Spline

Foreword

The Spline command creates curves (cubic splines) that interpolate a set of input points. A cubic spline that interpolates n points (called defining points) consists of n-1 consecutive arcs (called branches of the spline). At each of the defining points, the spline has curvature continuity (continuity 2).

At the first and last points to be interpolated (the endpoints of the spline) the interpolating curve may have one of the following shapes:

Null curvature — the section of the curve near the endpoint coincides with the tangent to the spline at the endpoint.
Fixed components — the section of the curve near the endpoint coincides with a direction tangent to a selected line or curve, or specified by entering the X, Y, and Z components.
Circular — the section of the curve near the endpoint coincides with a circle passing through the three defining points nearest to the endpoint.

Insert a spline curve

thinkdesign

Spline

To create a spline, you must do the following:

Define the shape at the first and second endpoints.

Specify the points to be interpolated.

Setting the conditions at the first endpoint
Under Start condition, choose the shape from the Type drop-down list that you want to assign to the section of the spline near the first endpoint. You can select one of the following:

Fixed components
When you select this condition, the section of the curve near the endpoint coincides with a given direction, which may be specified as one of the following:

A direction indicated by a selected line or by the tangent at a point to another selected curve. To specify the direction using this method, click the Select button adjacent to Curve, and then click on the line or curve.
A direction you specify by entering its components. To specify the direction using this method, type the values of the components in the adjacent X, Y and Z text boxes.

Selecting the Invert check box reverses the direction of the tangent at the endpoint so that its direction is opposite to that of the selected curve or line.
The following example illustrates the effect this check box has on the shape of the curve at the endpoint.

Circular

When you select this condition, the section of the curve near the endpoint coincides with a circle passing through the three defining points nearest to the endpoint.

Null curvature

Setting the conditions at the second endpoint
Under End condition, choose the shape from the Type drop-down list that you want to assign to the section of the spline near the second endpoint. The controls for defining the shape of the spline at the second endpoint are exactly the same as those for the first endpoint.

To make a closed spline, select the Close spline check box.

Selecting the through points
Under Select, specify the input points. You can define these points by using either of the following methods, or by using a combination of both methods:

Select the points one by one (by clicking on them or by using Snap).

Import the points from an ASCII Points file (a ".pt" file). To import the points from a file:
- Click the From file button. thinkdesign displays the Point file dialog box.
- Select the ASCII points file containing the points you want to import.
- Click the Open button.

End selection.

1	Setting the conditions at the first endpoint Under Start condition, choose the shape from the Type drop-down list that you want to assign to the section of the spline near the first endpoint. You can select one of the following:
	Fixed components When you select this condition, the section of the curve near the endpoint coincides with a given direction, which may be specified as one of the following: A direction indicated by a selected line or by the tangent at a point to another selected curve. To specify the direction using this method, click the Select button adjacent to Curve, and then click on the line or curve. A direction you specify by entering its components. To specify the direction using this method, type the values of the components in the adjacent X, Y and Z text boxes.
	Selecting the Invert check box reverses the direction of the tangent at the endpoint so that its direction is opposite to that of the selected curve or line. The following example illustrates the effect this check box has on the shape of the curve at the endpoint.
	Circular When you select this condition, the section of the curve near the endpoint coincides with a circle passing through the three defining points nearest to the endpoint.
	Null curvature When you select this condition, the section of the curve near the endpoint coincides with the tangent to the spline at the endpoint.
2	Setting the conditions at the second endpoint Under End condition, choose the shape from the Type drop-down list that you want to assign to the section of the spline near the second endpoint. The controls for defining the shape of the spline at the second endpoint are exactly the same as those for the first endpoint. To make a closed spline, select the Close spline check box.
3	Selecting the through points Under Select, specify the input points. You can define these points by using either of the following methods, or by using a combination of both methods: Select the points one by one (by clicking on them or by using Snap). Import the points from an ASCII Points file (a ".pt" file). To import the points from a file: Click the From file button. thinkdesign displays the Point file dialog box. Select the ASCII points file containing the points you want to import. Click the Open button.

4	End selection.