Game Physics Cookbook 1st Edition by Gabor Szauer 9781787120815 1787120813

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Product details:

ISBN 10: 1787120813
ISBN 13: 9781787120815
Author: Gabor Szauer

About This Book

• Get a comprehensive coverage of techniques to create high performance collision detection in games

• Learn the core mathematics concepts and physics involved in depicting collision detection for your games

• Get a hands-on experience of building a rigid body physics engine

Who This Book Is For

This book is for beginner to intermediate game developers. You don’t need to have a formal education in games—you can be a hobbyist or indie developer who started making games with Unity 3D.

What You Will Learn

• Implement fundamental maths so you can develop solid game physics

• Use matrices to encode linear transformations

• Know how to check geometric primitives for collisions

• Build a Physics engine that can create realistic rigid body behavior

• Understand advanced techniques, including the Separating Axis Theorem

• Create physically accurate collision reactions

• Explore spatial partitioning as an acceleration structure for collisions

• Resolve rigid body collisions between primitive shapes

In Detail

Physics is really important for game programmers who want to add realism and functionality to their games. Collision detection in particular is a problem that affects all game developers, regardless of the platform, engine, or toolkit they use.

This book will teach you the concepts and formulas behind collision detection. You will also be taught how to build a simple physics engine, where Rigid Body physics is the main focus, and learn about intersection algorithms for primitive shapes.

You’ll begin by building a strong foundation in mathematics that will be used throughout the book. We’ll guide you through implementing 2D and 3D primitives and show you how to perform effective collision tests for them. We then pivot to one of the harder areas of game development—collision detection and resolution.

Further on, you will learn what a Physics engine is, how to set up a game window, and how to implement rendering. We’ll explore advanced physics topics such as constraint solving. You’ll also find out how to implement a rudimentary physics engine, which you can use to build an Angry Birds type of game or a more advanced game.

By the end of the book, you will have implemented all primitive and some advanced collision tests, and you will be able to read on geometry and linear Algebra formulas to take forward to your own games!

Style and approach

Gain the necessary skills needed to build a Physics engine for your games through practical recipes, in an easy-to-read manner. Every topic explained in the book has clear, easy to understand code accompanying it.

Game Physics Cookbook 1st Table of contents:

1. Vectors

Introduction

Vector definition

Getting ready

How to do it…

How it works…

There’s more…

The W component

Component-wise operations

Getting ready

How to do it…

How it works…

Addition

Subtraction

Multiplication (Vector and Scalar)

