Generating a “3D” Image from One Continuous 2D Curve

Mayer D. Schwartz
Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture (2014)
Pages 445–448 Short Papers


An image which looks very three dimensional can be generated by a single two dimensional continuous curve. The curve serves as a guide for a series of plates which are placed at a constant distance apart along the curve. All of the plates have the same shape but each plate has its own color and opacity. The net effect can be color and shading changes within the 2D image which strongly suggests a 3D image but one that may not be physically realizable. To further enhance the 3D quality of the final image, a contrast curve may be applied to the 2D image. Often a more aesthetically pleasing final image can be obtained by applying a conformal map to the 2D image as well.