A free online book on fundamentals of ray tracing

Although this book does not cover acceleration structures, it does give a fair amount of detail for beginners. Thought of putting a blog post in for this invaluable free resource. Here are the table of contents at a glance

Chapter 1: Introduction

Chapter 2: Digital Images

2.1 Pixels and colors

2.2 An example

2.3 Resolution

Chapter 3: Cameras, Eyes, and Ray Tracing

3.1 Images distort reality

3.2 Perspective in art

3.3 Cameras

Chapter 4: Vectors and Scalars

4.1 Scalars

4.2 Vectors

4.3 Vector addition

4.4 Vector subtraction

4.5 Scalars multiplied by vectors

4.6 Vector magnitude

4.7 Unit vectors

4.8 Vector dot products

4.9 Vector cross products

4.10 Sine and cosine: a crash course

Chapter 5: C++ Code for Ray Tracing

5.1 Platforms and redistribution

5.2 Downloading and installing

5.3 Building on Windows

5.4 Getting ready to build under OS X

5.5 Building on Linux and OS X

5.6 Running the unit tests

5.7 Example of creating a ray-traced image

5.8 The Vector class

5.9 struct LightSource

5.10 The SolidObject class

5.11 SolidObject::AppendAllIntersections

5.12 struct Intersection

5.13 Scene::SaveImage

5.14 Scene::TraceRay

5.15 Saving the final image to disk

Chapter 6: Sphere Intersections

6.1 General approach for all shapes

6.2 Parametric ray equation

6.3 Surface equation

6.4 Intersection of ray and surface

6.5 Surface normal vector

6.6 Filling in the Intersection struct

6.7 C++ sphere implementation

6.8 Switching gears for a while

Chapter 7: Optical Computation

7.1 Overview

7.2 class Optics

7.2.1 Matte color

7.2.2 Gloss color

7.2.3 Avoiding amplification

7.2.4 Opacity

7.2.5 Splitting the light's energy

7.2.6 Surface optics for a solid

7.3 Implementation of CalculateLighting

7.3.1 Recursion limits

7.3.2 Ambiguous intersections

7.3.3 Debugging support

7.3.4 Source code listing

Chapter 8: Matte Reflection

8.1 Source code listing

8.2 Clear lines of sight

8.3 Brightness of incident light

8.4 Using CalculateMatte's return value

Chapter 9: Refraction

9.1 Why refraction before reflection?

9.2 Understanding the physics of refraction

9.3 Snell's Law adapted for vectors

9.3.1 Introduction to Snell's Law

9.3.2 Refractive reflection

9.3.3 Special case: total internal reflection

9.3.4 Setting up the vector equations for refraction

9.3.5 Folding the three equations into one

9.3.6 Dealing with the double cone

9.3.7 Constraining F to the correct plane

9.3.8 Reducing to a scalar equation in k

9.3.9 Picking the correct solution for k and F

9.4 Calculating refractive reflection

9.5 Ambient refractive index

9.6 Determining a point's refractive index

9.7 CalculateRefraction source code

Chapter 10: Mirror Reflection

10.1 The physics of mirror reflection

10.2 Two kinds of reflection, same vectors

10.3 Deriving the vector formula

10.4 Recursive call to CalculateLighting

10.5 CalculateReflection source code

Chapter 11: Reorientable Solid Objects

11.1 The challenge of rotation

11.2 The SolidObject_Reorientable class

11.3 Implementing a rotation framework

11.4 Complex numbers help rotate vectors

11.5 Rotation matrices

11.6 Translating between camera coordinates and object coordinates

11.7 Simple example: the Cuboid class

11.8 Another reorientable solid: the Cylinder class

11.9 Surface normal vector for a point on the tube surface

Chapter 12: The TriangleMesh class

12.1 Making things out of triangles

12.2 Intersection of a ray and a triangle's plane

12.3 Determining whether a point is inside the triangle

12.4 The surface normal vector of a triangle

12.5 An ambiguity: which perpendicular is correct?

12.6 Example: using TriangleMesh to draw an icosahedron

12.7 Using TriangleMesh for polygons other than triangles

Chapter 13: The Torus class

13.1 Mathematics of the torus

13.2 Intersection of a ray and a torus

13.3 Solving the quartic intersection equation

13.4 Surface normal vector for a point on a torus

Chapter 14: Set Operations

14.1 A simpler way to code certain shapes

14.2 SetUnion

14.3 SetIntersection

14.4 The SolidObject::Contains member function

14.5 SetComplement

14.6 SetDifference

14.7 Combining set operations in interesting ways

14.8 A set operator example: concrete block