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.

Skeletal implicit modelling systems have been used to design models of both organic and man-made structures, however existing systems lack convenient and accurate methods for users to define fillets when building prototype engineering models. In this work we extend the methodology and skeletal primitives found in the BlobTree and introduce an improved method for modelling fillets. This is done by interpolating between hard-edged and soft-edged representations of a primitive, using the field to control the interpolation. Blending planes are introduced as a way of providing user control for this interpolation. The new methods are expressed as blend operators between two objects and can thus be implemented as a new node in the BlobTree. In addition we introduce an efficient methodology for modelling hard edged primitives.