Real space: 3D curves
Analogous to plane curves in 2D space, CGRAPH can also display curves in 3D space, in which the x, y and z coordinates are functions of a parameter. With this definition, any line structure can be drawn in three-dimensional space.
For spatial curves, the availability of variable names in the function editor is limited to x and t, which can be used as synonyms for each other. The variable x or t is therefore no longer identical to the abscissa coordinate x – we therefore recommend always using the variable t. Only functions that contain the variables x, t and param are therefore permitted. Enter the desired function in the input field for the function, or select one of the existing functions by clicking on the arrow to the right of the input field.
If the function is only available as an implicit equation of the form f(x,y,z) = 0, the graph type Implicit surfaces can be used instead, which can also display space curves.
CGRAPH displays space curves within the range specified for the variable.
After clicking on the Create graph button, CGRAPH switches to the Graphics 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.
Double-clicking on the text next to the coloured symbol allows you to set the colour and appearance of the graph. Clicking on the coloured symbol itself hides or shows the graph.
The curve shown here is a circle in space. 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.