  In this paper, we present a new compositing approach to obtain stylized
reflections and refractions with a simple control. Our approach does not
require any mask or separate 3D rendering. Moreover, only one additional image
is sufficient to obtain a composited image with convincing qualitative
reflection and refraction effects. We have also developed linearized methods
that are easy to compute. Although these methods do not directly correspond to
the underlying physical phenomena of reflection and refraction, they can
provide results that are visually similar to realistic 3D rendering. The main
advantage of this approach is the ability to treat images as ``mock-3D'' shapes
that can be inserted into any digital paint system without any significant
structural change. The core of our approach is the shape map, which encodes 2D
shape and thickness information for all visible points of an image of a shape.
This information does not have to be complete or consistent to obtain
interesting composites. In particular, the shape maps allow us to represent
impossible and incoherent shapes with 2D non-conservative vector fields.
