Shapingslip

Shapingslip is a concept in geometric modeling and computer graphics describing a controlled local deformation of a shape achieved by applying a slip field along its surface or boundary. It is used to edit or align shapes while preserving much of the original topology and overall structure. The term often appears in discussions of non-rigid shape manipulation and registration, where precise, localized control of shape change is important.

Definition and model: For a shape S contained in a Euclidean space, shapingslip employs a vector field v defined on S to generate a family of deformations φ_t(x) = x + t v(x), with t in [0,1]. The deformed shape is S_t = φ_t(S). The slip can be characterized as tangential, normal, or a mixture relative to the surface, which influences how boundary, curvature, and area change during the deformation. If v is smooth and the resulting maps φ_t are diffeomorphisms for t in a chosen range, the deformation remains well-behaved and invertible.

Construction and constraints: Slip fields can be derived from various sources, including feature maps, curvature-driven flows, energy functionals that encourage alignment with a target shape, or user-specified control points. Practical implementations often impose constraints such as volume preservation, bounded distortion, or smoothness to prevent unwanted artifacts like self-intersections.

Applications: Shapingslip is used in non-rigid registration to align shapes from different modalities, in shape morphing and animation to achieve localized edits, in mesh editing to refine geometry, and in medical imaging for organ or tissue alignment with minimal structural disruption.

Limitations and considerations: Large slips can cause self-intersections or loss of invertibility. The results depend on the chosen slip field and regularization, and computational cost can be a factor in complex models.

See also: shape matching, non-rigid registration, mesh morphing, deformation field, diffeomorphic shape analysis.