Coordinate transformations : Transformation basis (3D)
CGRAPH enables the mapping of 3D coordinate systems using coordinate-based mapping functions. To assist users and improve the classification of the transformation, CGRAPH displays a rectangular cube grid that is transformed using the mapping functions.
Only functions containing the variables u, v, w 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 extension and position of the cube grid for the variables u, v and w, as well as the number of lines of the grid sides using the sliders.
If the Same extension for all coordinate axes field is selected, a simplified input for the extension and position of the cube grid is available. Then the centre point of the cube and the Aextension from the centre point can be specified. The result is always a cube with equal sides and the same number of lines.
The Display grid lines semi-transparent checkbox can be used to make the grid transparent. This box is automatically activated when additional function images or surface images are transformed in order to achieve a better overview.
After clicking on the Create graphic button, CGRAPH displays the graphic. However, it is also sufficient to switch to the Graphics tab.
The figure shown in the graphic transforms the Cartesian coordinate system into a polar cylindrical representation - u becomes the radius, v becomes the angle and w remains unchanged.
The Couple Original Image switch allows joint scaling and adjustment of the angles for rotation and tilt. All functions for changing the visible image area then affect both views equally.
The default values can be viewed in the tree on the left-hand side. 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 representation.