====== Extended space mapping ======
{{frep:shell.gif?nolink}}

We have introduced a general mathematical framework for transforming functionally defined shapes. The proposed model of extended space mappings considers transformations of a hypersurface in coordinate-function space with its projection onto geometric space. This model covers coordinate [[sculpt|space mappings]], [[metamor|metamorphosis]], and [[asum|algebraic operations]] on defining functions, and introduces several new types of transformations, such as function-dependent space mappings and combined mappings. The approach is illustrated by new local deformations created by means of function mappings, feature-based space mapping, offsetting along the normal, generation of a thin shell of a solid (figure above), 2D shape blending, and collision-free metamorphosis.

See the formulation of the extended space mapping and examples of applications in the paper

Savchenko V.V., Pasko A.A. " Transformation of functionally defined shapes by extended space mappings ", The Visual Computer, vol. 14, No. 5/6, 1998, pp. 257-270.
Electronic version: [[http://hyperfun.org/ESMapTVC98.pdf|PDF (581 K)]]