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Real plane : Implicit curves
Curves can also be defined in two-dimensional space by an implicit equation of the form f(x,y)=0. All y/y values that satisfy the equation belong to the curve. CGRAPH determines such pairs iteratively within a given value range and then displays them as a sequence of individual points.
For implicit curves, the availability of variable names in the function editor is limited to x and y. The parameter param is also permitted. Enter the desired term in the input field for the equation, or select one of the existing terms by clicking on the arrow to the right of the input field. The sum of the term is assumed to be zero. If you want to use an equation of the form f(x,y) = a, you must transform the term to f(x,y) - a so that the equation equals zero.
CGRAPH determines the values for x and y for implicit curves within the area visible in the graph. By activating the Define value range checkbox, you can select your own range – the values for x and y will then only be searched for within this range.
The Accuracy slider is only active if you have set your own Value range. While CGRAPH checks the result of the equation using the value ranges for x and y, all values that are closer to zero than the accuracy set here are valid results. Depending on the size of the graph and its relationship to the set value range, it may be necessary to readjust here if too few or too many results are displayed.
If the value range corresponds to the range visible in the graph (the Set value range checkbox is deactivated), the optimal accuracy is selected automatically.
After clicking the Create graph button, CGRAPH switches to the Display tab and displays the graph.
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 equation shown here is a simple circle around the zero point with a radius of 1. The default values 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.
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.