Geometry processing is mostly about applying algorithms to geometric models. If the algorithms represent the action, then the geometry is the object . In this section we are going to discuss various mathematical representations for geometric objects. While these representations can be 2D or 3D, the actual geometry that we are dealing with will always be the 2D surface of a 3D solid object. As we will see throughout this book, for each specific problem in geometry processing, we can identify a characteristic set of operations by which the computation is dominated, and hence we have to choose an appropriate representation that supports the efficient implementation of these operations.