Volumetric shape description of range data using “Blobby Model”
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Fast raster scan distance propagation on the discrete rectangular lattice
CVGIP: Image Understanding
Real functions for representation of rigid solids
Computer Aided Geometric Design
Implicit reconstruction of solids from cloud point sets
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Shape Representation Using a Generalized Potential Field Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicit functions with guaranteed differential properties
Proceedings of the fifth ACM symposium on Solid modeling and applications
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Transfinite interpolation over implicity defined sets
Computer Aided Geometric Design
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Weighted Extended B-Spline Approximation of Dirichlet Problems
SIAM Journal on Numerical Analysis
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Constructive sculpting of heterogeneous volumetric objects using trivariate B-splines
The Visual Computer: International Journal of Computer Graphics
Approximate distance fields with non-vanishing gradients
Graphical Models
Direct extraction of surface meshes from implicitly represented heterogeneous volumes
Computer-Aided Design
Geometrically adaptive numerical integration
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Incremental reconstruction of sharp edges on mesh surfaces
Computer-Aided Design
Automation of the volumetric models construction
Heterogeneous objects modelling and applications
Finite element analysis in situ
Finite Elements in Analysis and Design
Engineering analysis in imprecise geometric models
Finite Elements in Analysis and Design
Geometric interoperability via queries
Computer-Aided Design
Meshfree natural vibration analysis of 2D structures
Computational Mechanics
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Traditional mesh-based approaches to the modeling and analysis of physical fields within geometric models require some form of topological reconstruction and conversion in the mesh generation process. Such manipulations tend to be tedious and error-prone manual processes that are not easily automated. We show that most field problems may be solved directly by using approximate distance fields computed from designed or sampled geometric data, thus avoiding many of the difficult reconstruction and meshing problems. With distances we can model fields that satisfy boundary conditions while approximating the governing differential equations to arbitrary precision. Because the method is based on sampling, it provides natural control for multi-resolution both in geometric detail of the domain and in accuracy of the computed physical field. We demonstrate the field modeling capability with several heat transfer applications, including a typical transient problem and a 'scan and solve' approach to the simulation of a physical field in a real-world artifact.