2D computer graphics endowed with a self-rendering method—a procedure which assigns colors to the image pixels by an arbitrary algorithm. Complex models can be built by combining simpler objects, in the paradigms of object-oriented programming. In Euclidean geometry, a translation moves every point a constant distance in a specified direction. A translation can be described as a rigid motion: other rigid motions include rotations and reflections. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. A translation operator is an operator formula_1 such that formula_2 If v
Differential geometry of surfaces both lie in ). The right hand side is symmetric in and , so the shape operator is self-adjoint on the tangent space. The eigenvalues of are just the principal curvatures and at . In particular the determinant of the shape operator at a point is the Gaussian curvature, but it also contains other information, since the mean curvature is half the trace of the shape operator. The mean curvature is an extrinsic invariant. In intrinsic geometry, a cylinder is developable, meaning that every piece of it is intrinsically indistinguishable from a piece of a plane since its Gauss curvature