## Angular Dimensions

An angular dimension is defined for two geometric objects that have
vector guiding lines. The angular dimension value is specified in
radians, its values range from $0$ to $2\pi$ and it is defined by an
angle between the direction vectors of the first and second objects
measured counterclockwise. An angular dimension measured this way is
shown in Fig.1 as two intersecting lines with given directions. The
right part of Fig.2 shows a pair of lines that have the same angle
between vectors, but with the dimension measures a reverse angle sector.
The value of such dimension is determined by formula
$D = 2\pi - \alpha$, where $\alpha$ is the measured angle between the
vectors, and $D$ is the dimension value. This dimension is also called a
conjugate dimension. Another way to receive it is just to swap angular
dimension arguments.

```{figure} ../../pictures/S.2.7.1.png
:width: 15cm
:align: center

Fig. 1
```

```{figure} ../../pictures/S.2.7.2.png
:width: 15cm
:align: center

Fig. 2
```

There are four ways to define an angular dimension for one pair of
directions, including the two ways described above. Fig.3 shows a
dimension, its value is determined by adjacent angle formula:
$D = \pi - \alpha$. Fig.4 (right part) shows an alternate adjacent angle
version that is defined by the formula $D = \pi + \alpha$.

```{figure} ../../pictures/S.2.7.3.png
:width: 15cm
:align: center

Fig. 3
```

```{figure} ../../pictures/S.2.7.4.png
:width: 15cm
:align: center

Fig. 4
```

One more pattern associated with four ways to set the angular dimension
is that the dimension with the value $D = 2\pi - \alpha$ can be produced
from the dimension with the value $D = \alpha$ after a simple swap of
the first and second dimensional constraint objects. Similarly, the 4th
variant ($D = \pi + \alpha$) can be received from the 3rd one
($D = \pi - \alpha$) by swapping the arguments.

Angular dimension for a pair of directed objects, such as segments,
lines, or ellipses, is defined by the

```cpp
constraint_item GCE_AddAngle(GCE_system gSys, geom_item l1
                                            , geom_item l2
                                            , const GCE_adim_pars & dPars).
```

The function creates a new angular dimension defined for the **l1** and
**l**2 geometric objects in the **gSys** constraint system. The
dimension value and the way to define it are determined by the **dPars**
structure.

The function returns the descriptor of a new angular dimension.

The **dPars** structure determines the value of an angular dimension
defined using the **dPars.dPars** structure (**GCE_dim_par**), where the
dimension value is stored in **dPars.dPars.var** variable or if
**dPars.dPars.var = GCE_NULL_V** then the dimension value is defined by
**dPars.dPars.dimValue** independent numeric parameter, that makes it a
driving dimension. Driving and variational dimensions are further
described in Item [Driving and Variational
Dimensions](./Driving_and_Variational_Dimensions.md).

If **dPars.adjacent = false**, then the dimension value would be defined
by the formula $D = f \cdot \alpha$. The ***f*** factor in this formula
is defined by the **dPars.factor** parameter, and it permits to set the
angular dimension in other units. For example, if **dPars.factor** =
$180/\pi$, then the application can set the angular dimension in
degrees. To set the angular dimension with value
$D = f \cdot (2\pi - \alpha$), it is required to swap **l1** and **l2**.

To define the angular dimensions with adjacent angle variant shown in
Fig. 28.7.3 and Fig. 28.7.4, it is required to set the flag
**dPars.adjacent = true**. In this case, the dimension value will be
defined by formula $D = f \cdot (\pi - \alpha)$ or
$D = f \cdot (\pi + \alpha)$. The second formula is recieved by swapping
the arguments **l1** and **l2**. The ***f*** factor is also defined by
the **dPars.factor** parameter.