Linear algebra (also known as vector algebra) is a branch of mathematics that deals with vector spaces. Similar to other branches of mathematics, structure-preserving mappings, which in linear algebra are linear mappings, are of particular interest. CGRAPH allows the representation of lines, planes and spheres in 3D space and can calculate intersections.

A straight line in parametric representation has a starting point and a direction vector. Both can be entered separately for the x, y and z coordinates in the Straight lines tab. Clicking on the Add to list button then displays the straight line in the right-hand window. A check is performed to see whether the line is already part of the list. CGRAPH also recognises entries that do not have exactly the same definition (e.g. a different starting point) but still describe the same line.

A plane in parameter representation has a starting point and two independent direction vectors. They can be entered separately for the x, y and z coordinates in the Planes/Parameter Form tab. Clicking on the Add to List button then displays the plane in the right-hand window. A check is performed to see whether the plane is already part of the list. CGRAPH also recognises entries that do not have exactly the same definition (e.g. a different starting point) but still describe the same plane.

A plane in normal vector representation has a starting point and a vector that is perpendicular to the plane. Both can be entered separately for the x, y and z coordinates in the Planes/Normal Form tab. Clicking on the Add to list button then displays the plane in the right-hand window. A check is performed to see whether the plane is already part of the list. CGRAPH also recognises entries that do not have exactly the same definition (e.g. a different starting point) but still describe the same plane.

A sphere is described by the absolute value of the difference between a vector (x/y/z) and the centre of the sphere. For all (x/y/z) on the sphere, this absolute value is equal to the radius of the sphere. The radius and the vector (separately for the x, y and z coordinates) can be entered in the Spheres tab. Clicking on the Add to list button displays the sphere in the right-hand window. A check is performed to see if the sphere is already part of the list.

A circle is described by its centre point, a normal vector in the circle plane and its radius. The radius and the vectors (separately for the x, y and z coordinates) can be entered in the Circles tab. Clicking on the Add to list button then displays the circle in the right-hand window. A check is performed to see whether the circle is already part of the list.

A point is described by its position vector (x/y/z). The position vector can be entered (separately for x, y and z coordinates) in the Points tab. Clicking on the Add to list button then displays the point in the right-hand window. A check is performed to see whether the point is already part of the list.

In the graphic, points are represented as small cubes. They therefore have a certain extension beyond the actual point.

After clicking on the Create graphic button, CGRAPH switches to the Display tab and displays the graphic. However, the graphics are created in any case, as no calculation is required.

The default values can be viewed in the tree on the left-hand side.

The object list allows entire object lists to be exported and imported. In addition, individual entries can be deleted by selecting them.

The individual objects can also be displayed independently of each other. While only one base colour can be selected in the tree view, different colours or displays can be assigned to each individual object in the list. Double-clicking on the respective object opens a dialogue box for settings with which the object can be modified.

Note: if the colour of an object has been changed in this way, it can no longer be modified using the general colour selection in the tree view.

Notes on operating the graphic display

The Sections function can be used later to determine the intersection points of the objects. Unlike the other graphics, these are not determined graphically, but are actually calculated based on the values entered. The sections determined and saved there can therefore be loaded from a file and displayed again here.

Back to overview