You're reading from Game Physics Cookbook Discover over 100 easy-to-follow recipes to help you implement efficient game physics and collision detection in your games

Product type Paperback

Published in Mar 2017

Publisher Packt

ISBN-13 9781787123663

Length 480 pages

Edition 1st Edition

Languages

C++

Tools

Unity

Concepts

Game Design

Author (1):

Gabor Szauer

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Table of Contents (19) Chapters

Preface

What this book covers
What you need for this book
Who this book is for
Sections
Conventions
Reader feedback
Customer support

1. Vectors FREE CHAPTER

Introduction
Vector definition
Component-wise operations
Dot product
Magnitude
Normalizing
Cross product
Angles
Projection
Reflection

2. Matrices

Introduction
Matrix definition
Transpose
Multiplication
Identity matrix
Determinant of a 2x2 matrix
Matrix of minors
Cofactor
Determinant of a 3x3 matrix
Operations on a 4x4 matrix
Adjugate matrix
Matrix inverse

3. Matrix Transformations

Introduction
Matrix majors
Translation
Scaling
How rotations work
Rotation matrices
Axis angle rotation
Vector matrix multiplication
Transform matrix
View matrix
Projection matrix

4. 2D Primitive Shapes

Introduction
2D points
2D lines
Circle
Rectangle
Oriented rectangle
Point containment
Line intersection

5. 2D Collisions

Introduction
Circle to circle
Circle to rectangle
Circle to oriented rectangle
Rectangle to rectangle
Separating Axis Theorem
Rectangle to oriented rectangle
Oriented rectangle to oriented rectangle

6. 2D Optimizations

Introduction
Containing circle
Containing rectangle
Simple and complex shapes
Quad tree
Broad phase collisions

7. 3D Primitive Shapes

Introduction
Point
Line segment
Ray
Sphere
Axis Aligned Bounding Box
Oriented Bounding Box
Plane
Triangle

8. 3D Point Tests

Introduction
Point and sphere
Point and AABB
Point and Oriented Bounding Box
Point and plane
Point and line
Point and ray

9. 3D Shape Intersections

Introduction
Sphere-to-sphere
Sphere-to-AABB
Sphere-to-OBB
Sphere-to-plane
AABB-to-AABB
AABB-to-OBB
AABB-to-plane
OBB-to-OBB
OBB-to-plane
Plane-to-plane

10. 3D Line Intersections

Introduction
Raycast Sphere
Raycast Axis Aligned Bounding Box
Raycast Oriented Bounding Box
Raycast plane
Linetest Sphere
Linetest Axis Aligned Bounding Box
Linetest Oriented Bounding Box
Linetest Plane

11. Triangles and Meshes

Introduction
Point in triangle
Closest point triangle
Triangle to sphere
Triangle to Axis Aligned Bounding Box
Triangle to Oriented Bounding Box
Triangle to plane
Triangle to triangle
Robustness of the Separating Axis Theorem
Raycast Triangle
Linetest Triangle
Mesh object
Mesh optimization
Mesh operations

12. Models and Scenes

Introduction
The Model object
Operations on models
The Scene object
Operations on the scene
The Octree object
Octree contents
Operations on the Octree
Octree scene integration

13. Camera and Frustum

Introduction
Camera object
Camera controls
Frustum object
Frustum from matrix
Sphere in frustum
Bounding Box in frustum
Octree culling
Picking

14. Constraint Solving

Introduction
Framework introduction
Raycast sphere
Raycast Bounding Box
Raycast plane and triangle
Physics system
Integrating particles
Solving constraints
Verlet Integration

15. Manifolds and Impulses

Introduction
Manifold for spheres
Manifold for boxes
Rigidbody Modifications
Linear Velocity
Linear Impulse
Physics System Update
Angular Velocity
Angular Impulse

16. Springs and Joints

Introduction
Particle Modifications
Springs
Cloth
Physics System Modification
Joints

A. Advanced Topics

Introduction
Generic collisions
Stability improvements
Springs
Open source physics engines
Books
Online resources
Summary

Index

Chapter 1. Vectors

In this chapter, we will cover the following vector operations:

Addition
Subtraction
Multiplication
Scalar Multiplication
Cross Product
Dot Product
Magnitude
Distance
Normalization
Angle
Projection
Reflection

You're reading from Game Physics Cookbook Discover over 100 easy-to-follow recipes to help you implement efficient game physics and collision detection in your games

Table of Contents (19) Chapters

Chapter 1. Vectors

Authors (1)

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