Coordinate transformations : Transformation basis (2D)
CGRAPH enables the mapping of 2D coordinate systems using coordinate-based mapping functions
Only functions containing the variables x, y and param are permitted. Enter the desired functions in the input field for the functions, or select one of the existing functions by clicking on the arrow to the right of the respective input field.
In the lower area, you can also select the value ranges of the drawn grid for the variables x and y as well as the display form of the grid. The Number of lines slider can be used to adjust the size of the grid. This slider is not available if the Align transformation grid to background grid field is activated. The following images show the different representations of the transformation grid.
The display adjusted to the background grid is easier to see, but it changes when the image section is changed and the background grid is recalculated. The non-adjusted representation retains its shape at every zoom level and for every image section.
The grid can be made transparent using the Display grid lines semi-transparent checkbox. This is particularly useful if function images are also transformed.
After clicking the Create graphic button, CGRAPH displays the graphic. However, it is also sufficient to switch to the Graphics tab.
The figure shown in both graphics transforms the Cartesian coordinate system into a polar representation - x becomes the radius and y becomes the angle.
In the right-hand graphics window, a red dot (red arrow) indicates the coordinate occupied by the mouse pointer (green arrow) in the left-hand graphics window. In this way, individual values and their transformation can be determined.
The default values can be viewed in the tree on the left. Clicking on the (optional) parameter also activates the parameter's adjustability at the bottom. An explanation of this function can be found in the notes on changing the parameter in the graphic display.
The values can be changed retrospectively. The graphic is adjusted automatically, at the latest when the Create graphic button is clicked. Clicking on the coloured symbol for the graph allows you to quickly hide the graphic from the display. Double-clicking on the text allows you to adjust the graphical display.