‘ NOTE ^ Euler angles are probably the most familiar, and in most cases, the most practical way to represent the orientation of an object. A set of three Euler angles specifies the rotation around each axis, X, Y, and… читать далее

Look at your arm. Extend your limb out in front of you and take a look at it. Your arm has several bones, two main ones, and a bunch more in your hand and fingers. Move your fingers around, just… читать далее

Just what is a matrix you ask? Well, simply put, a matrix is a rectangular array of numbers. A few examples of matrices are shown in Figure 1.1. You know what they look like, but just what are they good… читать далее

Figure 2.9 A 2D representation of what SLERP and LERP do. SLERP interpolates along the arc of the circle, whereas LERP interpolates along a straight line from start to finish. Linear interpolation is by far the easier of the two… читать далее

J ust about everyone has played, or at least seen, Half-Life. This groundbreaking game from VALVe software became an instant success, eventually spawning the insanely popular counter-terrorism mod Counter-Strike (www. counter-strike. net). Figure 8.1 shows Half-Life in action. Figure 8.1… читать далее

If you are going to understand how vectors work, you first must under­stand the notation that will be used whenever vectors are talked about. There are three ways of representing the vectors. The first is shown in the graphical method.… читать далее

The MD2 format also contains instructions to let you use triangle fans and strips, instead ofjust raw triangles. Using triangle strips and fans can help you speed up the rendering of your 3D models. The secret? Triangles share two of… читать далее

W. R Hamilton created quaternions in 1843, in Dublin, England. Origi­nally used as a four-dimensional extension for complex numbers, it was proven that quaternions could be used to represent rotations in three­dimensional space as well.… читать далее

The root joint is the ultimate joint in the model. Every other joint eventually finds its way back to this one joint. Any operations done on the root joint, whether they be translation or rotation, affect every vertex in the… читать далее

If you recall your elementary school math experience, you hopefully remember that anything plus zero doesn’t change the original num­ber, nor does anything multiplied by one. Well, the same thing is true for matrices. For addition and subtraction of matrices… читать далее