Multiple-points constraints based deformation for free-form surfaces

There is an increasing demand in the conceptual design for more intuitive methods for creating and modifying free-form 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 free-form surface deformation representation. The model is a combination of two functions: a displacement function and a function for representing an existing NURBS surface called parent surface. Based on the surface model, the authors develop two deformation methods which are named SingleDef (Singlepoint constraint based deformation method), and MultiDef (Multiple-points constraints based deformation method). The techniques for free-form surface deformation allow conceptual designer to modify a parent surface by directly applying point constraints to the parent surface. The deformation methods are implemented and taken in an experimental CAD system. The results show that the designer can easily and intuitively control the surface shape.