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

Compositing with 2D Vector Fields by using Shape Maps that can represent Inconsistent, Impossible, and Incoherent Shapes