# does anyone know the mathematical equation of a cone?

Discussion in 'Archived Threads 2001-2004' started by felix_suwarno, Nov 5, 2002.

1. ### felix_suwarno Screenwriter

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if anybody here knows, please let me know. i have been searching on google and yahoo and still couldnt find it.

thanks

2. ### NickSo Producer

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What? the area/volume of a cone? or like an actual formula for a cone?

3. ### Christ Reynolds Producer

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well the volume of a cone is (pi/3)*r^2*h if thats what you are looking for, otherwise i'm not really sure what you mean.

CJ

4. ### Wayne Bundrick Cinematographer

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For a cone with radius r, with its base centered at the origin, swept around the z axis, and having height h:

x^2 + y^2 = (r - (rz/h))^2

where z is in the range [0,h]

5. ### Joe Hsu Supporting Actor

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hmmmm.....me wonders if he needs polar notation?
Either way, one of the previous equations should be what you're looking for.

6. ### felix_suwarno Screenwriter

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ok thanks guys!

but i do need one more thing. in order for my raytracer to work, i need to find the...

NORMAL VECTOR OF THE CONE.

does anybody know it? thats the single last piece of the puzzle that i need to know.

thanks in advance. i love HTF!

7. ### Wayne Bundrick Cinematographer

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I'm sure glad I'm not in school anymore.

8. ### Joe Hsu Supporting Actor

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hmmmmm....wasn't that long ago, and I already can't remember. Can you really find a normal vector for something that you haven't given parameters for yet? The vector you're looking for is the one that's orthogonal to the cone's surface, correct? So if you have any specs on the cone itself, just find the equation for any line that lies on the cone (or any circle, if you want), and find a vector that's perpendicular to it. ahhhh, cross products

9. ### dave_brogli Screenwriter

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damn i wish i knew math

10. ### PhilipW Second Unit

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Sounds foreign to me.

11. ### felix_suwarno Screenwriter

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"vector you're looking for is the one that's orthogonal to the cone's surface, correct? "

no, i need the vector that is perpendicular to the cone's surface. i found the hard way to do it, but according to my experience, i always do things the hard way because i am not good with numbers.

12. ### Joe Hsu Supporting Actor

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That's what orthogonal means Like I said, I don't remember exactly how, but if you do some reading, as long as you have a line on the cone's surface, that line's cross product with your new vector should be = 1. (or was it 0? Should be 1)

13. ### Gary King Second Unit

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No, you want the dot product of the normal with a vector tangent to the cone to be 0. The cross product is always a vector.

You need to take the cross product of the two partial derivatives of the parametric equation. It's easier if you transform the cone so that it is centered at the origin, pointing down a specific axis, with a unit-length radius.

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