Two-dimensional Potential Fields for Advanced Implicit Modeling Operators

Current methods for building models using implicit volume techniques present problems defining accurate and controllable blend shapes between implicit primitives. We present new methods to extend the freedom and controllability of implicit volume modeling. The main idea is to use a free-form curve to define the profile of the blend region between implicit primitives. The use of a free-form implicit curve, controlled point-by-point in the Euclidean user space, allows us to group boolean composition operators with sharp transitions or smooth free-form transitions in a single modeling metaphor. This idea is generalized for the creation, sculpting and manipulation of volume objects, while providing the user with simplicity, controllability and freedom in implicit modeling.