Curve fitting and fairing using conic splines

High-quality quadratic curve fitting for scanned data of styling design

“…Liming's work [13] is representative of the classical literature and presents an application to aircraft design. More recent studies [22,4,29] deal with G 2 stitching of quadratic curve segments with Bézier forms.…”

Finding planes in LiDAR point clouds for real-time registration

“…An ideal solution would be to find and fit all possible conics to this signal -conic sections with higher curvature correspond to more confident evidence of planes with a particular orientation, and those with lower or no curvature have much greater uncertainty about the possible planes that generated them (figure 2c). Unfortunately, finding and fitting general conics to unpartitioned data is neither easy nor fast when dealing with thousands of points [23]. As a fast approximation, we look for regions in the signal which correspond to smoothly varying segments that could possibly belong to a conic.…”

Approximation by Conic Splines

“…Pottmann [24] presents a local scheme, still achieving curvature continuity. Yang [28] constructs a curvature continuous conic spline by first fitting a tangent continuous conic spline to a point set and fairing the resulting curve. Li et al [16] show how to divide the initial curve into simple segments which can be efficiently approximated with rational quadratic Bézier curves.…”