Abstract
This paper presents a novel algorithm for planar G1 interpolation using typical curves with monotonic curvature. The G1 interpolation problem is converted into a system of nonlinear equations and sufficient conditions are provided to check whether there is a solution. The proposed algorithm was applied to a curve completion task. The main advantages of the proposed method are its simple construction, compatibility with NURBS, and monotonic curvature.
Highlights
G1 interpolation is an essential problem in many applications such as path planning and curve completion
The G1 interpolation problem based on typical curves is introduced briefly
G1 interpolation is preferable to G2 interpolation when considering cost effectiveness, such as curve completion or path planning using Euler spirals [1]
Summary
G1 interpolation is an essential problem in many applications such as path planning and curve completion. The goal is to find a transition curve that matches the positions and associated unit tangent vectors at two given endpoints [1]. Curve completion aims to find a pleasing contour to fill in an object boundary that is partially occluded [2, 3]. This process differs significantly for humans and computers. It is necessary to identify a fairing curve matching “boundary conditions” among potential transition curves, which is called curve completion
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