Coordinate transformations: Function mappings (2D)
In addition to the graphical representation of functions or plane curves, their graphs can also be coordinate-transformed. CGRAPH displays the Cartesian representation in the transformed coordinate system.
In addition to the transformation functions for the coordinate system, the mapping functions for the graphics must also be selected. For better differentiation, only functions containing the variables t 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. A checkbox allows the abbreviated entry of only one function if no curve x(t) and y(t) is to be displayed, but only one function y = f(t). In addition, the value range for the variable t can be selected.
After clicking on the Create graph button, CGRAPH displays the graph. However, it is also sufficient to switch to the Graphics tab.
In the example, a quadratic parabola is transformed into a polar coordinate system. The grid display of the transformation basis is set to transparent for a better overview.
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 of the graphics window. 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.