Enhancing graphical objects whose behaviors are governed by the laws of physics is an important requirement in modeling virtual physical environments. In such environments, the user can interact with graphical objects and is able to either feel the simulated reaction forces through a physical computer interface such as a force feedback mouse or through such interactions, objects behave in a natural way. One of the key requirements for such interaction is determination of the type of contact between the user controlled object and the objects representing the environment. This paper presents an approach for reconstructing the contact configuration between two objects. This is accomplished through usage of the time history of the motion of the approaching objects for inverse trajectory mapping of polygonal representation. In the case of deformable objects and through usage of mass-spring-damper system this paper also presents a special global filter that can map the local deformation of an object to the adjacent vertices of polygonal mesh. In addition to offering a fast computational framework, the proposed method also offers more realistic representation of the deformation. The results of this paper are shown through detailed examples and comparison analysis using different computational platforms.