## Resources

This page is intended for anyone who is wanting to improve their basic maths and physics skills and doesn’t quite know where to start!

### Contents

## Suggested Reading List

An incomplete list, but a good start. None of them are really for complete beginners; you’ll need to have a reasonable understanding of maths to make the most out of them.

- The VES Handbook of Visual Effects (Jeffery A Okun, Susan Zwerman)
- Fundamentals of Physics (David Halliday)
- Mathematics for Computer Graphics (John A Vince)
- Texturing and Modeling, Third Edition: A Procedural Approach (David S. Ebert, F. Kenton Musgrave, Darwyn Peachey, Ken Perlin, Steve Worley)
- Any of the Graphics Gems series of books.

## Online Resources By Subject

This is an ever-growing list I’ll continue to expand on and some links are still to be sourced. Most of the links point to relevant Khan Academy videos, but unfortunately only some are targetted at beginners. If you find a resource somewhere that you have found useful, please let me know in the comments below and I’ll add it to the list.

I’m happy to do my own tutorials if any subjects are difficult to find, so feel free to leave requests too.

- Maths
- Basic algebra
- Manipulation of equations
- Equations 1 by Khan Academy
- Equations 2 by Khan Academy
- Equations 3 by Khan Academy

- Quadratic equations
- Level 1 multiplying expressions by Khan Academy
- Solving a quadratic by factoring by Khan Academy
- Introduction to the quadratic equation by Khan Academy
- Quadratic Equation part 2 by Khan Academy

- Manipulation of equations
- Basic trigonometry
- General resources
- Trigonometry by Andy Nicholas

- Sine, Cosine, Tangent
- Sine, Cosine, and Tangent by Andy Nicholas
- Basic Trigonometry by Khan Academy
- Basic Trigonometry II by Khan Academy
- Radians and degrees by Khan Academy
- Using Trig Functions by Khan Academy
- Using Trig Functions Part II by Khan Academy

- Pythagorus
- Pythagorean Theorem by Andy Nicholas
- Pythagorean Theorem by Khan Academy
- Pythagorean Theorem 1 by Khan Academy
- Pythagorean Theorem 2 by Khan Academy

- Double angle and compound angle formulae
- Double Angle Identities by Andy Nicholas
- Product and Sum Identities by Andy Nicholas
- Trigonometric Identities by Khan Academy

- The Law of Cosines
- The Law of Cosines by Andy Nicholas
- The Law of Cosines by Khan Academy

- General resources

- Basic algebra
- Basic Geometry
- General resources
- paulbourke.net/geometry/ An awesome resource, lots of accessible information
- Vector Math for 3D Computer Graphics A solid set of course notes from Central Connecticut State University, Computer Science Department

- Vectors
- Unit Vectors
- Unit Vector Notation by Khan Academy

- Dot product
- Dot product
- The dot product by Khan Academy

- Cross product
- Cross product by University of Nebraska–Lincoln
- Cross product 1 by Khan Academy
- Cross Product 2 by Khan Academy
- Dot vs. Cross Product by Khan Academy

- Unit Vectors
- Matrices
- How to Read a 3×3 Matrix by Andy Nicholas
- Rotating Points With a 3×3 Matrix by Andy Nicholas

- Equation of a line
- Algebra: Slope and Y-intercept intuition by Khan Academy
- Algebra: Equation of a line by Khan Academy

- Circles
- Circles: Radius, Diameter and Circumference by Khan Academy
- Area of a circle by Khan Academy
- Language and Notation of the Circle by Khan Academy

- Equation of a plane
- Defining a plane in R3 with a point and normal vector by Khan Academy

- Cubic curves (Bezier, Hermite)
- Bezier curves by Darrel Plant
- Bezier curves – a primer by Mike Kamermans
- Bezier curves – with source code by Paul Bourke
- Spline curves with Java interactive demo by Andy Salter, Imperial College

- General resources
- Triangles
- Barycentric coordinates
- Normals
- Tangents

- Basic Calculus
- Differentiation
- Integration

- Physics
- Newtonian Mechanics
- Course Introduction and Newtonian Mechanics by Open Yale Courses

- Vectors in Physics
- Vectors in Multiple Dimensions by Open Yale Courses

- Newton’s Laws of Motion
- Newton’s Laws of Motion by Open Yale Courses
- Newton’s Laws (cont.) and Inclined Planes by Open Yale Courses

- Conservation of Energy
- Work-Energy Theorem and Law of Conservation of Energy by Open Yale Courses
- Law of Conservation of Energy in Higher Dimensions by Open Yale Courses

- Conservation of Momentum
- Dynamics of a Multiple-Body System and Law of Conservation of Momentum by Open Yale Courses

- Rotations
- Rotations, Part I: Dynamics of Rigid Bodies by Open Yale Courses
- Rotations, Part II: Parallel Axis Theorem by Open Yale Courses

- Torque
- Torque by Open Yale Courses

- Simple Harmonic Motion
- Simple Harmonic Motion by Open Yale Courses
- Simple Harmonic Motion (cont.) and Introduction to Waves by Open Yale Courses

- Waves
- Waves by Open Yale Courses

- Concepts and interrelationships of position, velocity, acceleration, force, energy
- Types of force and how to calculate them (drag/damping, spring, wind)
- Trajectory motion equations with constant force
- Analysis and resolution of forces on an object
- Circular motion
- Damped simple harmonic motion

- Newtonian Mechanics

#### Acknowledgements

Thanks to Paddy Finn (@Phinnelli) for the Physics links to the Open Yale Courses.

Yeah!said:Oh this a godsend. Yesterday I was searching for some introductory books to computer graphics for my ICE learning with no luck. and you came up with this article. man I’m so pumped. Thank You!

AndyN (author)said:No problem! Let me know if you find any that help you in particular.

Cheers,

Andy

FMsaid:Hi Andy,

I was wondering if you would upload the presentation you did during the FX masterclass on the 25th of November.

Thanks

FM

AndyN (author)said:Hi,

Yes, it’s available. Rather than post a link on my website, I’m just providing it to those people who came along on the day and ask me for it.

I’ll send you a link via email when I get a sec.

Cheers,

Andy

Francescsaid:Ei Andy,

Thanks a lot for all this material. Really helpfull.

I think I’m starting to love math because of ICE.

Cheers

Francesc

AndyN (author)said:Thanks Francesc, good to know that it helps.

Cheers,

Andy

juansaid:hey andy

thank you very much this.

i was thinking of starting my own \’commomly used maths for cg\’ page, but i believe this is it.

it would cool to have most of these with python examples. probably avoiding softimage or maya specific commands to keep them open.

i might start doing some work when i get free time.

again, cheers

juan

AndyN (author)said:Thanks Juan. Yes, that’s a good idea about having python examples.

It’s worth mentioning that if you’re looking for a compact math library for doing vector math in python, you could do a lot worse than to have a look at pyeuclid:

http://code.google.com/p/pyeuclid/

Cheers,

Andy

juansaid:ever so useful!

i use numpy for most of these but this quite neat.

cheers again andy.