沿 A-B 线计算距 A 给定距离的点

问题描述

我非常疯狂地试图计算沿给定线 A-B 的点，距离 A 的给定距离，这样我就可以绘制"两个给定点之间的线.一开始听起来很简单，但我似乎无法正确理解.更糟糕的是，我不明白我哪里出错了.几何(和一般的数学)不是我的强项.

I'm going quite mad trying to calculate the point along the given line A-B, at a given distance from A, so that I can "draw" the line between two given points. It sounded simple enough at the outset, but I can't seem to get it right. Worse still, I don't understand where I've gone wrong. Geometry (and math in general) is NOT my strong suite.

我已经阅读了类似的问题，并且在 SO 上有答案.事实上，我直接从 Mads Elvheim 的回答中提升了当前对 CalculatePoint 函数的实现:给定起点和终点以及距离，计算沿线的点(加上修正稍后发表评论 - 如果我理解正确的话)因为我独立尝试解决问题的尝试让我无处可去，除了头等舱特快票令人沮丧的地方.

I have read similar questions and there answers on SO. In fact I lifted my current implementation of CalculatePoint function directly from Mads Elvheim's answer to: Given a start and end point, and a distance, calculate a point along a line (plus a correction in a later comment - if I understand him correctly) because my indepedent attempts to solve the problem were getting me nowhere, except a first class express ticket frusterpationland.

这是我的更新代码(请参阅帖子底部的编辑注释):

Here's my UPDATED code (please see the EDIT notes a bottom of post):

using System;
using System.Drawing;
using System.Windows.Forms;

namespace DrawLines
{
    public class MainForm : Form
    {
        // =====================================================================
        // Here's the part I'm having trouble with. I don't really understand
        // how this is suposed to work, so I can't seem to get it right!
        // ---------------------------------------------------------------------

        // A "local indirector" - Just so I don't have go down and edit the 
        // actual call everytime this bluddy thing changes names.
        private Point CalculatePoint(Point a, Point b, int distance) {
            return CalculatePoint_ByAgentFire(a, b, distance);
        }

        #region CalculatePoint_ByAgentFire
        //AgentFire: Better approach (you can rename the struct if you need):
        struct Vector2
        {
            public readonly double X;
            public readonly double Y;
            public Vector2(double x, double y) {
                this.X = x;
                this.Y = y;
            }
            public static Vector2 operator -(Vector2 a, Vector2 b) {
                return new Vector2(b.X - a.X, b.Y - a.Y);
            }
            public static Vector2 operator *(Vector2 a, double d) {
                return new Vector2(a.X * d, a.Y * d);
            }
            public override string ToString() {
                return string.Format("[{0}, {1}]", X, Y);
            }
        }
        // For getting the midpoint you just need to do the (a - b) * d action:
        //static void Main(string[] args)
        //{
        //    Vector2 a = new Vector2(1, 1);
        //    Vector2 b = new Vector2(3, 1);
        //    float distance = 0.5f; // From 0.0 to 1.0.
        //    Vector2 c = (a - b) * distance;
        //    Console.WriteLine(c);
        /