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

Spherical linear interpolation is not all that hard either. The only thing you have to watch out for is making sure you take the shortest route. If you look at Figure 2.9 again, you will see that you could go… читать далее

B ack at the beginning of the book you learned about the MD2 format used in id Software’s Quake II. Since then, Quake and its file format have matured. MD2’s bigger brother, MD3, was created for use in Quake III.… читать далее

Vectors have a magnitude, usually depicted and thought about as length and written as NvN, meaning the magnitude of the vector v, where v is any vector. As with a line segment, the length or magnitude of a vector can… читать далее

N ext in line is the OBJ file format. This is a great format for static objects in a game, such as simple pieces of level geometry, weap­ons lying on the ground, and power-ups scattered throughout a level. The OBJ… читать далее

Quaternions can be treated simply as four-dimensional vectors for the purposes of addition, subtraction, and scalar multiplication. Quater­nion addition is exactly the same as vector addition, meaning you simply add the components of the first quaternion to the correspond­ing components… читать далее

A joint can have parent and child joints. The parent of a joint affects everything it does. The parent’s rotations and translations are all taken into account when computing the current joint’s new position. Using the arm analogy again, the… читать далее

Now, on to the fun part, matrix math! As strange as matrices may seem, a majority of the mathematical operations that can be per­formed on them are relatively easy. Nearly everything that can be done with real numbers can be… читать далее

There you have it, the basic operations of quaternions. Hopefully you now have enough information to get some use out of them. Throughout the next few chapters, you will use them to provide smooth animation for your 3D models. If… читать далее

If you want to have lighting in your scene, it is essential to have at the very least a normal vector for each triangle. Failure to do this will cause certain parts of the model to be unlit, or lit… читать далее