Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In the context of a game, I want to draw gears. The most common curves available on the platforms I'm using are third degree Bézier curves.

Is there an exact representation of the involute gear using only Bézier curves ?

share|improve this question
2  
Exact? No. But within screen resolution of your game, yes. –  Hagen von Eitzen Oct 6 '12 at 11:49
    
What is the nature of this curve ? –  Antoine Lecaille Oct 6 '12 at 12:04

2 Answers 2

up vote 3 down vote accepted

No. From this paper that discusses approximating an involute curve using a 4th degree Bezier:

The circle involute curves are by definition transcendental and cannot be expressed by algebraic equations

share|improve this answer
    
Thanks for the link. It looks close enough for me. –  Antoine Lecaille Dec 17 '12 at 16:30

While researching gear profile approximations, I came across this SE.

I wanted to add that I found this site: http://www.arc.id.au/GearDrawing.html which describes the usage of cubic (3rd degree) bezier curves about halfway down.

I know this is an old post, just thought I'd update some more relevant information because the answer was given for 4th order only. That paper is referenced heavily within the site.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.