## Geometric Object Control Points

Among the geometric types supported by the solver (see Item [Supported
Geometry Types](./Supported_Geometry_Types.md)), a **point** plays a
special role. First of all, a point is the most elementary geometric
object. Secondly, all other geometry types can be expressed using points
that are called *control* points. For example, a circle is expressed by
the \<C,R\> structure, where C is the center point, and R is a scalar
that determines the numeric radius value. Thirdly, control points can
independently take part in constraints as their arguments. For example,
they permit to define constraints both for a circle and for each its
separate point, for example, the distance from the circle center to the
line (see Fig. 1).

```{figure} ../../pictures/S.1.11.1.png
:width: 15cm
:align: center

Fig. 1
```

С is the center control point,

T is the tangency of the circle and the line,

D is the distance between the center and the line. In order to work with
control point as an independent point, you need to request its
descriptor from the geometric object using

```cpp
geom_item GCE_PointOf(GCE_system gSys, geom_item g, point_type pnt).
```

The function returns a descriptor of the control point of the geometric
object **g** that belongs to the **gSys** constraint system. The **pnt**
parameter determines what control point of the object is requested and
it takes one of the following values:

-   GCE_FIRST_END is the starting point of the curve (the first end);

-   GCE_SECOND_END is the end point of the curve (the second end);

-   GCE_CENTRE is the center of circle, ellipse, or its arc (bounded
    curve);

-   GCE_Q1 is an ellipse quadrantal point (3 hours);

-   GCE_Q2 is an ellipse quadrantal point (12 hours);

-   GCE_Q3 is an ellipse quadrantal point (6 hours);

-   GCE_Q4 is an ellipse quadrantal point (9 hours).

Control points of spline curve can be requested using

```cpp
geom_item GCE_SplinePoint(GCE_system gSys, geom_item spl, size_t pntIdx).   
```

The function returns a descriptor of the **spl** spline control point
with the **pntIdx** number, that takes values from 0 to N--1, where N is
the number of the spline control points. Fig. 2 shows a spline that has
N = 7 control points (red circles) numbered starting from 0.

```{figure} ../../pictures/S.1.11.2.png
:width: 15cm
:align: center

Fig. 2
```