Calculate a point along the line A-B at a given distance from A

Question

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

Answer 1

OK guys, I found my major bug. It was a classic Doh! My Draw method was painting at p.X, p.X

So, I finally got something that works. Please note that I am not saying that this a "good solution", or "the only working solution" I'm just saying that it does what I want it to do ;-)

Here's my UPDATED working code: (complete and selfcontained this time ;-)

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

namespace DrawLines
{
    public class MainForm : Form
    {
        #region constants and readonly attributes

        private const int CELL_SIZE = 4; // width and height of each "cell" in the bitmap.

        private readonly Bitmap _myBitmap; // to draw on (displayed in picBox1).
        private readonly Graphics _myGraphics; // to draw with.

        // actual points on _theLineString are painted red.
        private static readonly SolidBrush _thePointBrush = new SolidBrush(Color.Red);
        // ... and are labeled in /*Bold*/ Black, 16 point Courier New
        private static readonly SolidBrush _theLabelBrush = new SolidBrush(Color.Black);
        private static readonly Font _theLabelFont = new Font("Courier New", 16); //, FontStyle.Bold);

        // the interveening calculated cells on the lines between actaul points are painted Silver.
        private static readonly SolidBrush _theLineBrush = new SolidBrush(Color.Silver);

        // the points in my line-string.
        private static readonly Point[] _thePoints = new Point[] {
            //          x,   y      c i
            new Point(170,  85), // A 0 
            new Point( 85,  70), // B 1
            new Point(209,  66), // C 2
            new Point( 98, 120), // D 3
            new Point(158,  19), // E 4
            new Point(  2,  61), // F 5
            new Point( 42, 177), // G 6
            new Point(191, 146), // H 7
            new Point( 25, 128), // I 8
            new Point( 95,  24)  // J 9
        };

        #endregion

        public MainForm() {
            InitializeComponent();
            // initialise "the graphics system".
            _myBitmap = new Bitmap(picBox1.Width, picBox1.Height);
            _myGraphics = Graphics.FromImage(_myBitmap);
            picBox1.Image = _myBitmap;
        }

        #region DrawPoints upon MainForm_Load

        private void MainForm_Load(object sender, EventArgs e) {
            DrawPoints();
        }

        // draws and labels each point in _theLineString
        private void DrawPoints() {
            char c = 'A'; // label text, as a char so we can increment it for each point.
            foreach ( Point p in _thePoints ) {
                DrawCell(p.X, p.Y, _thePointBrush);
                DrawLabel(p.X, p.Y, c++);
            }
        }

        #endregion

        #region DrawLines on button click

        // =====================================================================
        // Here's the interesting bit. DrawLine was called Draw

        // Draws a line from A to B, by using X-values to calculate the Y values.
        private void DrawLine(Point a, Point b)
        {
            if ( a.Y > b.Y ) // A is below B
                Swap(ref a, ref b); // make A the topmost point (ergo sort by Y)
            Debug.Assert(a.Y < b.Y, "A is still below B!");

            var left = Math.Min(a.X, b.X);
            var right = Math.Max(a.X, b.X);
            int width = right - left;
            Debug.Assert(width >= 0, "width is negative!");

            var top = a.Y;
            var bottom = b.Y;
            int height = bottom - top;
            Debug.Assert(height >= 0, "height is negative!");

            if ( width > height ) {
                // use given X values to calculate the Y values, 
                // otherwise it "skips" some X's
                double slope = (double)height / (double)width; 
                Debug.Assert(slope >= 0, "slope is negative!");
                if (a.X <= b.X)     // a is left-of b, so draw left-to-right.
                    for ( int x=1; x= 0, "slope is negative!");
                if (a.X <= b.X) {     // a is left-of b, so draw left-to-right. (FG)
                    for ( int y=1; y
        /// Required method for Designer support - do not modify
        /// the contents of this method with the code editor.
        /// 
        private void InitializeComponent() {
            this.picBox1 = new System.Windows.Forms.PictureBox();
            this.btnDrawLines = new System.Windows.Forms.Button();
            ((System.ComponentModel.ISupportInitialize)(this.picBox1)).BeginInit();
            this.SuspendLayout();
            // 
            // picBox1
            // 
            this.picBox1.Dock = System.Windows.Forms.DockStyle.Fill;
            this.picBox1.Location = new System.Drawing.Point(0, 0);
            this.picBox1.Name = "picBox1";
            this.picBox1.Size = new System.Drawing.Size(1000, 719);
            this.picBox1.TabIndex = 0;
            this.picBox1.TabStop = false;
            // 
            // btnDrawLines
            // 
            this.btnDrawLines.Location = new System.Drawing.Point(23, 24);
            this.btnDrawLines.Name = "btnDrawLines";
            this.btnDrawLines.Size = new System.Drawing.Size(77, 23);
            this.btnDrawLines.TabIndex = 1;
            this.btnDrawLines.Text = "Draw Lines";
            this.btnDrawLines.UseVisualStyleBackColor = true;
            this.btnDrawLines.Click += new System.EventHandler(this.btnDrawLines_Click);
            // 
            // MainForm
            // 
            this.AutoScaleDimensions = new System.Drawing.SizeF(6F, 13F);
            this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
            this.ClientSize = new System.Drawing.Size(1000, 719);
            this.Controls.Add(this.btnDrawLines);
            this.Controls.Add(this.picBox1);
            this.Location = new System.Drawing.Point(10, 10);
            this.MinimumSize = new System.Drawing.Size(1016, 755);
            this.Name = "MainForm";
            this.SizeGripStyle = System.Windows.Forms.SizeGripStyle.Hide;
            this.StartPosition = System.Windows.Forms.FormStartPosition.Manual;
            this.Text = "Draw Lines on a Matrix.";
            this.Load += new System.EventHandler(this.MainForm_Load);
            ((System.ComponentModel.ISupportInitialize)(this.picBox1)).EndInit();
            this.ResumeLayout(false);
        }

        private System.Windows.Forms.PictureBox picBox1;
        private System.Windows.Forms.Button btnDrawLines;
        #endregion
    }

}

EDIT - UPDATED ABOVE CODE: This version draws "solid" lines. The previously posted version skipped cells in nearly vertical lines, so I inverted the algorithm to calculate the X value (instead of the Y value) in these cases... now I can use it to set (and draw) a "solid fence" around a "navigable area" ;-)

Here's an UPDATED picture of the correct results.

Thanks again to everybody who helped... and you did help ;-)

Cheers. Keith.