Abstract: The present invention is a system that produces a position of a rigid object, such as a button, on a deformed model, such as an animated piece of cloth, at each cycle in an animation of the model by isotropically finding a linear approximation of the deformation at the model and finding a rotation of the object allowing attachment of the object to the model. The system removes shear and scaling from a linear transformation of an average deformation of the model. A volumetric area of the deformed model in which the object will reside and which is used for the position determination is specified essentially as a mapping of the object onto the model. The average deformation of the area is calculated and the linear transformation of the object is performed with the average deformation. In finding the rotation a rotation characteristic matrix is created and Eigen vectors or directions are extracted and correspond to the rotation.