Detecting approximate symmetries of parts of a model is important when attempting to determine the geometric design intent of approximate boundary-representation (B-rep) solid models produced e.g. by reverse engineering systems. For example, such detected symmetries may be enforced exactly on the model to improve its shape, to simplify its analysis, or to constrain it during editing. We give an...

Symmetry is one of the most important properties of a shape, unifying form and function. It encodes semantic information on one hand, and affects the shape’s aesthetic value on the other. Symmetry comes in many flavors, amongst the most interesting being intrinsic symmetry, which is defined only in terms of the intrinsic geometry of the shape. Continuous intrinsic symmetries can be represented ...

Approximate symmetries of a mathematical model describing one-dimensional motion in a nonlinear medium with a small dissipation are studied. In a physical application, the approximate solution is calculated making use of the approximate generator of the first-order approximate symmetry.

There is a problem of defining energy in time-varying spacetimes as energy is not conserved in them. The problem is particularly severe for gravitational waves as there is no conventional stress-energy tensor. The gravitational field is given by the Weyl tensor. The gravitational field is given by the Weyl tensor but that does not provide a measure of the energy. Pseudo tensors are introduced b...

A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poi...