如何计算两个给定点和给定距离之间的点？

Question

我有点A (35.163 , 128.001)和点B (36.573 , 128.707)

我需要计算点在A点和B点之间的点

我找到了使用2点之间的标准距离公式 D = 266.3

线AB内的每个点(黑点p1,p2,... p8)以相等的距离分开 d = D / 8 = 33.3

我如何计算p1,p2,... p8的X和Y？

欢迎使用Java或C#语言的示例

或者只是指出一个公式或方法会做.

谢谢.

**以上计算实际上用于计算地图中阴影级别的虚拟点并用于阴影区域插值目的*

Answer 1

这很容易,但你需要一些数学知识.

        PointF pointA, pointB;

        var diff_X = pointB.X - pointA.X;
        var diff_Y = pointB.Y - pointA.Y;
        int pointNum = 8;

        var interval_X = diff_X / (pointNum + 1);
        var interval_Y = diff_Y / (pointNum + 1);

        List<PointF> pointList = new List<PointF>();
        for (int i = 1; i <= pointNum; i++)
        {
            pointList.Add(new PointF(pointA.X + interval_X * i, pointA.Y + interval_Y*i));
        }

Answer 2

Straitforward三角解决方案可能是这样的:

// I've used Tupple<Double, Double> to represent a point;
// You, probably have your own type for it
public static IList<Tuple<Double, Double>> SplitLine(
  Tuple<Double, Double> a, 
  Tuple<Double, Double> b, 
  int count) {

  count = count + 1;

  Double d = Math.Sqrt((a.Item1 - b.Item1) * (a.Item1 - b.Item1) + (a.Item2 - b.Item2) * (a.Item2 - b.Item2)) / count;
  Double fi = Math.Atan2(b.Item2 - a.Item2, b.Item1 - a.Item1);

  List<Tuple<Double, Double>> points = new List<Tuple<Double, Double>>(count + 1);

  for (int i = 0; i <= count; ++i)
    points.Add(new Tuple<Double, Double>(a.Item1 + i * d * Math.Cos(fi), a.Item2 + i * d * Math.Sin(fi)));

  return points;
}

...

IList<Tuple<Double, Double>> points = SplitLine(
  new Tuple<Double, Double>(35.163, 128.001),
  new Tuple<Double, Double>(36.573, 128.707),
  8);

结果(分):

(35,163, 128,001)                    // <- Initial point A
(35,3196666666667, 128,079444444444)
(35,4763333333333, 128,157888888889)
(35,633, 128,236333333333)
(35,7896666666667, 128,314777777778)
(35,9463333333333, 128,393222222222)
(36,103, 128,471666666667)
(36,2596666666667, 128,550111111111)
(36,4163333333333, 128,628555555556)
(36,573, 128,707)                    // <- Final point B