Sliding Deformation: Shape Preserving Per-Vertex Displacement

We present a novel algorithm for deforming a locally smooth polygonal mesh by sliding its vertices over the surface. This sliding deformation creates the visual appearance of texture animation without requiring an explicit global surface parameterization or the overhead of storing texture coordinates. The proposed deformation algorithm can also be employed to slide vertices over the surface to increase or decrease resolution in desired regions. To produce the sliding displacement, we define a deformation space that couples the precision of a local parameterization with the advantages of a global parameterization, needed for consistency of displacements over the affected region. On demand, we establish a set of local parameterization spaces that minimize distortion error around each displaced vertex. To propagate the displacement direction across the set of spaces while ensuring coherency, we calculate a representation of global direction in each local space. To map a displaced vertex from the deformation space back to the surface with minimal distortion, we use the local parameterization space of the given vertex. Our method is inherently parallelizable, works on arbitrary topology, and provides a user-friendly, intuitive interface.