贝塞尔曲线

• generate Bézier curves using continuity conditions C2 and C1
• Smooth Bézier Spline Through Prescribed Points

generate Bézier curves using continuity conditions C2 and C1

只有两个点,考虑方向

Catmull-Rom splines: pass through all control points

• Catmull-Rom splines

长度: 根据三次多项式积分得到曲线长度

collision

interact for line to curve:

distance for point to curve:

极值点： 通过极值点构造bounding box， 缩小碰撞检测范围

numerical solution

• spiral-curves

g1 spiral

• G1fitting blog

• G1fitting

• Spiral Curves for Highway Alignment

• Spiral curves

• construction-surveying-curves

• spiral-curves

优化

• 萧潇子：Apollo ReferenceLine Smooth--Polynomial Spiral平滑原理
• spiral_reference_line_smoother

ref

• blog
  • A Primer on Bézier Curves
  • CAGD/Bézier Curves
• code
  • path smoothing
  • Bezier-Curve
• paper
  • Continuous Curvature Path Generation Based on B¶ezier Curves for Autonomous Vehicles
  • Bezier曲线的拼接及其连续性
  • An Analytical Continuous-Curvature Path-Smoothing Algorithm
  • On the generation of spiral-like paths within planar shapes