3DICA

2.1 The Relationship Between 2D and 3D Worlds A point in 3-space is defined by three coordinates : x, y, and z. We can't draw a point like this straight to the computer screen. Hence, we need a formula with which we can make the x and y coordinates somehow dependent on the z coordinate. Let's think about the case. A point can be multiplied by a constant the result point staying on a line that goes through the origin and the original point: k \cdot (X, Y, Z) = (kX, kY, kZ) If we define the origin as the location of the camera, we can use this formula and take 1/z as k. Now the z coordinate is a constant: \frac {1}{Z} \cdot (X,...

1.1 Vectors 1.1.1 General Vectors are lines which have a constant direction and length (or magnitude), and can be moved arbitrarily in a given coordinate system. A vector is drawn as in the following picture (a short perpendicular line (not necessary) at the starting point, and an arrowhead at the ending point): Vectors are usually marked the same way as the coordinates of a point: a=(x_1, y_1, z_1) , where x_1 is the x-axis vector coefficient, y_1 and z_1 respectively. This vector \vec a can be drawn so that we draw a point into the coordinates (x_1,y_1,z_1) , and a line from the origin to that point. The x-, y-, and z-axis unit vectors...

0.0 LICENSE AGREEMENT 0.0.1 DISCLAIMER 3DICA PROGRAMMING TUTORIAL IS SUPPLIED AS-IS. THE AUTHOR DISCLAIMS ALL WARRANTIES, EXPRESSED OR IMPLIED, INCLUDING, WITHOUT LIMITATION, THE WARRANTIES OF MERCHANTABILITY AND OF FITNESS FOR ANY PURPOSE. THE AUTHOR ASSUMES NO LIABILITY FOR DAMAGE TO ANY LIVING / DEAD CREATURE OR EQUIPMENT, DIRECT OR CONSEQUENTIAL, WHICH MAY RESULT FROM THE USE OF THE 3DICA PROGRAMMING TUTORIAL. 0.0.2 LIMITED WARRANTY SATISFACTION GUARANTEE. If you are dissatisfied with this product you downloaded from some F..ine BBS or the Internet, you may delete it at any time up to 30 days after download and you will get your ...

* A C source treating the subject included 0 General Things 0.0 LICENSE AGREEMENT 0.0.1 DISCLAIMER 0.0.2 LIMITED WARRANTY 0.0.3 Seriously 0.0.4 3dica careware -- what does that mean? 0.1 Authors, Greets, etc. 0.1.1 Ica 0.1.2 Chem 0.1.3 Hubris Productions 0.1.4 Thanks for help 0.1.5 Greets 0.1.6 Thanks for support 0.2 About the Document 0.2.1 Where can I get the newest version of 3dica? 0.2.2 What has happened since the last version? 0.2.3 Features to be added 0.3 3D Terms etc. 0.4 FAQ 0.5 Recommended References 0.6 A Quick Introduction to Radians 1 Vector and Matrix Algebra 1.1 Vectors 1.1.1 General 1.1.2 Vector equation 1.1.3 Vector leng...