3dtut.html

COM Component designed to make full screen scrolling maps easy, especially from Visual Basic. This i

    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">W</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">1</div>
    </td>
  </tr>
</table>
<p>Rotation around Z</p>
<table width="40%" border="0">
  <tr> 
    <td>&nbsp; </td>
    <td> 
      <div align="center">X</div>
    </td>
    <td> 
      <div align="center">Y</div>
    </td>
    <td> 
      <div align="center">Z</div>
    </td>
    <td> 
      <div align="center">W</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">X</div>
    </td>
    <td> 
      <div align="center">cos(q)</div>
    </td>
    <td> 
      <div align="center">sin(q)</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">Y</div>
    </td>
    <td> 
      <div align="center">-sin(q)</div>
    </td>
    <td> 
      <div align="center">cos(q)</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">Z</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">1</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">W</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">1</div>
    </td>
  </tr>
</table>
<p>Translation</p>
<table width="40%" border="0">
  <tr> 
    <td>&nbsp; </td>
    <td> 
      <div align="center">X</div>
    </td>
    <td> 
      <div align="center">Y</div>
    </td>
    <td> 
      <div align="center">Z</div>
    </td>
    <td> 
      <div align="center">W</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">X</div>
    </td>
    <td> 
      <div align="center">1</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">Y</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">1</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">Z</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">1</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">W</div>
    </td>
    <td> 
      <div align="center">x</div>
    </td>
    <td> 
      <div align="center">y</div>
    </td>
    <td> 
      <div align="center">z</div>
    </td>
    <td> 
      <div align="center">1</div>
    </td>
  </tr>
</table>
<p>Scaling</p>
<table width="40%" border="0">
  <tr> 
    <td>&nbsp; </td>
    <td> 
      <div align="center">X</div>
    </td>
    <td> 
      <div align="center">Y</div>
    </td>
    <td> 
      <div align="center">Z</div>
    </td>
    <td> 
      <div align="center">W</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">X</div>
    </td>
    <td> 
      <div align="center">a</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">Y</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">a</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">Z</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">a</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">W</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">1</div>
    </td>
  </tr>
</table>
<p>Skewing</p>
<table width="40%" border="0">
  <tr> 
    <td>&nbsp; </td>
    <td> 
      <div align="center">X</div>
    </td>
    <td> 
      <div align="center">Y</div>
    </td>
    <td> 
      <div align="center">Z</div>
    </td>
    <td> 
      <div align="center">W</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">X</div>
    </td>
    <td> 
      <div align="center">a</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">Y</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">b</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">Z</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">c</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
  </tr>
  <tr> 
    <td> 
      <div align="center">W</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">0</div>
    </td>
    <td> 
      <div align="center">1</div>
    </td>
  </tr>
</table>

<p>View/Projection: You don't need these unless you plan to build your own engine. 
  If you are reading this, you probably don't know enough to do it.</p>
<p>&nbsp;</p>
<h3 align="center"> Degrees go out the window </h3>
<p>Yep, no more degrees like math in school, the unit the computer uses is radians. 
  <br>
  A circle is 2*pi radians, 90 degrees is pi/2 radians. <br>
  One degree is pi/180 radians.</p>
<p> R = (180*D)/pi <br>
  D = (R*pi)/180 </p>
<p>Code: <br>
  #define int ToDegrees(x) { return (x*g_PI)/180; }; <br>
  #define int ToRads(x) { return (x*180)/g_PI; };</p>
<p>&nbsp;</p>
<h3 align="center"> Vectors</h3>
<p>Traditionally, a vector is a line specifing direction and magnitude with two 
  points. </p>
<p>Vectors in 3d <i>usually</i> have (0, 0, 0) as their first point. </p>
<p>The magnitude of a vector is the square root of the square of the x, y & z 
  values:<br>
  mag = sqrt( x*x + y*y + z*z )</p>
<p>Dividing a vector by its magnitude gives a normalized vector; one with a magnitude 
  of 1.</p>
<p> A vector can be expressed in several ways. The cartesian plane is the standard 
  form. <br>
  In the polar coordinate system, the point is expressed by a magnitude and n-1 
  angles of rotation (n = # of axes) I'll be using the standard form throughout. 
</p>
<p><b>Operations on vectors</b>: A vector can be modified just like a point, in 
  fact, they <i>are</i> points (if it has a center at the origin) </p>
<p>- Dot Product: 
<br>
<blockquote>Used to determine the angle of seperation between two vectors, the 
  dot product returns a single value. A, B & C are vectors, q is the angle: 
<br>
  <blockquote> 
    <p>Equation:<br>
      A