C++实现二阶 三阶贝塞尔曲线

C++实现贝塞尔曲线

已经存在许多讲解得比较清楚的解释。如https://www.jianshu.com/p/0c9b4b681724

贝塞尔曲线包含多阶。贝塞尔曲线的阶数和次数是一样的，二阶贝塞尔，三个点，最高次数二次。例：二阶贝塞尔：三个点，两个线段，以所有等比的点组合成的曲线叫做二阶贝塞尔曲线。如下图。

根据贝塞尔曲线的公式直接根据控制点缺点阶数，。

定义.h头文件

class Bezier {
     
public:
  Bezier() = default;
  const std::vector<hybrid_astar::Vector2D>& CalculateSpline(
      const std::vector<hybrid_astar::Vector2D>& control_points,
      const int& points_number);
  void CalculateSecond();
  void CalculateCubic();
private:
  int ctrl_num_;  //控制点数量
  int order_;     //阶数，表示曲线为几阶曲线，为控制点数-1
  int knot_num_;  //节点数是分布在0-1之间有多少个点
  std::vector<hybrid_astar::Vector2D> control_points_;
  std::vector<hybrid_astar::Vector2D> path_points_;

};

定义cpp文件

const std::vector<hybrid_astar::Vector2D>& Bezier::CalculateSpline(
    const std::vector<hybrid_astar::Vector2D>& control_points,
    const int& knot_number) {
     
  ctrl_num_ = control_points.size();
  control_points_ = control_points;
  knot_num_ = knot_number;
  //点数-1为阶数l
  order_ = control_points_.size() - 1;
  switch (order_) {
     
    case 2:
      CalculateSecond();
      break;
    case 3:
      CalculateCubic();
      break;
    default:
      std::cout << "No define order: " << order_ << std::endl;
      break;
  }
  return path_points_;
}

void Bezier::CalculateSecond() {
     
  if (ctrl_num_ != 3)
    return;
  path_points_.clear();
  double t = 0;
  double delta_t = 1.0 / (static_cast<double>(knot_num_));
  double f1, f2, f3;
  for (double i = 0; i <= knot_num_; ++i) {
     
    t = delta_t * i;
    f1 = (1 - t) * (1 - t);
    f2 = 2 * (1 - t) * t;
    f3 = t * t;
    path_points_.push_back(
          hybrid_astar::Vector2D(f1 * control_points_[0].getX() +
          f2 * control_points_[1].getX() + f3 * control_points_[2].getX(),
        f1 * control_points_[0].getY() + f2 * control_points_[1].getY() +
        f3 * control_points_[2].getY()));
  }
}

void Bezier::CalculateCubic() {
     
  if (ctrl_num_ != 4)
    return;
  path_points_.clear();
  double t = 0;
  double delta_t = 1.0 / (static_cast<double>(knot_num_));
  double f1, f2, f3, f4;
  for (double i = 0; i <= knot_num_; ++i) {
     
    t = delta_t * i;
    f1 = (1 - t) * (1 - t) * (1 - t);
    f2 = 3 * (1 - t) * (1 - t) * t;
    f3 = 3 * (1 - t) * t * t;
    f4 = t * t * t;
    path_points_.push_back(
          hybrid_astar::Vector2D(f1 * control_points_[0].getX() +
          f2 * control_points_[1].getX() + f3 * control_points_[2].getX() +
        f4 * control_points_[3].getX(),
        f1 * control_points_[0].getY() + f2 * control_points_[1].getY() +
        f3 * control_points_[2].getY() + f4 * control_points_[3].getY()));
  }
}