cutting cone with a plane

[siadajpan]

Hi

I'm searching information about the modelling a cut through the cone with a plane.

I have a cone and I cut it from above with a plane at different angles. That way I will always end up having parabolas or triangle shapes. I'd like to know what is the angle difference between parabola arms at different cuts.

At the end, I'd like to create a function that would input cone dimensions, and the normal vector of the plane outputting the angles of lines tangential to parabola arms.

What would be the best way to achieve this function that would give me fast answer?

Thanks for ideas

[JÞB · Accepted solution]

Conic functions are a basic set of Euclidean geometry. most of those properties have been known for @2300 years or so.  

Triangles won't be formed by a plane cutting a cone (a line, hyperbola, ellipse, circle or hyperbola are the only possibilities in 3D space)  The exception, is a plane not normal to the focus and passing though an an angle greater than the cone(Slicing both section any angle less than that is called a "Point".)  But, those are really special hyperbolae, since the triangles have no "Base" yet they are "triangle-ishly" shaped at one vertex.  You might have missed something usually taught in high-school mathematics.  This is not really a "LabVIEW" question.  But, we can help you use LabVIEW to implement those algorithms if you explain your requirements a bit better. 

[altenbach]

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@JÞB wrote:

Triangles won't be formed by a plane cutting a cone (a line, hyperbola, ellipse, circle or hyperbola are the only possibilities in 3D space)  

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You forgot the parabola, but mentioned hyperbola twice. 😉

(If the axis of the cone lies in the cutting plane, you get two straight lines, basically a triangle with two infinitely long sides :D.)

[JÞB]

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@altenbach wrote:

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@JÞB wrote:

Triangles won't be formed by a plane cutting a cone (a line, hyperbola, ellipse, circle or hyperbola are the only possibilities in 3D space)  

---

You forgot the parabola, but mentioned hyperbola twice. 😉

(If the axis of the cone lies in the cutting plane, you get two straight lines, basically a triangle with two infinitely long sides :D.)

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Damned auto spell check,  And a triangle has a base!  I edited THAT at least.  The solution will probably involve the simpler complex datatype anyway.  (Bows to the master) 

[siadajpan]

Hi

Thanks, I thought that I would have to use some kind of Cone model and cut it. Didn't know how to search for that equations.

Thanks!