Free-form deformation of constructive shell models

Free-form deformation (FFD) is known to be a powerful technique for deforming an object independent of its representation. A point on a solid is deformed by specifying the point relative to a coordinate system defined with a lattice of control points. Adjusting the control points of the lattice deforms the object. The deformed object can be visualized by sampling points on the object surfaces, or by approximating the object with a polyhedral model. However, a conversion of the polyhedral model to the underlining solid representation is required if further solid operations (e.g. Boolean operation) is to be applied. This paper presents a technique for applying FFD on constructive shell models (CSR). A CSR object is constructed by subtracting a set of depression (negative) trunctets from the union of a set of outer (positive) trunctets and a polyhedron core. FFD is applied to the polyhedron core and the trunctets of the model. A trunctet is deformed by applying FFD to a set of selected surface points on the trunctet. The deformed trunctet is obtained by interpolating a surface through the deformed surface points. In the deformation of a trunctet, an outer trunctet may become a depression trunctet (or vice versa). By using the concept of mating trunctet, and an approach for classifying the shape of a trunctet, shape changes of a trunctet in a deformation can be determined. Deformation of a trunctet may also result in an invalid trunctet that bulges out of its enclosing tetrahedron. Besides, the degree of the algebraic surface used determines the size of a trunctet relative to the distance between adjacent lattice control points. A subdivision of a trunctet may have to be performed to maintain the validity of a deformation.