This paper describes the use of cubic splines for interpolating monotonic data sets. Interpolating cubic splines are popular for 1tting data because they use low-order polynomials and have C continuity, a property that permits them to satisfy a desirable smoothness constraint. Unfortunately, that same constraint often violates another desirable property: monotonicity. It is possible for a set o...

We present a novel trajectory computation algorithm to smooth jerky collision-free paths computed by samplebased motion planners. Our approach uses cubic B-splines to generate G or curvature continuous trajectories. The algorithm performs local spline refinement to compute smooth, collision-free paths in narrow passages and satisfy velocity and acceleration constraints. We also present a fast a...

We present a novel trajectory computation algorithm to smooth piecewise linear collision-free trajectories computed by samplebased motion planners. Our approach uses cubic B-splines to generate trajectories which are C almost everywhere, except on a few isolated points. The algorithm performs local spline refinement to compute smooth, collision-free trajectories and it works well even in enviro...

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In this lecture we generalize the polar form and blossoming and introduce NURBS(non-uniform rational B-spline), then we extend the discussion to 2D about surfaces. 1 NURBS NURBS is an industry standard tool for the representation and design of geometry. It is the non-uniform and rational extension of B-splines. We will introduce these properties one by one using blossoming. A cubic polar form i...

This paper presents an algorithm to solve the approximate implicitization of planar parametric curves using cubic algebraic splines. It applies piecewise cubic algebraic curves to give a global G2 continuity approximation to planar parametric curves. Approximation error on approximate implicitization of rational curves is given. Several examples are provided to prove that the proposed method is...