Alignment of an Unmarked Deformable Sheet Like Object Based on NURBS Fitting In this paper, we proposed a method to realize automatic labeling task of a flexible sheet like object. It is a demonstration to the similar operations widely adopted in industrial production line such as those in flexible printed circuits assembly. In these operations, it needs to precisely position a specific part within a deformable sheet to a predefined position. In many applications involving such operations, the usage of artificial markers are not allowed and the target may lack enough features for tracking. Thus 3D position of the alignment reference has to be estimated from its contour. The task of aligning an unmarked paper sheet considered in this paper well demonstrates these situations. In this paper, Nonuniform rational BSplines (NURBS) fitting is utilized for tracking the shape variation of the paper. It is proved that for an unstretchable sheet like object, the fitted NURBS plane can be used in the way of servo control for regulating the shape. It provides a simple way to track the featureless points described with the paper undeformed generally as a sketch. The advantage of the proposed method is verified by successful alignment experiment in which a certain line defined on an undeformed paper sheet is aligned to the predefined position on a box.

Constrained fitting with freeform curves and surfaces Abstract   The accurate reconstruction of engineering parts from measured data is a challenging problem, in particular, when various geometric constraints need to be imposed to meet requirements in downstream CADCAM applications. There is a wide range of constraints including incidence, tangency, orthogonality, parallelism, symmetry and many others. In the majority of cases, only regular surfaces (planes, natural quadrics, sweeps) are involved; however, imposing constraints on objects with freeform curves and surfaces is also necessary in engineering practice; this motivated our work.  We numerically optimize complex systems of nonlinear equations, containing unknown control points and auxiliary geometric entities. We show that auxiliaries are indispensable; their use simplifies the algebra of the constraint equations and speeds up computations. We do not require the auxiliaries to be fixed in advance, rather propose incorporating them into the constraint system. As a result, the procedure will automatically substantiate various entities that have been unknown beforehand, for example, points of intersection or constrained trim curves on Bspline surfaces.  After formulating equations for a representative set of freeform constraints, we will discuss how this technique can be applied in practical reverse engineering. We will present case studies and analyze how surfaces get improved by means of constrained fitting.