Proceedings on Mathematics of surfaces II
The displacement method for implicit blending surfaces in solid models
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Real functions for representation of rigid solids
Computer Aided Geometric Design
Blend surfaces for set theoretic volume modelling systems
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Implicit Gn-blending of vertices
Computer Aided Geometric Design
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
SCCG '01 Proceedings of the 17th Spring conference on Computer graphics
Implicit Modelling with Skeleton Curves: Controlled Blending in Contact Situations
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Local metamorphosis of functionally defined shapes
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Blending implicit shapes using fuzzy set operations
WSEAS Transactions on Information Science and Applications
2D piecewise algebraic splines for implicit modeling
ACM Transactions on Graphics (TOG)
Computer-Aided Design
Technical Section: Locally restricted blending of Blobtrees
Computers and Graphics
Technical Section: WarpCurves: A tool for explicit manipulation of implicit surfaces
Computers and Graphics
Space-time blending with improved user control in real-time
ACM SIGGRAPH ASIA 2010 Sketches
Bounding volumes for implicit intersections
ACM SIGGRAPH ASIA 2010 Posters
Real-time space-time blending with improved user control
MIG'10 Proceedings of the Third international conference on Motion in games
SMI 2011: Full Paper: Feature based volumes for implicit intersections
Computers and Graphics
Procedural function-based modelling of volumetric microstructures
Graphical Models
A gradient-based implicit blend
ACM Transactions on Graphics (TOG)
SMI 2013: Adequate inner bound for geometric modeling with compact field functions
Computers and Graphics
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We propose new analytical formulations of bounded blending operations for the function-based constructive shape modeling. The blending set operations are defined using R-functions and displacement functions with the localized area of influence. The shape and location of the blend is defined by control points on the surfaces of two solids or by an additional arbitrary bounding solid also defined by a real-valued function. The proposed blending using a bounding solid can be applied to a single selected edge, a vertex, or another blend. We introduce new types of blends such as a multiple blend with the disconnected bounding solid and a partial edge blend. We show that the proposed operations can replace pure set-theoretic operations in the solid model without rebuilding the entire construction tree data structure. The proposed blending is shown to have versatile applications in interactive design. Influence of all parameters on the blend shape and location is illustrated.