Extensions in variational geometry that generate and modify object edges composed of rational Bézier curves

Abstract Variational geometry is a powerful method for the definition and modification of geometric models, as it constrains object geometry as sets of functional constraints rather than nominal Cartesian elements. This allows one to capture design intent by specifying geometric and engineering constraints that, when resolved using a nonlinear equation solver, define the geometry of the object. The paper explores some of the issues raised when rational Bezier curves are used to generate the edges of a model, that is, specifically, the representation of basic model edges: straight lines and conics. Rational Bezier curves are investigated as they can be used to represent conics precisely in addition to being well equipped to represent and manipulate free-form curves and surfaces.