Create an arc

Create a parametric line as an arch at a point of intersection between two parametric lines (or one parametric point) as a center point, a viewing angle determined via the parametric line and a radius that is to be defined.

When defining the point of intersection of two parametric lines as the center of the arc, there are two possibilities and different procedures depending on this. The third option for defining the center of the arc at a parametric point has certain restrictions. The three options are described in principle below. For detailed step-by-step instructions, see below.

Note: For the definition of boundary lines along arcs, see the corresponding notes in To create boundary lines via points/lines.

Option 1: Selection of both parametric lines, the point of intersection of which is the center of the circle

(This is the recommended and simplest procedure in general cases)

In this case, the parametric line selected first defines the start line (initial radius of the arc) and the second parametric line that was selected defines the end line (end radius of the arc). Moving the mouse in a corresponding arc (between selecting the first and second parametric line) defines the sense of rotation of the arc from the start line to the end line (clockwise or anti-clockwise) and therefore also the opening angle of the arc. (If automatic detection of the sense of rotation is not as desired, this can be reversed in the next input step or at any time later via the properties window). The size of the radius is initially defined by the position of the click on the second parametric line, then can be defined precisely if desired. For the creation of semi-circles and full circles, corresponding options are available in the properties window, whereby in these cases the circular arc always runs from the start line to the start line, i.e. in the case of semi-circles from one side of the start line to the opposite side of the start line (180 degrees in relation to the point of intersection) and in the case of full circles from one side of the start line to the same side of the start line (360 degrees) - for more details, see the explanations on the start and end line side below.

Option 2: Defining direct selection of the point of intersection of two parametric lines

With this procedure, the center of the arc is defined directly via the point of intersection of two parametric lines. In this case, the start line and the end line as well as the sense of rotation and the radius are automatically defined for the time being. In the next input step, the individual parameters can be subsequently adjusted using the corresponding options in the "Radius", "Sense of rotation" and "Side of the start/end line" properties window. See below for details. For the creation of semi-circles and full circles, see option 1 above.

Option 3: Selecting a parametric point as the center of the arc.

A parametric point has two "imaginary" parametric lines in the background that run parallel to the two main coordinate axes. These represent the start and end lines of the arc. Consequently, only full circles, quarter or three-quarter circles and semi-circles whose start and end radii correspond to the orthogonal start and end lines can be mapped using this method. For semicircles, there is the additional restriction that they can only use the parametric line parallel to the z-axis as the start and end line. (i.e. they can only be drawn "up" or "down", but not "left" and "right").

Option 1

How to create an arc via two parametric lines (point of intersection = center point)

1. Click Arc.
2. Click the first parametric line, which sets out the start line (start radius) of the arc.
3. Click the second parametric line defining the end line (end radius) of the arc, where you describe the desired arc when moving from the first to the second parametric line so as to define its sense of rotation at this point.

   Note: The best way to automatically recognize the sense of rotation is to pay particular attention to the curvature when describing the arc with the mouse and to ensure that it is not too straight. If automatic detection does not work as desired, the direction of the arc can be corrected very easily in the next step. Furthermore, the position of the click on the second parametric line defines the size of the radius, which can also be optionally defined numerically or geometrically in the next step.

4. Move the mouse slightly and in the input field that opened, enter the desired radius of the arc. Alternatively, you can set the position directly with the mouse cursor. In both cases, confirm the entry with the Enter key or the left mouse button. One option is to define the radius via Click point of intersection (Option Radius via point of intersection in the properties window) (For details see Radius via the point of intersection option below)).

   Note: The Sense of rotation and Side of start/end line (see below for further explanations) options in the Properties window can be used to amend the sense of rotation or the sides of the parametric lines for the start or end line to define the desired arc (see below for further explanations). The sense of rotation can also be changed directly by moving the mouse to the desired opposite area.

   Note: To define semi-circles or full circles, select the corresponding option in the properties window. For more information, see the description of option 1 above.

5. Create further arcs directly (back to point 2 of one of the three options) or exit the function with ESC.

Option 2

To create an arc directly over the point of intersection of two parametric Lines

1. Click Arc.
2. Click the point of intersection of two parametric lines to set out the center point of the arc.

   The arc is represented in one of the possibilities resulting from the two straight lines (i.e. the sense of circumference and the start and end lines are determined "randomly").

3. Use the Sense of rotation and Side of start/end line options in the Properties window to adjust the sense of rotation or the sides of the parametric lines for the start or end line to define the desired arc (see below for further explanations).