Comparison

There’s more…

Dot product

How to do it…

How it works…

There’s more…

Geometric definition

Magnitude

Getting ready

How to do it…

How it works…

There’s more…

Normalizing

Getting ready

How to do it…

How it works…

Cross product

Getting ready

How to do it…

How it works…

Angles

Getting ready

How to do it…

How it works…

There’s more…

Radians and degrees

Projection

Getting ready

How to do it…

How it works…

Reflection

Getting ready

How to do it…

How it works…

2. Matrices

Introduction

Matrix definition

Getting ready

How to do it…

How it works…

Transpose

Getting ready

How to do it…

How it works…

Multiplication

Getting ready

How to do it…

How it works…

Identity matrix

Getting ready

How to do it…

How it works…

Determinant of a 2×2 matrix

How to do it…

How it works…

Matrix of minors

Getting ready

How to do it…

How it works…

Minor of a 2×2 matrix

Minor of a 3×3 matrix

Cofactor

Getting ready

How to do it…

How it works…

Determinant of a 3×3 matrix

Getting ready

How to do it…

How it works…

Operations on a 4×4 matrix

Getting ready

How to do it…

How it works…

Adjugate matrix

Getting ready

How to do it…

How it works…

Matrix inverse

Getting ready

How to do it…

How it works…

There’s more…

Expanding the inverse

3. Matrix Transformations

Introduction

Matrix majors

Translation

Getting Ready

How to do it…

How it works…

Scaling

Getting ready

How to do it…

How it works…

How rotations work

Getting ready

How to do it…

How it works…

Rotation matrices

Getting ready

How to do it…

How it works…

X-Basis vector

Y-Basis vector

Z-Basis vector

There’s more…

X and Y rotation

Axis angle rotation

Getting ready

How to do it…

How it works…

Vector matrix multiplication

Getting ready

How to do it…

How it works…

Transform matrix

Getting ready

How to do it…

How it works…

View matrix

Getting ready

How to do it…

How it works…

Projection matrix

Getting ready

How to do it…

How it works…

4. 2D Primitive Shapes

Introduction

2D points

Getting ready

How to do it…

How it works…

2D lines

Getting ready

How to do it…

How it works…

Circle

Getting ready

How to do it…

How it works…

Rectangle

Getting ready

How to do it…

How it works…

Oriented rectangle

Getting ready

How to do it…

How it works…

Point containment

Getting ready

How to do it…

How it works…

Point on a line

Point in a circle

Point in a rectangle

Point in an oriented rectangle

Line intersection

Getting ready

How to do it…

How it works…

Line circle

Line rectangle

Line oriented rectangle

5. 2D Collisions

Introduction

Circle to circle

Getting ready

How to do it…

How it works…

Circle to rectangle

Getting ready

How to do it…

How it works…

There’s more…

Circle to oriented rectangle

Getting ready

How to do it…

How it works…

Rectangle to rectangle

Getting ready

How to do it…

How it works…

Separating Axis Theorem

Getting ready

How to do it…

How it works…

There’s more…

Determining which axis to test

Rectangle to oriented rectangle

Getting ready

How to do it…

How it works…

Oriented rectangle to oriented rectangle

Getting ready

How to do it…

How it works…

6. 2D Optimizations

Introduction

Containing circle

Getting ready

How to do it…

How it works…

Containing rectangle

Getting ready

How to do it…

How it works…

Simple and complex shapes

Getting ready

How to do it…

How it works…

Quad tree

Getting ready

How to do it…

How it works…

Broad phase collisions

Getting ready

How to do it…

How it works…

7. 3D Primitive Shapes

Introduction

Point

Getting ready

How to do it…

How it works…

Line segment

Getting ready

How to do it…

How it works…

Ray

Getting ready

How to do it…

How it works…

Sphere

Getting ready

How to do it…

How it works…

Axis Aligned Bounding Box

Getting ready

How to do it

How it works

Oriented Bounding Box

Getting ready

How to do it

How it works

Plane

Getting ready

How to do it

How it works

Triangle

Getting ready

How to do it

How it works

8. 3D Point Tests

Introduction

Point and sphere

Getting ready

How to do it…

How it works…

Point and AABB

Getting ready

How to do it…

How it works…

Point and Oriented Bounding Box

Getting ready

How to do it…

How it works…

Point and plane

Getting ready

How to do it…

How it works…

Point and line

Getting ready

How to do it…

How it works…

Point and ray

Getting ready

How to do it…

How it works…

9. 3D Shape Intersections

Introduction

Sphere-to-sphere

Getting ready

How to do it…

How it works…

Sphere-to-AABB

Getting ready

How to do it…

How it works…

Sphere-to-OBB

Getting ready

How to do it…

How it works…

Sphere-to-plane

Getting ready

How to do it…

How it works…

AABB-to-AABB

Getting ready

How to do it…

