她道歉，她早矢香不必经过这一切。
She apologizes to Sayaka for her having to go through all this.
通过计算环的最大坐标值点处相邻两条边的切矢的叉积来判断环的方向。
The loop direction is judged through the vector product of the adjacent two edges on the vertex with maximum coordinate value.
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。
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.
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