The displacement method for implicit blending surfaces in solid models
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
An implicit formulation for precise contact modeling between flexible solids
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Bounded Blending for Function-Based Shape Modeling
IEEE Computer Graphics and Applications
Sketching Variational Hermite-RBF implicits
Proceedings of the Seventh Sketch-Based Interfaces and Modeling Symposium
Sketch based construction and rendering of implicit models
Computational Aesthetics'05 Proceedings of the First Eurographics conference on Computational Aesthetics in Graphics, Visualization and Imaging
Matisse: painting 2D regions for modeling free-form shapes
SBM'08 Proceedings of the Fifth Eurographics conference on Sketch-Based Interfaces and Modeling
Implicit skinning: real-time skin deformation with contact modeling
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
SMI 2013: Adequate inner bound for geometric modeling with compact field functions
Computers and Graphics
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We introduce a new family of binary composition operators that solves four major problems of constructive implicit modeling: suppressing bulges when two shapes merge, avoiding unwanted blending at a distance, ensuring that the resulting shape keeps the topology of the union, and enabling sharp details to be added without being blown up. The key idea is that field functions should not only be combined based on their values, but also on their gradients. We implement this idea through a family of C∞ composition operators evaluated on the GPU for efficiency, and illustrate it by applications to constructive modeling and animation.