ∈ : f (x) < 0} [27].”