Help, conic/conic, conic/spline, spline/spline, intersections?

Help, conic/conic, conic/spline, spline/spline, intersections?

Post by Andrew Tyldesl » Fri, 05 Mar 1993 00:28:43


My math is a bit (quite a bit?) rusty. I need to calculate the  
intersections of two conics, in 2D, of the general form:

        ax^2 + 2bxy + cy^2 + dx +ey +f = 0

If it makes it easier one of the conics can be in the form:

        x^2/b^2 + y^2/a^2 = 1

I would just adjust the one conic so its position remains the same  
relative to the other. I am primarily interested in ellipses if this  
makes the problem easier.

Also, does anyone know of any reference material on intersecting  
conics, B-splines, and nth degree Bezier curves with one another?

Any help would be greatly appreciated. Thanks
Ditek International Inc.


1. conic intersections?

I am trying to calculate the equation of an ellipse or a parabola, given
a plane in 3D, and a cone in 3D.

can anyone help?

Most textbooks explain how the 3D intersections produce the 2D shapes of
the conics shortly, but they fail to give a clear relationship.

In fact to be specific:

say I have a list of 3D vertices that define a polygon. All of the
vertices are coplanar (lie on the same plane in 3D). I also have a cone
defined by two 3D points (top, and direction) and an angle in the cone

say the plane intersects the cone to create an ellipse. What is the
equation of this ellipse?

any pointers wuld help...

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