Table of Contents
Complex plane : Line segments
In CGRAPH, line segments, i.e. lines with defined start and end points, can be mapped onto the complex plane. Either the end point or the length and angle of the line segment can be specified.
The function is defined uniformly above the default values for all types of area mappings, because common mappings only make sense if the same function is used. The variable names z and param (as complex numbers) as well as x and y (as the real and imaginary parts of the variable z) are permitted.
CGRAPH provides several input options:
Input via default values
Line segments can be defined in the area on the left-hand side.
The fields Starting point and End point are complex numbers. When they are entered, the values in the Angle and Length fields change accordingly. It is also possible to enter a line segment using its Angle and Length instead of its endpoint. CGRAPH then automatically calculates the endpoint.
The angle is entered in degrees. Formulas can also be entered. The angle is measured counterclockwise mathematically positive from the positive x-axis.
Only real, positive values are permitted for the length. If formulas are used, they must return positive values. Any imaginary parts are ignored.
The Add to list button transfers the entries to the List of line segments figures.
Graphical input
By switching the tab in the area on the right to Graphical input, it is possible to create line segments graphically. A graphics window is displayed on the right-hand side for this purpose. The first click in the graphics window defines the starting point. A blue line then appears, which can be used to define the end point with the next click. The entry is then transferred to the List of straight lines.
If you press the Shift key while selecting the end point, the angle jumps in increments of 15 degrees. This makes it easier to enter ‘round’ values.
Editing line segments
Once an entry in the list of line segments is selected, it can be edited.
The default values of the selected entry in the list are displayed on the left-hand side and can now be changed. Once you have finished making changes, click on Change values. If you want to leave the list entry unchanged, click on Cancel change.
An entry selected in the list can be removed by clicking on the Delete entry button.
The Export… and Load from file buttons can be used to create and reload semicolon-separated CSV files. The format for this is start point;end point
Multiple straight lines can be added in one go using the Set of straight lines button. They can then also be edited.
After clicking on the Create graphic button, CGRAPH switches to the Graphics tab and shows the graphic - the original on the left and the image above the function on the right.
The default values can be viewed in the tree on the left. If the function contains a parameter, it is displayed as a red square in the original image. Double-clicking on this square allows you to change the parameter graphically by simply moving the mouse. Clicking on the original image deactivates the parameter change. If you press the Shift key at the same time, the original parameter is restored. A more detailed explanation of this function can be found in the notes on changing a complex parameter in the graphic display.
The specified straight lines can be changed retrospectively – clicking on one of the values switches CGRAPH back to the tab with the default values. The graphic is adjusted as soon as the Create graphic button is clicked.