Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
The Computation of Visible-Surface Representations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Polygonization of implicit surfaces
Computer Aided Geometric Design
Guaranteed ray intersections with implicit surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Fast Surface Interpolation Using Hierarchical Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Volumetric shape description of range data using “Blobby Model”
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
An implicit surface polygonizer
Graphics gems IV
Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Using particles to sample and control implicit surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A framework for interactive texturing on curved surfaces
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Shape transformation using variational implicit functions
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Priors Stabilizers and Basis Functions: From Regularization to Radial, Tensor and Additive Splines
Priors Stabilizers and Basis Functions: From Regularization to Radial, Tensor and Additive Splines
Discovering Process Models from Unlabelled Event Logs
BPM '09 Proceedings of the 7th International Conference on Business Process Management
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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.