# Using Mid Point Displacement to Create Cracks

4/8/2008

One of the many things that you will have to deal with in procedural texture generation is cracks and fractures. There's many ways to deal with this problem, L-Systems, stress based fracturing, etc. (In fact there are a couple of systems to deal with fracturing of 3D objects like this one) However the easiest system to set up is to simply use mid point displacement.

## Pseudo code

I know I usually just give you code but this one is simple enough that you should be able to create it from pseudo code. Anyway, all that you do is the following:

`   1: public void GenerateCracks() `
`   2:  `
`   3: { `
`   4:  `
`   5: Generate line and save it to a list `
`   6:  `
`   7: for x=0 to number of iterations `
`   8:  `
`   9: determine a spot on the line `
`  10:  `
`  11: if the slope of the line is greater than 1 then `
`  12:  `
`  13: Move that point that we picked along the x axis by a predetermined amount `
`  14:  `
`  15: else `
`  16:  `
`  17: Move that point that we picked along the y axis by a predetermined amount `
`  18:  `
`  19: Create a new line going from the start of the line to the newly picked spot `
`  20:  `
`  21: Create a new line going from the newly picked spot to the end of the line `
`  22:  `
`  23: Save the lines to the list and remove the original line `
`  24:  `
`  25: Divide the amount to change the position by 2 `
`  26:  `
`  27: Next x `
`  28:  `
`  29: Draw the lines that were generated `
`  30:  `
`  31: } `

And that's all there is to it. And while I'm at it, I might as well give you code... Although you might not want to use it as I was extremely tired when creating it but it gives you an idea of what to do.

