Constrained deformation of freeform surfaces using surface features for interactive design

There is an increasing demand in conceptual design for more intuitive methods for creating and modifying freeform curves and surfaces in CAD modeling systems. The methods should be based not only on the change of the mathematical parameters but also on the user's specified constraints and shapes. This paper presents a new surface representation model for freeform surface deformation representation. The model is a combination of two functions: a displacement function and a function for representing an existing NURBS surface called a parent surface. Based on the surface model, the authors develop several novel deformation methods which are named SingleDef (Single-point constraint based deformation method), MultiDef (Multiple-points constraints based deformation method), CurDef (Curve constraints based deformation method) and FeatDef (Feature constraint based deformation method). The techniques for freeform surface deformation allow conceptual designers to modify a parent surface by directly applying point constraints, curve constraint or a surface constraint to the parent surface. The deformation methods are implemented in an experimental CAD system. The results show that designers can easily and intuitively control the surface shape.