Geometric modeling
Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
The Euclidean distance transform
The Euclidean distance transform
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Real functions for representation of rigid solids
Computer Aided Geometric Design
Using Geometric Distance Fits for 3-D Object Modeling and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
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)
Numerical implicitization for intersection and Gn-continuous blending of surfaces
Computer Aided Geometric Design
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
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
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
Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design
Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design
Robot Motion Planning
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
IEEE Computer Graphics and Applications
Voxel-Based Modeling for Layered Manufacturing
IEEE Computer Graphics and Applications
Modelling of Material Property Variation for Layered Manufacturing
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Bilateral Recovering of Sharp Edges on Feature-Insensitive Sampled Meshes
IEEE Transactions on Visualization and Computer Graphics
B-rep SE: simplicially enhanced boundary representation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Direct extraction of surface meshes from implicitly represented heterogeneous volumes
Computer-Aided Design
A B-spline-based approach to heterogeneous objects design and analysis
Computer-Aided Design
Heterogeneous object modeling: A review
Computer-Aided Design
A CAD modeling system for heterogeneous object
Advances in Engineering Software
Multi-component heart reconstruction from volumetric imaging
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Transfinite Interpolation for Well-Definition in Error Analysis in Solid Modelling
Reliable Implementation of Real Number Algorithms: Theory and Practice
Material-solid modeling of human body: A heterogeneous B-spline based approach
Computer-Aided Design
Approach of heterogeneous bio-modeling based on material features
Computer-Aided Design
Modeling complex heterogeneous objects with non-manifold heterogeneous cells
Computer-Aided Design
Single-set and class-of-sets semantics for geometric models
Computer-Aided Design
Incremental reconstruction of sharp edges on mesh surfaces
Computer-Aided Design
Heterogeneous object design: an integrated CAX perspective
Heterogeneous objects modelling and applications
Modelling function-based mixed-dimensional objects with attributes
Heterogeneous objects modelling and applications
SARDF: signed approximate real distance functions in heterogeneous objects modeling
Heterogeneous objects modelling and applications
Feature-based material blending for heterogeneous object modeling
Heterogeneous objects modelling and applications
Heterogeneous objects modelling and applications
Distance to objects built with set operations in constructive solid modeling
Proceedings of the 13th International Conference on Humans and Computers
Technical note: Signed Lp-distance fields
Computer-Aided Design
SMI 2013: Morphological shape generation through user-controlled group metamorphosis
Computers and Graphics
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We propose a universal approach to the problem of computer modeling of shapes with continuosly varying material properties satisfying prescribed material conditions on a finite collection of material features and global constraints. The central notion is a parameterization of space by distances from the material features-either exactly or approximately. Functions of such distances provide a systematic and intuitive means for modeling: of desired material distributions as they arise in design, manufacturing, analysis and optimization of components with varying material properties.The proposed framework subsumes and generalizes a number of earlier proposals for heterogeneo as material modeling. It is theoretically complete in the sense that it allows representation of all material property functions. We demonstrate that the approach can be implemented within the existing framework of solid modeling and its numerous advantages, including: precise and intuitive control using explicit, analytic, differential, and integral constraints specified on the native geometry; guaranteed smoothness and analytic properties without meshing; and applicability to material features of arbitrary dimension, shape, and topology.