Perspective drawings of reflective spheres

Abstract

We give an analysis of the planar perpspective images of reflections of lines in a mirrored sphere, paying particular attention to the number and location of their vanishing points. We use this analysis to describe how to draw the images of boxes reflected in a mirrored sphere, providing an analogy of what, in linear perspective, would be one-point perspective drawings. We contrast this with the work of Termes. In addition, we provide an analysis of two methods for computing viewing distance between the artist and the sphere for existing drawings of spherical reflections. One method uses distances between vanishing points; the other is an estimate that requires knowing a single small measurement from the ‘real world’.

Keywords:

• perspective
• vanishing points
• reflective spheres
• mirrors

AMS Subject Classifications:

• 51N15
• 00A66
• 97M80

Acknowledgements

The author wishes to thank the several referees who read through a highly distorted version of this manuscript, and whose helpful comments were right on point. The author is also extremely grateful to Martina Mincheva, whose student research project became the basis for both 5 and this article.