General Conic

This option creates conic sections by using either one of the various loft conic methods or the general conic equation. The resulting conic is either a circle, an ellipse, a parabola, or a hyperbola; depending on the mathematical results of the input data. The General Conic option is more flexible than the ellipse, parabola, and hyperbola options, since it allows several different methods for defining the curve. For a basic description of conics, see the Overview of Conic Curves.

To create a general conic:

  1. Choose a construction method.

  2. Indicate the location of the first point of the conic using the Point Constructor or define the first coefficient.

  3. Specify the remaining points of the conic and/or define the slope, anchor, Rho, or remaining coefficients.

  4. Note:

     If you are working in Sketcher with an active sketch, clicking the General Conic icon opens the Point Constructor dialog. See General Conic Within a Sketch for help.

Construction Methods

General Conic Construction Methods

5 Points

Creates a conic section defined by five coplanar points.

4 Points, 1 Slope

Creates a conic section defined by four coplanar points, with a slope at the first point.

3 Points, 2 Slope

Creates a conic section defined by three points, the slope at the first point, and the slope at the third point.

3 Points, Anchor

Creates a conic section defined by three points on the conic and the intersection point of the two end tangent vectors.

2 Points, Anchor, Rho

Creates a conic given two points on the conic section, an anchor point to determine the starting and ending slopes, and the projective discriminant, Rho (which is used to determine a third point on the conic section).

Coefficients

Creates a conic using an equation where the controlling conic parameters are user defined.

2 Points, 2 Slope, Rho

Creates a conic given two points on the conic section, the starting and ending slopes, and the projective discriminant, Rho.

The conic always passes through each point you specify, unless points lie on the two branches of a hyperbola. With the two methods utilizing slopes, the slope(s) lies at the end(s) of the conic.

The slope is projected to the plane of the conic. If the slopes are not in the plane generated by the points defining the conic, the conic is not created and an error message is displayed.