Question for math geeks

[Orrex]

Given a particular angle, how do you determine the equation of the curve that best "fits" into that angle?

I'm sorry that I don't know the proper terminology, but you can see therefore why I'm having trouble researching the solution for myself. For all I know, it might be terrifically simple but I'm over-thinking it.

For example, if you have a 45° angle, what's the formula for the angle that snuggles into it most comfortably? What's this process called, if indeed it has a name?


A request for anyone who's passionate about the subject: be merciful and not too complainy about my awkward terminology; if I knew a better way to ask the question I would do so, so don't jump on me for a lack of precision, please!


Thanks!

[HopeHoops]

1. Well any parabola will. I'm really not sure what you're getting at. I'm a math geek - PM me.

[Orrex]

2. Thanks--I'll send you more info when I get home from work.

I appreciate your inpu!

[HopeHoops]

3. Be detailed.

[Orrex]

4. Detailed PM sent

I didn't specify numbers, because I don't yet have them, but I think that I gave a better description of what I'm seeking.


Thanks!

[pokerfan]

5. any circle will, as well

Smaller circles will fit 'deeper' into the angle.

[HopeHoops]

7. It really depends on what you're trying to represent. Any curve will fit.

Well, a portion of it at least. The choice is mostly a matter of how precise your representation needs to be. A parabola is easier to adjust for three dimensions than a circle - just by where you cut off the sides.

[Dr. Strange]

25. Stop naming conic sections!

But yeah, I think a hyperbola would be the best. The sides of the angle could be the asymptotes, and you can jiggle the eccentricity to have the curve snuggle up as close as you want.

[Lionel Mandrake]

8. x tan(a/2) = sqrt(y^2 + 1)

where a is the angle in radians. This is one half of a hyperbola.

[Orrex]

10. No shit? I'll give that a try!

Thanks!

[Lionel Mandrake]

13. You're welcome!

I hope this is what you were looking for.

[madinmaryland]

9. Anyone who uses "snuggles" in a math formula really has no clue about mathematics and

should not be attempting to understand it. eom

[Orrex]

11. It keeps all of the variables nice and cozy

[madinmaryland]

14. Dammit! Stop it!!

[pokerfan]

16. This subthread is only tangentially related to the OP (nt)

[Lionel Mandrake]

17. If the curve osculates with (kisses) the straight lines forming the angle,

then the relationship is tangential.

Snuggling and kissing - who knows what that might lead to?

Even a hyperbola which approaches the angle asymptotically can be said to osculate with the angle at infinity. But that's kind of standoffish and not very sexy.

[madinmaryland]

18. It is spelled "oscillates". Here is a graph of oscillation...

[Lionel Mandrake]

23. That's a different word.

A curve C containing a point P where the radius of curvature equals r, together with the tangent line and the osculating circle touching C at P

The term derives from the Latinate root "osculate", to kiss, because the two curves contact one another in a more intimate way than simple tangency.

To read more, search for "Osculating curve" on Wikipedia

[madinmaryland]

27. Alerting! No porn allowed!!

[Lionel Mandrake]

28. What, you didn't like my dirty pictures?...n/t

[pokerfan]

19. Are you inflecting that this subthread is silly? (nt)

[Lionel Mandrake]

24. Don't worry - it's not inflectious...n/t

[swimboy]

12. Don't be an assymptote.

[SwissTony]

15. Can I ask what exactly are you trying to do and why?

We have a pretty good idea on intersecting straight lines and angles. What needs to be "fitted"?

[Dr. Strange]

20. I'm guessing it's a porn video.

[Orrex]

22. You signed the release, so shut your damn mouth.

[backscatter712]

21. Are you thinking Bezier curves? or NURBS curves?

This takes me back to my days of learning computer graphics as a computer science major.

Beziers can be used for taking a group of control points, say the points used to describe a pair of lines forming a 45 degree angle, to create a curve that tracks the angle somewhat.

http://en.wikipedia.org/wiki/B%C3%A9zier_curve

Another related mathematical construct is a NURBS curve. NURBS curves have the virtue of being more controllable than Bezier splines.

http://en.wikipedia.org/wiki/Non-uniform_rational_B-spline