# Trig. idiot need help, compound angles.

#### justinreeves

Hey If anyone has time or can point me to a link, I am low in math skills and need to know how to calculate compound angles.
I am a 3D animator also and there is a lot of use where Trig. is helpfull
but I have no Idea how to figure what any of these things mean or the context in wich they are used.
I am the type of person who needs to use the equation in a real life situation to get some type of context to base things off of.

Homework Helper

#### TenaliRaman

Justin,
If you are a 3D animator, then you need to get good books.

Two books i can suggest off-hand are,
1. Computer Graphics by Hearn and Baker
2. Computer Graphics: Principles and Practice by James D. Foley, et. al

You will not come across a lot of compound angles during various transforms, still if you feel you need to brush up through them then,
http://www.projectalevel.co.uk/maths/compound.htm

This link gives most of the commonly used compound angle formulae. Try to prove them, if you wish. The proofs are also available online, in case you are stuck.

-- AI

#### BobG

Homework Helper
justinreeves said:
Hey If anyone has time or can point me to a link, I am low in math skills and need to know how to calculate compound angles.
I am a 3D animator also and there is a lot of use where Trig. is helpfull
but I have no Idea how to figure what any of these things mean or the context in wich they are used.
I am the type of person who needs to use the equation in a real life situation to get some type of context to base things off of.
I have a feeling that what you really mean by compound angles is that some of the tensor equations or rotation matrices used for rotations have cosine or sine of an angle multiplied by the cosine or sine of a different angle. The angles you're probably talking about are the Euler angles. You rotate about one axis by a certain amount, rotate about a second axis by a certain amount, and then rotate about the third axis by a certain amount. In practice, all three rotations can be combined - hence the 'compound' angles.

The trig you need to learn is pretty easy.

You also need to learn some linear algebra - how to construct and multiply your rotation matrices together to rotate the vector in 3 dimensions. You'll soon learn there's some problems with using Euler angles for computer animations. You'll eventually need to move on to using a direction cosine matrix or quaternions. Quaternions are the most popular method.

I'd recommend getting a book. Quaternions and Rotation Sequences : A Primer With Applications to Orbits, Aerospace & Virtual Reality by Jack B. Kuipers is very good, especially if you have a limited math background. It was designed for the reader with a limited math background (keep in mind the term 'limited math background' is a relative term, so it may not be an easy read - but he starts at a pretty basic level).

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