Book Image

C++ Game Animation Programming - Second Edition

By : Michael Dunsky, Gabor Szauer
4.5 (2)
Book Image

C++ Game Animation Programming - Second Edition

4.5 (2)
By: Michael Dunsky, Gabor Szauer

Overview of this book

If you‘re fascinated by the complexities of animating video game characters and are curious about the transformation of model files into 3D avatars and NPCs that can explore virtual worlds, then this book is for you. In this new edition, you’ll learn everything you need to know about game animation, from a simple graphical window to a large crowd of smoothly animated characters. First, you’ll learn how to use modern high-performance graphics, dig into the details of how virtual characters are stored, and load the models and animations into a minimalistic game-like application. Then, you’ll get an overview of the components of an animation system, how to play the animations and combine them, and how to blend from one animation into another. You’ll also get an introduction to topics that will make your programming life easier, such as debugging your code or stripping down the graphical output. By the end of this book, you’ll have gained deep insights into all the parts of game animation programming and how they work together, revealing the magic that brings life to the virtual worlds on your screen.
Table of Contents (22 chapters)
1
Part 1:Building a Graphics Renderer
7
Part 2: Mathematics Roundup
10
Part 3: Working with Models and Animations
15
Part 4: Advancing Your Code to the Next Level

A quick take on splines

In computer graphics, a spline is a curve, defined piecewise by polynomials. A polynomial for splines is a formula, where a single variable is used with different exponents and the results are summed up:

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" display="block"><mml:msub><mml:mrow><mml:mi mathvariant="bold-italic">h</mml:mi></mml:mrow><mml:mrow><mml:mn>00</mml:mn></mml:mrow></mml:msub><mml:mfenced separators="|"><mml:mrow><mml:mi mathvariant="bold-italic">t</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant="bold-italic">t</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mo>-</mml:mo><mml:mn>3</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant="bold-italic">t</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>

In the preceding formula, the first of the four base polynomials of a cubic Hermite spline is shown. Here, the t variable is used in a cubic and a squared version, and a real number is added to the polynomial.

Different spline variants use different polynomials to generate the resulting curved lines. The plots for the basic functions of the usually used spline variants – B-splines, Bezier, and Hermite splines – are drawn in Figure 7.12:

Figure 7.12: The basic functions for B-splines, Bezier, and Hermite splines

Figure 7.12: The basic functions for B-splines, Bezier, and Hermite splines

The construction of a spline can be done with numerical calculations, by solving all the polynomials for the given interpolation point between 0 and 1. Other splines can be created more easily by using...