This paper explores the notion of a general rubber sheet transformation and its use as a tool in an interactive font design environment. The designer works with graph-paper-like orthogonal grids and applies the rubber sheet transformation to the gridspace to obtain new shapes. Further, he or she may subsequently work on the transformed gridspace to fine-tune the shapes. A computationally efficient deformation mapping technique for use in such an interactive design environment has been presented. An important feature is that the order of the high-level outline definitions of the deformed shape is the same as that of the original design. The shape deformation takes place in three stages. In the first stage, the original 2D shape is mapped onto a user definable doubly-curved surface. Next the surface is affinely transformed, once again under the control of the user. In the last stage the transformed 3D shape is projected onto a plane to get the deformed shape. We discuss this deformation technique, and a refinement of this technique, where the x and y coordinates are handled independently. This technique has been incorporated in a font design system, Vinyas, to produce the transformed letterforms as new typefaces in scalable outline form. © 1993.
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