Curve - Conic arc

Navigation: Geometry > Curves > Conic Arc

Conic Arc

Page Contents

Description

•Ellipse, Parabola, Hyperbola

•Starting and ending X and Y values

Related Topics

Description

The Conic Arc Curve type is based upon the general conic equation Ax² + Bxy +Cy² +Dx +Ey + F = 0 and is generally used for IGES import. The following relationships apply to the conic arc:

•A and C are non-zero valued, the function f(x,y) is a second-degree curve.

•B² = 4AC, the curve is a parabola

•AC > 0, the curve is an ellipse

•A = C, the curve is a circle whose radius is sqr(|F|)

•AC < 0, the curve is a hyperbola

•The B coefficient represents a rotation of the coordinate axes. If B = 0, the curves are not rotated about the local x- and y-axes.

•The D and E coefficients represent coordinate shifts.

User inputs include the desired coefficients and the range of values over which the curve is defined: x_start, y_start and x_end, y_end. These points do not have to lie on the curve. Rather, these points define the polar angle subtended by the curve in a manner analogous to the convention used for the circular arc. The starting and ending angles are simply:

Navigation

A Conic Arc curve type can be created in the following ways:

•Create a new curve and select "Conic arc (defined by coefficients of quadratic equation)" as the curve type.

Controls

Control	Inputs / Description	Defaults
Logical Parent	Name of the Custom Element containing the curve.	Selected custom element at the time of curve creation.
Name	Name of curve.	Curve n
Description	Description of curve.	Blank
Type	Curve type. Select "Conic arc (defined by coefficients of quadratic equation)" from the drop-down list.	Circular Arc
Conic arc Options
A	The X² term of the conic equation.	1
B	The XY term of the conic equation.	0
C	The Y² term of the conic equation.	1
D	The X term of the conic equation.	0
E	The Y term of the conic equation.	0
F	The constant term of the conic equation.	-1
Start X, Start Y	Starting sweep direction (see Application Notes).	1,0
End X, End Y	Ending sweep direction (see Application Notes).	1,0

OK	Accept settings and close the dialog box.
Cancel	Discard settings and close the dialog box.
Apply	Apply settings and keep the dialog box open.
Help	Access the Help.

Application Notes

Curve visualization

In order for the curve to be drawn in the 3D view, the Draw option must be checked on the Visualization Tab of the curve dialog box.

Ellipses, parabolas and hyperbolas

For a description of these specific curve types, please see the help topics ellipse, hyperbola, and parabola.

Starting and ending X and Y values

The (Start X, Start Y) and (End X, End Y) entries denote points in space connected to the curve's local origin. The Conic arc curve is defined in an angular region between these two vectors and therefore these points do not have to lie on the curve. For example, consider the elliptical curve 10x² + 7y² = 1, where A = 10, C = 7, F = -1 and B = D = E = 0. In order to define the curve in the first quadrant only, Start X = 1, Start Y = 0 and End X = 0, End Y = 1. These could just as easily be points on the curve; Start X = Sqrt( 0.1 ) = 0.3162 Start Y = 0 and End X = 0, End Y = Sqrt( 1/7 ) = 0.378:

If the same curve is to be defined from x = -0.3 and x = +0.2, then Start X = 0.2, Start Y=0.29277 and End X = -0.3, End Y = 0.360555. The values for Start Y and End Y are found by solving the curve equation for values Start X = 0.2 and End X = -0.3, respectively.