Design of solids for antigravity motion illusion

This paper presents a method for designing solid shapes containing slopes where orientation appears opposite to the actual orientation when observed from a unique vantage viewpoint. The resulting solids generate a new type of visual illusion, which we call “impossible motion”, in which balls placed on the slopes appear to roll uphill thereby defying the law of gravity. This is possible because a single retinal image lacks depth information and human visual perception tries to interpret images as the most familiar shape even though there are infinitely many possible interpretations. We specify the set of all possible solids represented by a single picture as the solution set of a system of equations and inequalities, and then relax the constraints in such a way that the antigravity slopes can be reconstructed. We present this design procedure with examples.