#### Overview of this book

Animation is one of the most important parts of any game. Modern animation systems work directly with track-driven animation and provide support for advanced techniques such as inverse kinematics (IK), blend trees, and dual quaternion skinning. This book will walk you through everything you need to get an optimized, production-ready animation system up and running, and contains all the code required to build the animation system. You’ll start by learning the basic principles, and then delve into the core topics of animation programming by building a curve-based skinned animation system. You’ll implement different skinning techniques and explore advanced animation topics such as IK, animation blending, dual quaternion skinning, and crowd rendering. The animation system you will build following this book can be easily integrated into your next game development project. The book is intended to be read from start to finish, although each chapter is self-contained and can be read independently as well. By the end of this book, you’ll have implemented a modern animation system and got to grips with optimization concepts and advanced animation techniques.
Preface
Chapter 1: Creating a Game Window
Free Chapter
Chapter 2: Implementing Vectors
Chapter 3: Implementing Matrices
Chapter 4: Implementing Quaternions
Chapter 5: Implementing Transforms
Chapter 6: Building an Abstract Renderer
Chapter 7: Exploring the glTF File Format
Chapter 8: Creating Curves, Frames, and Tracks
Chapter 9: Implementing Animation Clips
Chapter 10: Mesh Skinning
Chapter 11: Optimizing the Animation Pipeline
Chapter 12: Blending between Animations
Chapter 13: Implementing Inverse Kinematics
Chapter 14: Using Dual Quaternions for Skinning
Chapter 15: Rendering Instanced Crowds
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# Understanding cubic Bézier splines

To implement game animation, you need some understanding of curves. Let's start with the basics—a cubic Bézier spline. A Bézier spline has two points to interpolate between and two control points that help generate a curve. This is what a cubic Bézier spline looks like:

Figure 8.2: A cubic Bézier spline

Given the two points and the two controls, how is the curve generated? Let's explore interpolating the curve for a given time, t. Start by drawing a line from P1 to C1, from C1 to C2, and from C2 to P2. Then, linearly interpolate along those lines with the value of t:

Figure 8.3: Linearly interpolating between points and control points

The interpolated points from P1 to C1 is A, from C2 to P2 is B, and from C1 to C2 is C. Next, you need to repeat this process, drawing lines and interpolating from A to C and from C to B. Let's call these newly...