如何计算两个给定点和给定距离之间的点？ [英] How to calculate the points between two given points and given distance?

问题描述

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

我需要计算点在A点和B点之间使用2点之间的标准距离公式，我发现 D = 266.3

每个点位于AB线（黑点p1，p2，...） 。如何计算X的值？如何计算X的值？如何计算X的值？如何计算X和Y为p1，p2，... p8？

欢迎使用Java或C＃语言的示例

或者只是指给我一个公式或方法就行。

谢谢。

**以上计算是实际上用于计算我地图中阴影级别的虚拟点，并用于阴影区域插值目的*

解决方案

双>代表一个观点;
//你可能有你自己的类型
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）））;

回报点;
}

...

IList< Tuple< Double，Double>>点= SplitLine（
新元组< Double，Double>（35.163,128.001），
新元组< Double，Double>（36.573,128.707），
8）;

结果（分）：

<$ p $ （35,163,128,001）// < - 初始点A
（35,3196666666667,128,079444444444）
（35,4763333333333,128,157888888889）$ b $ b（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）// < - 最终点B


I have point A (35.163 , 128.001) and point B (36.573 , 128.707)

I need to calculate the points lies within point A and point B

using the standard distance formula between 2 points, I found D = 266.3

each of the points lies within the line AB (the black point p1, p2, ... p8) are separated with equal distance of d = D / 8 = 33.3

How could I calculate the X and Y for p1 , p2, ... p8?

example of Java or C# language are welcomed

or just point me a formula or method will do.

Thank you.

**The above calculation is actually used to calculate the dummy point for shaded level in my map and working for shaded area interpolation purpose*

解决方案

Straitforward trigonometric solution could be something like that:

// 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);

Outcome (points):

(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

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