How it works…

AABB-to-OBB

Getting ready

How to do it…

How it works…

AABB-to-plane

Getting ready

How to do it…

How it works…

OBB-to-OBB

Getting ready

How to do it…

How it works…

OBB-to-plane

Getting ready

How to do it…

How it works…

Plane-to-plane

Getting ready

How to do it…

How it works…

10. 3D Line Intersections

Introduction

Raycast Sphere

Getting ready

How to do it…

How it works…

Raycast Axis Aligned Bounding Box

Getting ready

How to do it…

How it works…

Raycast Oriented Bounding Box

Getting ready

How to do it…

How it works…

Raycast plane

Getting ready

How to do it…

How it works…

Linetest Sphere

Getting ready

How to do it…

How it works…

Linetest Axis Aligned Bounding Box

Getting ready

How to do it…

How it works…

Linetest Oriented Bounding Box

Getting ready

How to do it…

How it works…

Linetest Plane

Getting ready

How to do it…

How it works…

11. Triangles and Meshes

Introduction

Point in triangle

Getting ready

How to do it…

How it works…

Closest point triangle

Getting ready

How to do it…

How it works…

Triangle to sphere

Getting ready

How to do it…

How it works…

Triangle to Axis Aligned Bounding Box

Getting ready

How to do it…

How it works…

Triangle to Oriented Bounding Box

Getting ready

How to do it…

How it works…

Triangle to plane

Getting ready

How to do it…

How it works…

Triangle to triangle

Getting ready

How to do it…

How it works…

Robustness of the Separating Axis Theorem

Getting ready

How to do it…

How it works…

Raycast Triangle

Getting ready

How to do it…

How it works…

Linetest Triangle

Getting ready

How to do it…

How it works…

Mesh object

Getting ready

How to do it…

How it works…

Mesh optimization

Getting ready

How to do it…

How it works…

Mesh operations

Getting ready

How to do it…

How it works…

There’s more…

12. Models and Scenes

Introduction

The Model object

Getting ready

How to do it…

How it works…

Operations on models

Getting ready

How to do it…

How it works…

The Scene object

Getting ready

How to do it…

How it works…

There’s more

Operations on the scene

Getting ready

How to do it…

How it works…

The Octree object

Getting ready

How to do it…

How it works…

Octree contents

Getting ready

How to do it…

How it works…

Operations on the Octree

Getting ready

How to do it…

How it works…

Octree scene integration

Getting ready

How to do it…

How it works…

13. Camera and Frustum

Introduction

Camera object

Getting ready

How to do it…

How it works…

Camera controls

Getting ready

How to do it…

How it works…

Frustum object

Getting ready

How to do it…

How it works…

Frustum from matrix

Getting ready

How to do it…

How it works…

Sphere in frustum

Getting ready

How to do it…

How it works…

Bounding Box in frustum

Getting ready

How to do it…

How it works…

Octree culling

Getting Ready

How to do it…

How it works…

Picking

Getting ready

How to do it…

How it works…

There’s more…

14. Constraint Solving

Introduction

Framework introduction

Getting ready

How to do it…

How it works…

There’s more…

Raycast sphere

Getting ready

How to do it…

How it works…

Raycast Bounding Box

Getting ready

How to do it…

How it works…

Raycast plane and triangle

Getting ready

How to do it…

How it works…

Physics system

Getting ready

How to do it…

How it works…

Integrating particles

Getting ready

How to do it…

How it works…

There’s more…

Solving constraints

Getting ready

How to do it…

How it works…

Verlet Integration

Getting ready

How to do it…

How it works…

15. Manifolds and Impulses

Introduction

Manifold for spheres

Getting ready

How to do it…

How it works…

Manifold for boxes

Getting ready

How to do it…

How it works…

There’s more…

Duplicate points

Rigidbody Modifications

Getting ready

How to do it…

How it works…

Linear Velocity

Getting ready

How to do it…

How it works…

Linear Impulse

Getting ready

How to do it…

How it works…

Linear Impulse

Friction

There’s more…

Physics System Update

Getting ready

How to do it…

How it works…

Angular Velocity

Angular Velocity and Acceleration

Tangential Acceleration

Centripetal Acceleration

Torque

Inertia Tensor

Getting ready

How to do it…

How it works…

There’s more…

Tensors

Angular Impulse

Getting ready

How to do it…

How it works…

There’s more…

Non-linear projection

16. Springs and Joints

Introduction

Particle Modifications

Getting ready

How to do it…

How it works…

Springs

Getting ready

How to do it…

How it works…

Cloth

Getting ready

How to do it…

How it works…

Physics System Modification

Getting ready

How to do it…

How it works…

Joints

Getting ready

How to do it…

How it works…

There’s more…

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