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Extended space mapping

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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
space mappings,
metamorphosis, and
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: PDF (581 K)

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