Inserting connecting curves - Automatic mode

To accomplish this task, open file "connect.e3".

1 After starting the Connect Curve command, click on the first and on the second curve close to the end points to connect, or, if you prefer, use the snap commands.



Then set the Edit Mode drop-down list to Automatic (if not already set so).


Filtering selection on end points
You can enable the command to select points, curves and surfaces and curves or restrict selection to curves and surface curve boundaries only. A context menu is available when right-clicking on First endpoint or Second endpoint:



  • Curves Only — enables selection of curves and surface boundaries.
  • Points - Curves - Surfaces Points - Curves — enables selection of points , curves and surfaces, but does not allow selection of surface boundaries and curves.

As soon as the curves are selected, the 1st U and 2nd U mini-dialog box/handle pairs are displayed on the endpoints:



You can always change the position of the endpoints either by dragging the handles or by specifying the desired value of parameter U. You can assign a numeric value, called weight, to each of the curves to be connected so as to control the shape of the connecting curve. A handle is also available to change the weight interactively. The higher the weight, the longer the section of connecting curve that follows the shape of the connected curve starting from the point of connection. See also step 6 for further details on weights.
2 You can set the same continuity conditions at both endpoints of the blending curve, or different conditions at each endpoint. To set the same conditions, select the Same continuity check box. To set different conditions, uncheck the box: a separate Continuity By drop-down list will show up at each endpoint.



Suppose you have checked the Same continuity box. Only one drop-down list will be available in the selection list. The default value is Tangency, but you can set continuity to each of the following Continuity Types:
Position specifies that only geometric continuity is required at the endpoints.
Tangency specifies that the blending curve must share the same tangent line as the parent curve at the given end.
Curvature specifies that the blending curve must have the same value of curvature as the parent curve at the given end.
Torsion specifies that the blending curve must have the same value of torsion as the parent curve at the given end.
Smooth curvature specifies that the parent curve's curvature plot and the blending curve's curvature plot must be tangent continuous at the specified end.
Curvature plot curvature specifies that the parent curve's curvature plot and the blending curve's curvature plot must be curvature continuous at the specified end.

By selecting the Curve Curvature command you can also display a curvature plot which will help you check the shape and the smoothness of the resulting curve.
3 By selecting the options of the Result drop-down list you can specify what kind of result you want to obtain:
Connect curve only the only result of the command will be the connecting curve.
Split original curves the result of the command will be curves split from the original curves in addition to the connecting curve. These curves will join the connecting curve with the specified continuity at their ends. Thus, the maximum number of curves you will obtain with this option is three.
Join original curves the result will be a single curve made of the connecting curve and the two curves derived from the original ones according to the chosen endpoints and to the specified continuity conditions.
A Hide check box shows up when the Split original curves or Join original curves options are selected: when checked, the original curves will be hidden as soon as the connecting curve is created.
When Join original curves is selected, three further additional options are available:
Max. No. arcs specifies the maximum number of arcs (parametric spans) you want the resulting curve to be composed of.
Max. Degree specifies the maximum degree to use in the resulting joined curve.
Tolerance specifies the tolerance for the resulting joined curve, which is an Euclidean space tolerance for the parameter equal distance between the resulting joined curve and the original parent and blending curves.
4 In the Default drop-down list under More Options you can choose the type of construction for the connecting curve.
Single arc produces a single arc curve (a Bezier control point curve) with a degree determined by the specified geometric continuity conditions at the endpoints.
Minimum degree produces a NURBS curve with multiple arcs. The degree — at least three — will be the minimum necessary to maintain the specified geometric continuity conditions both internally and at the endpoints.
5 When the continuity conditions are set to Curvature or higher, the Weight Mode drop-down list shows up under More Options, enabling you to select the type of weights to be set.
Tangency in this case weights specify the lengths of the tangent vectors: the higher the weight, the longer the section of connecting curve that follows the shape of the connected curve starting from the point of connection (about the meaning of weights, see also Significance of Tangent Weights).
Second Derivative in this case weights specify the length of the second derivative in the direction of the tangent for the first and second curve respectively, which is the "speed" of the curvature change (the higher the weight, the speedier the curvature change).
Third Derivative (available only if continuity is set to Torsion or higher) in this case weights specify the length of the third derivative in the direction of the tangent for the first and second curve respectively.
Fourth Derivative (available only if continuity is set to Curvature plot curvature or higher) in this case weights specify the length of the fourth derivative in the direction of the tangent for the first and second curve respectively.


Reset
When the mode is set to Automatic, the Reset button will compute the blending curve resulting from the specified geometric continuity at each end, the tangent weights at each endpoint and the setting of the Default mode (Single arc or Minimum degree).
If you had previously specified curvature weights, these values will be reset to defaults and curvature weights will no longer be maintained.

 
6 Click or to confirm your selections and create the curve (s). In the following illustration you can see the curve obtained setting the Result to Connect curve only, continuity conditions to Tangency and Weight to 1 at both endpoints.



Click to discard your changes.
Blend Curve
Tips and Tricks