Proceedings on Mathematics of surfaces II
Blend surfaces for set theoretic volume modelling systems
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Design of solids with free-form surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Interactive techniques for implicit modeling
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Implicit reconstruction of solids from cloud point sets
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Efficient estimation of 3D Euclidean distance fields from 2D range images
VVS '02 Proceedings of the 2002 IEEE symposium on Volume visualization and graphics
Distance Field Manipulation of Surface Models
IEEE Computer Graphics and Applications
Computational Methods for Geometric Processing. Applications to Industry
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Geometric clipping using boolean textures
VIS '93 Proceedings of the 4th conference on Visualization '93
Bounded Blending for Function-Based Shape Modeling
IEEE Computer Graphics and Applications
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Computer Aided Geometric Design
Designing with distance fields
ACM SIGGRAPH 2006 Courses
SIGGRAPH '04 ACM SIGGRAPH 2004 Sketches
Implicit curve and surface design using smooth unit step functions
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Computer-Aided Design
Computer Aided Geometric Design
Technical Section: Locally restricted blending of Blobtrees
Computers and Graphics
A gradient-based implicit blend
ACM Transactions on Graphics (TOG)
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To date, methods that blend solids, that is, B-rep or CSG models, with implicit functions require successive composition of the blending functions to handle an arbitrary solid model. The shape of the resulting surfaces depends upon the algebraic distances defined by these functions. To achieve meaningful shapes, previous methods have relied on blending functions that have a pseudo-Euclidean distance measure. These methods are abstracted, resulting in some general observations. Unfortunately, the functions used can exhibit unwanted discontinuities. A new method, the displacement form of blending, embeds the zero surface of the blending functions in a form for which algebraic distance is C1 continuous in the entire domain of definition.Characteristics of the displacement form are demonstrated using the superelliptic blending functions. Intuitive and mathematical underpinnings are provided.