CST2013: Create an Analytical Curve

Modeling: CurvesCurvesAnalytical Curve

In this dialog box you may specify an analytical curve by defining the analytical functions for x(t), y(t), z(t), and the range for the parameter t. The construction will always be performed in the currently active coordinate system.

Each analytical curve will be assigned to a previously defined curve. Thus the corresponding menu or toolbar items will only be active if at least one curve has been defined before (Navigation Tree: Curves:New Curve).

Within its curve each item is identified by a unique name. The curve item can be addressed by this name for subsequent editing operations.

As soon as the curve item is defined it will appear in the main plot window and on the navigation tree .

Name

Specify the unique name for the analytical curve.

X(t), Y(t), Z(t)

Specify a valid function dependent on the parameter t for the defining the coordinates of the analytical curve in global coordinates. Please note that these entries only appear when the global coordinate system is currently active.

U(t), V(t), W(t)

Specify a valid function dependent on the parameter t for defining the coordinates of the analytical curve in local coordinates. Please note that these entries only appear when a local coordinate system is currently active.

Min(t), Max(t)

Specify a valid parameter range for the parameter t.

Curve

Select the curve to which this analytical curve item will be assigned from the list of previously defined curves or enter a new name.

OK

Press this button to finally create the circle.

Preview

Press this button to create a preview image of the analytical curve. This option is very useful to check the settings before you actually create the analytical curve.

Cancel

Closes this dialog box without performing any further action.

Help

Shows this help text.

Example

A parabolic curve

X: t

Y: t^2 - 4

Z: 0

Range: -3 to 3

Note: An analytical curve can only be created when its first derivative exists in the given parameter range.

Example

Analytical curve creation fails for the following definition because the first derivative for sqr(t) at t=0 is not defined:

X: t

Y: sqr(t)

Z: 0

Range: 0 to 1

Use a mathematical substitution with  t = u^2:

X: u^2

Y: sqr(u^2) = u

Z: 0

Range: 0 to 1

Now, for the substituted definition the analytical curve creation succeeds:

X: t^2

Y: t

Z: 0

Range: 0 to 1