Sketcher ConstrainTangent/it

Descrizione
Il vincolo Tangente costringe due curve ad essere tangenti. Le linee sono trattate come infinite, e gli archi sono trattati come cerchi o ellissi completi. Il vincolo è anche in grado di collegare due curve costringendole ad essere tangenti nella giunzione, e quindi rende levigata la loro congiunzione.

Uso
Il vincolo può essere applicato in quattro modi diversi:
 * 1) tra due curve (non disponibile per tutte le curve)
 * 2) tra due punti finali di curve, crea una giunzione liscia
 * 3) tra una curva e il punto finale di un'altra curva
 * 4) tra due curve in un punto definito dall'utente

Per applicare il vincolo di tangenza, si dovrebbe usare la seguente procedura:
 * Selezionare due o tre entità nello schizzo.
 * Invocare il vincolo facendo clic sull'icona nella barra degli strumenti, oppure selezionando la voce del menu, oppure usando la scorciatoia da tastiera.

Tra due curve (tangenza diretta)


Rende tangenti due curve, e il punto di tangenza è implicito. Questa modalità si applica se sono state selezionate due curve.

Selezioni accettate: Se tra le curve selezionate la "tangenza diretta" non è supportata (ad esempio, tra un cerchio e un'ellisse), nello schizzo viene automaticamente aggiunto un punto di supporto e viene applicata la "tangenza nel punto".
 * linea +  linea, cerchio, arco, ellisse, arco-di-ellisse
 * cerchio, arco +  cerchio, arco

It is not recommended to reconstruct the point of tangency by creating a point and constraining it to lie on both curves. It will work, but the convergence will be seriously slower, jumpier, and will require about twice as many iterations to converge than normal. Use other modes of this constraint if the point of tangency is needed.

Between two endpoints (point-to-point tangency)


In this mode, the endpoints are made coincident, and the joint is made tangent (C1-smooth, or "sharp", depending on the placement of curves before the constraint is applied). This mode is applied when two endpoints of two curves were selected.

Accepted selection:
 * endpoint of line/arc/arc-of-ellipse +  endpoint of line/arc/arc-of-ellipse (i.e., two endpoints of any two curves)

Between curve and endpoint (point-to-curve tangency)


In this mode, an endpoint of one curve is constrained to lie on the other curve, and the curves are forced tangent at the point. This mode is applied when a curve and an endpoint of another curve were selected.

Accepted selection:
 * line, circle, arc, ellipse, arc-of-ellipse +  endpoint of line/arc/arc-of-ellipse (i.e., any curve  +  endpoint of any curve)

Between two curves at point (tangent-via-point) (v0.15)


In this mode, two curves are made tangent, and the point of tangency is tracked. This mode is applied when two curves and a point were selected.

Accepted selection: "Any point" can be a lone point, or a point of something, e.g. a center of a circle, an endpoint of an arc, or the origin.
 * any line/curve +  any line/curve  +  any 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 curves will be forced tangent at the point. These helper constraints are plain regular constraints. They can be added manually, or deleted.

Compared to direct tangency, this constraint is slower, because there are more degrees of freedom involved, but if the point of tangency is needed, it is the recommended mode because it offers better convergence compared to direct tangency + point on two curves.

The placement of the point before the constraint is applied is a hint for the solver for where the tangency should be. With this constraint, one can constrain two ellipses to touch each other in two places.

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

where:
 * Sketch is a sketch object
 * icurve1, icurve2 are two integers identifying the curves to be made tangent. The integers are indexes in the sketch (the value, returned by Sketch.addGeometry).
 * pointpos1, pointpos2 should be 1 for start point and 2 for end point.
 * geoidpoint and pointpos in TangentViaPoint are the indexes specifying the point of tangency.