Jörg Peters, University of Florida, Gainesville
Mid-Structures Linking Curved and Linear Geometry
Bèzier or b-spline control meshes are quintessential CAGD tools because they link linear and curved geometry providing a linear, refinable approximation that exaggerates features and is, up to reparametrization, in 1-1 correspondance with the curved geometry. However, for a given budget of line segments, Bèzier and b-spline control meshes are usually far from the 'nearest' piecewise linear approximand to the curved geometry.
This talk derives and analyzes a {mid-structure} (mid-path, mid-patch) that comes close to being the 'nearest' piecewise (bi-)linear approximand while retaining the 1-1 correspondance and the computational efficiency of control meshes. Several applications in analysis and design demonstrate increased efficiency when complementing control meshes with mid-structures.