用二次插值实现近似弧长参数化

A NEARLY ARC LENGTH PARAMETERIZATION METHOD BY USING QUADRATIC INTERPOLATION

分段二次 Hermite插值用来保单调地反插值参数曲线的弧长函数 .所作近似弧长参数化曲线在插值节点处 ,近似弧长是精确的 ,并且具有与精确弧长参数曲线同方向的单位切矢 .在整个近似弧长参数区间 ,近似弧长的误差可达到 o((Δ t) 2 ) (Δ t为节点步长 ) .

The paper applies the piecewise quadratic Hermite interpolation to interpolate inversly and monotonely preserving the arc length function. At any knots, the nearly arc length are precise for the resulting nearly arc length parametric curve, and it has the unit tangent same as that of the real arc length parametric curve. The error of the nearly arc length gets to o((Δt) 2) (Δt is the knots space)on the arc length parametric interval. Some numerical results are presented.