Geometric modeling
Subdivision algorithms converge quadratically
Journal of Computational and Applied Mathematics
Applications of power series in computational geometry
Computer-Aided Design
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
On local implicit approximation and its applications
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Real-time robot motion planning using rasterizing computer graphics hardware
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Construction and optimization of CSG representations
Computer-Aided Design - Beyond solid modelling
Numerical methods for hypersingular and near-singular boundary integrals in fracture mechanics
Numerical methods for hypersingular and near-singular boundary integrals in fracture mechanics
Separation for boundary to CSG conversion
ACM Transactions on Graphics (TOG)
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A haptic interaction method for volume visualization
Proceedings of the 7th conference on Visualization '96
Shape Representation Using a Generalized Potential Field Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional distance field metamorphosis
ACM Transactions on Graphics (TOG)
Using distance maps for accurate surface representation in sampled volumes
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Numerical implicitization for intersection and Gn-continuous blending of surfaces
Computer Aided Geometric Design
Proceedings of the fifth ACM symposium on Solid modeling and applications
Three dimensional freeform sculpting via zero sets of scalar trivariate functions
Proceedings of the fifth ACM symposium on Solid modeling and applications
Implicit functions with guaranteed differential properties
Proceedings of the fifth ACM symposium on Solid modeling and applications
Shape transformation using variational implicit functions
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Approximate implicitization using monoid curves and surfaces
Graphical Models and Image Processing
Numerical parameterization of curves and surfaces
Computer Aided Geometric Design
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Volumetric multi-texturing for functionally gradient material representation
Proceedings of the sixth ACM symposium on Solid modeling and applications
Transfinite interpolation over implicity defined sets
Computer Aided Geometric Design
The Mathematica Book
Robot Motion Planning
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Level set surface editing operators
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
A Level-Set Approach for the Metamorphosis of Solid Models
IEEE Transactions on Visualization and Computer Graphics
Distance Field Manipulation of Surface Models
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Generalized sweep templates for implicit modeling
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Vector field based shape deformations
ACM SIGGRAPH 2006 Papers
Designing with distance fields
ACM SIGGRAPH 2006 Courses
Field modeling with sampled distances
Computer-Aided Design
Implicit boundary control of vector field based shape deformations
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
SARDF: signed approximate real distance functions in heterogeneous objects modeling
Heterogeneous objects modelling and applications
Optimization of continuous heterogeneous models
Heterogeneous objects modelling and applications
SMI 2011: Full Paper: Feature based volumes for implicit intersections
Computers and Graphics
Technical note: Signed Lp-distance fields
Computer-Aided Design
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For a given set of points S, a Euclidean distance field is defined by associating with every point p of Euclidean space Ed a value that is equal to the Euclidean distance from p to S. Such distance fields have numerous computational applications, but are expensive to compute and may not be sufficiently smooth for some applications. Instead, popular implicit modeling techniques rely on various approximate fields constructed in a piecewise manner. All such constructions lead to sacrifices in distance properties that have not been properly studied or characterized. We show that the quality of an approximate distance field may be characterized locally near the boundary by its order of normalization and can be studied in terms of the field derivatives. The approach allows systematic quantitative assessment and comparison of various construction methods. In particular, we provide detailed analysis of several popular field construction methods that rely on set decompositions and R-functions, as well as identify the key factors affecting the quality of the constructed fields.