A kinetic framework for computational geometry

Contributing vertices-based Minkowski sum computation of convex polyhedra

“…Guibas et al [30,31] presented a kinetic framework in two dimensions. An accomplishment of this framework was to define the operation of convolution on planar tracings in 2D.…”

New Approximation Methods for Planar Offset and Convolution Curves

“…Convolution is a classic operation which has been used as a tool for computing collision-free paths in robot motion planning [3,16,27]. Moreover, the convolution operation has applications in character font design [13,14], offset and rounding [30], and shape transformation [21].…”

“…Given two regular parametric curves: C 1 (t) = (x 1 (t), y 1 (t)), t 0 ≤ t ≤ t 1 , and C 2 (s) = (x 2 (s), y 2 (s)), s 0 ≤ s ≤ s 1 , we define their convolution curve (C 1 * C 2 )(t) as follows (see [3,16]):…”

“…Guibas et al [16] investigated some important properties of convolution curves. Convolution has a close relationship to other geometric entities such as common tangent and curve intersection.…”

“…1, the inner envelope curves do not contribute to the offset and convolution boundaries; their elimination is a direct consequence of the condition: C 1 (t), C 2 (s(t)) > 0. Offset and convolution computations are classic operations in CAD/CAM, which can be used in various interesting geometric applications such as NC machining [8,17], motion planning [3,16,27], character font and brush stroke design [13,14], blending [30], and shape transformation [21].…”