`   1: /*`
`   2: Copyright (c) 2010 <a href="http://www.gutgames.com">James Craig</a>`
`   3: `
`   4: Permission is hereby granted, free of charge, to any person obtaining a copy`
`   5: of this software and associated documentation files (the "Software"), to deal`
`   6: in the Software without restriction, including without limitation the rights`
`   7: to use, copy, modify, merge, publish, distribute, sublicense, and/or sell`
`   8: copies of the Software, and to permit persons to whom the Software is`
`   9: furnished to do so, subject to the following conditions:`
`  10: `
`  11: The above copyright notice and this permission notice shall be included in`
`  12: all copies or substantial portions of the Software.`
`  13: `
`  14: THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR`
`  15: IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,`
`  16: FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE`
`  17: AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER`
`  18: LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,`
`  19: OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN`
`  20: THE SOFTWARE.*/`
`  21:  `
`  22: #region Usings`
`  23: using System;`
`  24: using System.Collections.Generic;`
`  25: using System.Linq;`
`  26: using System.Text;`
`  27: using System.Drawing;`
`  28: using System.Drawing.Imaging;`
`  29: #endregion`
`  30:  `
`  31: namespace Utilities.Media.Image`
`  32: {`
`  33:     /// <summary>`
`  34:     /// Helper class for generating cracks by midpoint displacement`
`  35:     /// </summary>`
`  36:     public static class MidpointDisplacement`
`  37:     {`
`  38:         #region Functions`
`  39:  `
`  40:         /// <summary>`
`  41:         /// Generates an image that contains cracks`
`  42:         /// </summary>`
`  43:         /// <param name="Width">Image width</param>`
`  44:         /// <param name="Height">Image height</param>`
`  45:         /// <param name="NumberOfCracks">Number of cracks</param>`
`  46:         /// <param name="Iterations">Iterations</param>`
`  47:         /// <param name="MaxChange">Maximum height change of the cracks</param>`
`  48:         /// <param name="MaxLength">Maximum length of the cracks</param>`
`  49:         /// <param name="Seed">Random seed</param>`
`  50:         /// <returns>An image containing "cracks"</returns>`
`  51:         public static Bitmap Generate(int Width,int Height,int NumberOfCracks,int Iterations,`
`  52:             int MaxChange,int MaxLength,int Seed)`
`  53:         {`
`  54:             Bitmap ReturnValue = new Bitmap(Width, Height);`
`  55:             List<Line> Lines = GenerateLines(Width,Height,NumberOfCracks, Iterations, MaxChange, MaxLength, Seed);`
`  56:             using (Graphics ReturnGraphic = Graphics.FromImage(ReturnValue))`
`  57:             {`
`  58:                 foreach (Line Line in Lines)`
`  59:                 {`
`  60:                     foreach (Line SubLine in Line.SubLines)`
`  61:                     {`
`  62:                         ReturnGraphic.DrawLine(Pens.White, SubLine.X1, SubLine.Y1, SubLine.X2, SubLine.Y2);`
`  63:                     }`
`  64:                 }`
`  65:             }`
`  66:             return ReturnValue;`
`  67:         }`
`  68:  `
`  69:         private static List<Line> GenerateLines(int Width,int Height,int NumberOfCracks, int Iterations, int MaxChange, int MaxLength, int Seed)`
`  70:         {`
`  71:             List<Line> Lines = new List<Line>();`
`  72:             System.Random Generator = new System.Random(Seed);`
`  73:             for (int x = 0; x < NumberOfCracks; ++x)`
`  74:             {`
`  75:                 Line TempLine = null;`
`  76:                 int LineLength = 0;`
`  77:                 do`
`  78:                 {`
`  79:                     TempLine = new Line(Generator.Next(0, Width), Generator.Next(0, Width),`
`  80:                         Generator.Next(0, Height), Generator.Next(0, Height));`
`  81:                     LineLength = (int)System.Math.Sqrt((double)((TempLine.X1 - TempLine.X2) * (TempLine.X1 - TempLine.X2))`
`  82:                         + ((TempLine.Y1 - TempLine.Y2) * (TempLine.Y1 - TempLine.Y2)));`
`  83:                 } while (LineLength > MaxLength&&LineLength<=0);`
`  84:                 Lines.Add(TempLine);`
`  85:                 List<Line> TempLineList = new List<Line>();`
`  86:                 TempLineList.Add(TempLine);`
`  87:                 for (int y = 0; y < Iterations; ++y)`
`  88:                 {`
`  89:                     Line LineUsing=TempLineList[Generator.Next(0,TempLineList.Count)];`
`  90:                     int XBreak=Generator.Next(LineUsing.X1,LineUsing.X2)+Generator.Next(-MaxChange,MaxChange);`
`  91:                     int YBreak = 0;`
`  92:                     if (LineUsing.Y1 > LineUsing.Y2)`
`  93:                     {`
`  94:                         YBreak = Generator.Next(LineUsing.Y2, LineUsing.Y1) + Generator.Next(-MaxChange, MaxChange);`
`  95:                     }`
`  96:                     else`
`  97:                     {`
`  98:                         YBreak = Generator.Next(LineUsing.Y1, LineUsing.Y2) + Generator.Next(-MaxChange, MaxChange);`
`  99:                     }`
` 100:                     Line LineA=new Line(LineUsing.X1,XBreak,LineUsing.Y1,YBreak);`
` 101:                     Line LineB=new Line(XBreak,LineUsing.X2,YBreak,LineUsing.Y2);`
` 102:                     TempLineList.Remove(LineUsing);`
` 103:                     TempLineList.Add(LineA);`
` 104:                     TempLineList.Add(LineB);`
` 105:                 }`
` 106:                 TempLine.SubLines=TempLineList;`
` 107:             }`
` 108:             return Lines;`
` 109:         }`
` 110:  `
` 111:         #endregion`
` 112:     }`
` 113:  `
` 114:     #region Internal classes`
` 115:  `
` 116:     internal class Line`
` 117:     {`
` 118:         public Line(){}`
` 119:  `
` 120:         public Line(int X1,int X2,int Y1,int Y2)`
` 121:         {`
` 122:             if (X1 > X2)`
` 123:             {`
` 124:                 int Holder = X1;`
` 125:                 X1 = X2;`
` 126:                 X2 = Holder;`
` 127:                 Holder = Y1;`
` 128:                 Y1 = Y2;`
` 129:                 Y2 = Holder;`
` 130:             }`
` 131:             this.X1=X1;`
` 132:             this.X2=X2;`
` 133:             this.Y1=Y1;`
` 134:             this.Y2=Y2;`
` 135:         }`
` 136:  `
` 137:         public int X1;`
` 138:         public int X2;`
` 139:         public int Y1;`
` 140:         public int Y2;`
` 141:         public List<Line> SubLines = new List<Line>();`
` 142:     }`
` 143:  `
` 144:     #endregion`
` 145: }`

Anyway, this technique is probably the easiest to create something that works but at the same time it doesn't exactly create the best results. You can get slightly better results if you only move the lines in one direction (I'm moving the break point in both the X and Y), but it's about the same either way. Anyway, it's not perfect but if all you want is something basic it is probably the easiest solution. So try out the code, leave feedback, and happy coding.