Graphics gems IV
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
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
Rapid and accurate computation of the distance function using grids
Journal of Computational Physics
A Level-Set Approach for the Metamorphosis of Solid Models
IEEE Transactions on Visualization and Computer Graphics
Constructive hypervolume modeling
Graphical Models - Volume modeling
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Efficient algorithms for solving static hamilton-jacobi equations
Efficient algorithms for solving static hamilton-jacobi equations
Heterogeneous material modeling with distance fields
Computer Aided Geometric Design
Approximate distance fields with non-vanishing gradients
Graphical Models
Spline approximation of general volumetric data
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
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Distribution of material density and other properties of heterogeneous objects can be parametrized by the Euclidean distance function from the object boundary or from special material features. For objects constructed using geometric primitives and set-theoretic operations, an approximation of the distance function can be obtained in a constructive manner by applying special compositing operations to the distance functions of primitives. We describe such operations based on a smooth approximation of min/max functions and prove their C1 continuity. These operations on distance functions are called SARDF operations for Signed Approximate Distance Functions. We illustrate their applications by 2D and 3D objects models with heterogeneous material distribution.