Spherical Perspective

Abstract

We survey the present state of spherical perspective, regarding both mathematical structure and drawing practice, with a view to applications in the visual arts. We define a spherical perspective as the entailment of a conical anamorphosis with a compact flattening of the visual sphere. We examine a general framework for solving spherical perspectives, exemplified with the azimuthal equidistant ("fisheye") and equirectangular cases. We consider the relation between spherical and curvilinear perspectives. We briefly discuss computer renderings, but focus on methods adapted to freehand sketching or technical drawing with simple instruments such as ruler and compass. We discuss how handmade spherical perspective drawings can generate immersive anamorphoses, which can be rendered as virtual reality panoramas, leading to hybrid visual creations that bridge the gap between traditional drawing and digital environments.

Workshop - Drawing Equirectangular Perspectives for VR Panoramas with Eq A Sketch 360

“…The theory will follow the spherical perspective survey in [6], quickly introducing the general relation between anamorphosis and spherical perspectives, and drawing methods focusing on transformation groups. Spherical perspectives are seen as two-step entailments of anamorphosis followed by cartographic mapping, and it is shown how the flattening transformation groups result in mechanical drawing methodsin this case the sliding grid method.…”

“…The ping-pong snake method. We apply the zig-zag method of [6] to make a uniform tiling of the plane (e.g. a checkered floor) by bouncing a line between two diagonals vanishing to a common point at 45 degrees to the tile axis.…”

“…Currently, three spherical projections are well understood as perspectives [6]: equirectangular, azimuthal equidistant, and cubical. In this workshop we will focus on equirectangular.…”