Beziers are the building blocks of all the objects in Stardraw A/V Lite. They are simple but powerful entities and their versatility sometimes means that people can become overawed. This section is intended to calm people's fears about this misunderstood tool.
A Bezier is simply a curve. It has a startpoint, an endpoint and 2 control points which create the curve.
If there were no control points the bezier would merely be a straight line between the start and endpoint. The control points are there to force the line to bend and they could be said to exert a force on this line, pulling it towards them. The line still has to pass through the start and endpoints but the further away the control points are the stronger their pull on the line, as if they were connected to it with unbreakable elastic. By moving the control points, any shape of curve can be produced and if the control points are on the start- and endpoints, the curve will be a straight line again as no "force" is being exerted on it.
When you draw a bezier curve using the Bezier tool the first time you push the mouse button down sets the location of the startpoint. When you release the mouse button you set control point 1.
The next time you press the mouse button down you set the startpoint of the next bezier and when you release it you set control point 1 of the next bezier. Because symmetry is active this also sets control point 2 of the first bezier. This control point's position is the mirror image of control point 1 of the second bezier where the mirroring point is the endpoint of the first bezier (which is also the startpoint of the second bezier).
When drawing joined beziers, the endpoint of one is the startpoint of another and control point 2 of the first is the mirror of control point 1 of the next using the common end/startpoint as the mirror.
In the example here, the beziers were drawn thus:
Click on point 1, drag to point A and release.
Click on point 2, drag to point B and release.
Click on point 3 and release.
Doubleclick.
Bezier 1 (Bez1) curves from points 1 to 2, bezier 2 (Bez2) curves from points 2 to 3.
By dragging from 1 to A you have set the start point of Bez1 at 1 and control point 1 of Bez1 at A (release always sets control point 1 of the current bezier).
By clicking at 2 you set the start point of Bez2 at 2 (this also sets the endpoint of Bez1 at 2). Clicking always sets the start point of the next bezier.
By dragging from 2 to B Bez2's control point 1 is set at B (because re-leasing always sets the current bezier's control point 1). Simultaneously this sets control point 2 of the previous bezier through symmetry. Control point 2 of Bez1 is the mirror image of control point 1 of Bez2. The common start/end point (point 2) is the point through which the control point is mirrored.
By clicking at 3 you set the start point of the next bezier at 3 (this also sets the endpoint of Bez2 at 3). By releasing at 3 you set control point 1 of the next bezier at 3 also. This sets control point 2 of Bez2 at 3 through symmetry. By doubleclicking you end the drawing action and the third bezier is discarded.
You might want to read that lot again - actually it's simpler than it sounds.
Note that if you just click and release to position a point on a bezier, the startpoint and control point 1 will be at the same position. In this way you will only draw straight lines. You have to drag your mouse with the left button pressed down for the control point to have an effect and bend the curve. Always doubleclick to finish drawing your bezier after setting the final point.
If you call up the properties sheet of a bezier it will look something like the example shown here. You have control over the positions of the start, end and control points of each bezier you draw. Use the spin controls to adjust them and see the effect they have.
If you have drawn more than one bezier in a chain you can change the bezier number in this dialog to see the properties of each curve in the chain. When you have more than one bezier and the "Joined" box is checked it means that the endpoint of one is the startpoint of the next so changes that you make to the one will have an effect on the other.
If the "Symmetry" box is checked it means that control point 2 of the first bezier is affected by changes to control point 1 of the second. If you move the latter, an equal and opposite effect will be made on the former e.g. if you move control point 1 of the second bezier 1m to the right, control point 2 of the first will move 1m to the left.
You can, of course, use the Edit Node Cursor to move all points on a be-zier, though not when the Bezier Properties Sheet is displayed.
All 2 dimensional objects are constructed from bezier curves although their use is transparent, being controlled and implemented through the 2D drawing tools. Bezier curve constructions are as follows:
|
Object |
Bezier Curve Construction |
|
Line |
Single bezier where control point 1 sits on the start point and control point 2 sits on the endpoint. |
|
Rectangle |
Four straight chained beziers at 90° to each other. |
|
Circle |
Four chained beziers. Each bezier's control points are on top of each other. A line drawn from the start point to the control points to the endpoint would form a right-angled isosceles triangle. |
|
Polygon |
Chained beziers where, for every bezier, the position of the start point equals the position of control point 1 and the position of the end point equals the position of control point 2. |
|
Text |
Each letter is constructed from chained bezier curves to represent a TrueType character. |
The Convert to Curves command converts objects into their component beziers (yes, it's true: that rectangle was four beziers all along!) so you can manipulate objects in some surprising ways. Try it with text: convert a text object to curves then move the newly created nodes using the Edit Node cursor.