Sketcher ConstrainAngle

Description
Angle constraint is a datum constraint intended to fix angles in sketch. It is capable of setting slopes of individual lines, angles between lines, angles of intersections of curves, and angle spans of circular arcs.

Usage
There are four different ways the constraint can be applied:
 * to individual lines
 * between lines
 * to intersections of curves
 * to arcs of circles

To apply angle constraint, one should the follow the steps:
 * 1) Select one, two or three entities in the sketch. The mode will be chosen depending on the selection.
 * 2) Invoke the constraint using several methods:
 * 3) * Pressing the button in the toolbar.
 * 4) * Using the keyboard shortcut. (A is for Angle)
 * 5) * Using the form the top menu entry
 * 6) A datum edit dialog box pops up.
 * 7) Modify the angle if necessary. Note: The angle can be entered as an expression that will be evaluated and the result will be stored.
 * 8) Click

As with any datum constraint, it is possible to change the angle value later by double-clicking the constraint in constraint list or 3d view. Entering a negative value will cause the angle direction to flip.

Line slope angle
Accepted selection: line



The constraint sets the polar angle of line's direction. It is the angle between the line and X axis of the sketch.

Arc span (v0.15)
Accepted selection: arc of circle



In this mode, the constraint fixes angular span of a circular arc.

Between lines
Accepted selection: line +  line



In this mode, the constraint sets the angle between two lines. It is not required that the lines intersect.

Between curves at intersection (angle-via-point) (v0.15)
Accepted selection: any line/curve +  any line/curve  +  any point



In this mode, angle between two curves is constrained at the point of their intersection. The intersection point can be on curves' extensions. The point should be specified explicitly, since curves typically intersect in more than one point.

For the constraint to work correctly, the point must be on both curves. So, as the constraint is invoked, the point will be automatically constrained onto both curves (helper constraints will be added, if necessary), and the angle between curves will be constrained at the point. These helper constraints are plain regular constraints. They can be added manually, or deleted. There are no helper constraints on the example picture above, because the point selected is already the intersection of curves.

Interior vs. Exterior angles
There are two possible arcs along which an angle constraint can be set, with angles differing by 180 degrees. FreeCAD's internal logic for setting this constraint is (as of 0.20) somewhat unstable and the rules are not easily described.

One case, however, is stable: if two lines join at a point, and you select those lines and the point, the constraint will be set on the interior angle.

Scripting
Angle Constraint can be created from macros and from the python console by using the following:

where:
 * is a sketch object
 * are integers specifying the lines by their ordinal numbers in.
 * should be 1 for start point and 2 for end point. The choice of endpoints allows to set internal angle (or external), and it affects how the constraint is drawn on the screen.
 * and in  are the indexes specifying the point of intersection.
 * is the angle value in radians. The angle is counted between tangent vectors in counterclockwise direction. Tangent vectors are pointing from start to end for the lines (or vice versa if ending point is supplied in angle between lines mode), and along counterclockwise direction for circles, arcs and ellipses. Quantity is also accepted as an angle (e.g. )

The Sketcher scripting page explains the values which can be used for, , , , , and  and contains further examples on how to create constraints from Python scripts.