Free-form design using axial curve-pairs

Deformation of 3D shapes usually requires the use of a deformation tool. The freeform deformation technique requires the use of a lattice of control point for deforming an object. This may require a synchronized movement of the lattice control points in order to obtain the desired effects. The axial deformation technique allows an object to be deformed by manipulating an axial curve. However, unexpected twist of the object may be obtained. This is a result of the lack of control on the local coordinate frame of the curve. This paper presents a technique for deforming objects with a set of axial curve-pairs. The use of a curve-pair allows the local coordinate frame to be controlled intuitively. A curve-pair is composed of a primary and an orientation curve. The orientation curve is an approximate offset of the primary curve. A technique is proposed for maintaining the relation between the primary and the orientation curve when the curve-pair is adjusted. By associating a complex 3D object to a curve-pair, the object can be stretched, bended, and twisted intuitively through manipulating the curve-pair. This deformation technique is particularly suitable for manipulating complex shapes (e.g. decorative components) in industrial and aesthetic design, and is also suitable for modelling characters and animals with ¯exible bodies. Adjusting the curve-pair according to some motion constraints produces different postures of a character or animal model. This in turn can be used as decorative components for aesthetic design.