Real space: Implicit surfaces
Surfaces can also be defined in three-dimensional space by an implicit equation of the form f(u,v,w)=0. All u/v/w values that satisfy the equation belong to the surface. CGRAPH determines such value triples iteratively within a given value range and then displays them as a point cloud.
For implicit surfaces, the availability of variable names in the function editor is limited to u, v and w. 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(u,v,w) = a, you must transform the term to f(u,v,w) - a so that the equation equals zero.
CGRAPH determines the values for u, v, and w for implicit surfaces within the specified values. Optionally, uniform values can be used for all three coordinates, starting from a centre point, if the Same value range for all coordinates field is selected.
If the Same value range for all coordinates field is not selected. individual value ranges can be specified for u, v and w, within which the implicit equation is examined.
While CGRAPH checks the result of the equation using the value ranges for u, v and w, all results that are closer to zero than the value set on the Accuracy slider are valid results. Depending on the size of the graphic and its relationship to the set value range, it may be necessary to readjust here if too few or too many results are displayed.
After clicking the Create graphic button, CGRAPH switches to the Graphics tab and shows the graphic. The calculated points are displayed as small cubes of uniform size. Due to the 3D view, cubes further back appear smaller than those in the foreground.
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 sphere around the centre 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 representation to change the display of the individual cubes. Among other things, you can also specify whether and when the cubes are to be edged.