   Use the Radius or Radius (by point of intersection) option in the properties window to adjust the radius of the arc (for details on this and on defining half or full circles, see option 1, step 4).

4. Create further arcs directly (back to point 2 of one of the three options) or exit the function with ESC.

Option 3

How to create an arc over a parametric point (= center point)

1. Click Arc.
2. Click a parametric point to set out the center point of the arc.

   An arc is created as an example at the selected point of intersection.

3. Use the options Arc (= in this case (three-)quarter circle), Semicircle, Full circle in the properties window to define the type of circular arc (for more information, see the description of option 3 above).
4. Use the Sense of rotation and Side of start/end line in the Properties window to adjust the sense of rotation or the sides of the parametric lines for the start or end line to define the desired arc (see below for further explanations) and the Radius option to adjust the size of the radius of the arc (See option 1, step 4 for details), where the Radius via point of intersection option can be used for any point of intersection between two parametric lines to define the radius.
5. Create further arcs directly (back to point 2 of one of the three options) or exit the function with ESC.

Explanation of the options in the properties window during input

Mode

Radius

Radius of the arc via numerical input or direct interactive definition with the mouse cursor

Radius (via the point of intersection)

Radius of the arc via geometric definition through selection of a point of intersection

Note: In principle, any point of intersection of two parametric lines can be used to define the length of the radius. The distance from the center of the arc to the selected point of intersection is always measured and used as the value for the radius. The arc itself remains defined in the area between the start and end line.

In practical application, option 3 allows the arc to run from the defined center point through a specific point, which can be at any position. With options 1 and 2, these points of intersection usually lie on the start/end line in practice, for example to define an arc starting from a specific point and thus to easily create two consecutive arcs with different radii at one point without having to determine or enter the second radius.

Sense of rotation

Direction of the arc, which always runs from the start line to the end line (clockwise or anti-clockwise)

The sense of rotation can be changed back and forth during input after selecting the option by simply clicking (in any area). This can be done afterwards when editing the arc in the properties window using the two option buttons Clockwise / Anti-clockwise.

The sense of rotation is indicated by a black arrow on the start line at the beginning of the arc (tangential).

Side of the start/end line

Change of the side of the start line or end line of the arc relative to its origin, i.e. point of intersection of the parametric lines (= center of the arc)

Relative to their origin, both parametric lines have a positive and a negative side. After selecting this option, the side for the start line or end line can be changed by simply clicking on a point on the opposite side of the corresponding parametric line. This can be changed later when editing the arc in the properties window using the Positive/Negative buttons for the start and end lines.

The direction of the positive sides of the two parametric lines is indicated by two black arrows at their point of intersection.

By adjusting the options for the sense of rotation and the circle sector to that effect, the arc can be created in any sections between the two parametric lines, but only from the start line (side can be changed) to the end line (side can be changed) in a specific (changeable) sense of rotation.

General

Arc shape

Shape of the arc to be defined (arc, semicircle, full circle)

For details, see the description of option 1 above.

After creating an arc, the following parameters are available for editing or as information in the properties window:

Properties window

General

Name

Editable name of the parametric line of the arc

Type [informative]

Type of parametric line

Dependencies

Center point [informative]

Center point of the arc depending on the point of intersection of two parametric lines or as parametric Dot

In the first case, the first parametric line is also the start line and the second parametric line represents the end line of the arc.

Geometric parameter

Sense of rotation

Select the sense of rotation of the arc from the start line to the end line (clockwise or anti-clockwise) - see above for details.

Radius

Input of the radius of the arc with optional assignment of a variable

Side of the start line / end line

Select the positive or negative side of the parametric line for definition of the start or end line - see above for details.

Arc shape

Select the shape of the arc (circular arc / semi-circle / full circle)

Calculated

Calculated values of the arc

All coordinates and angles in relation to the cross-sectional coordinate system (angle starting at the z-axis anti-clockwise)

Center (Z,Y)

Z- and Y-coordinates of the center of the arc

Starting point (Z,Y)

Z and Y coordinates of the arc’s starting point (on the start line)

End point (Z,Y)

Z and Y coordinates of the arc’s starting point (on the end line)

Angle of the start tangent

Angle of the tangent at the starting point of the arc

Angle of the end tangent

Angle of the tangent at the end point of the arc

Starting angle of the sector

Angle of the radius at the starting point of the arc

End angle of the sector

Angle of the radius at the end point of the arc

Angle of the sector (amount)

Amount of the center point angle of the circular sector described by the arc (amount of difference between the end angle and the start angle)