Hey, what do you know, the last part of the matrix section is here already. That wasn’t so bad was it? This section is on the inverse of a matrix. The inverse of a matrix satisfies the following equation: M(M-1)… читать далее

Triangles in MD2 files are made using vertex indexes. For each tri­angle, three two-byte integer values are stored, each representing a vertex in the vertex array. If the three values are 4, 6, and 14, those values can be used… читать далее

Often in computer graphics and game programming, you will need to use matrices to move vectors and points around onscreen, such as to move a point or piece of geometry to a new position. This process is called trans­formation. Matrices… читать далее

C ontains skeletal animation! Revolutionary skeletal animation system! Realistic animations! Look at almost any new 3D game’s box—these words, or some form of them, jump right out at you. It seems that every new game uses some form of skeletal… читать далее

As you have probably noticed, there is a CD attached to the back cover of the book. There is lots of cool stuff on there. All of the source code for all the model formats discussed in the book, plus… читать далее

There is one huge reason that conversion between Euler angles and quaternions is necessary—ease of use. Because it is impossible to visualize a quaternion, it is very hard to enter one into a program. If a modeling program wants you… читать далее

That pretty much wraps up the introduction to skeletal animation. But before you go, take a look at some of cool stuff that can be done with more advanced techniques, beyond the scope of this book. Figure 5.11 shows a… читать далее

Transposing matrices is important in game programming because it is a fast, easy way to calculate the inverse of orthogonal matrix. Now, let your brain relax a bit; this operation is much easier. To transpose a matrix all you have… читать далее

I bet you are anxious to see some results of your hard work, even though you haven’t added textures yet. In this section, you learn how to render the frames by themselves. A frame in the case of an MD2… читать далее

Take a look at the following directory on the CD: /Code/Chapterl/ or /Code/Math. Here, you will find C++ classes to store and manipulate matrices and vectors. There are separate classes for 3×3 and 4×4 matrices, both defined and implemented in… читать далее