https://cgraph.de/ 2026-04-16T14:42:31+00:00 https://cgraph.de/ https://cgraph.de/lib/exe/fetch.php?media=logo.png text/html 2026-03-08T12:51:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:2d_graphics&rev=1772974317&do=diff Settings: 2D graphics Here you can define the display of 2D graphics. In the Graphic display section, you can decide whether axes, background grids and labels are visible. You can also specify whether the calculated support values of the graphic should be connected by lines. For each graphic, these settings can be made again text/html 2026-03-08T12:53:40+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:3d_graphics&rev=1772974420&do=diff Settings: 3D graphics The initial parameters for 3D graphics are defined here. Sliders allow you to adjust the rotation around the z-axis and the inclination of the z-axis (tilt). This ensures that the z-axis always remains aligned upwards. The 3D graphics allow for further text/html 2026-03-06T09:38:05+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:abbildungenimraum&rev=1772789885&do=diff Real space: mappings in 3D space This graphic offers the most comprehensive mapping options in real 3D space. For each of the coordinate axes x, y and z, a separate mapping function can be defined that depends on three variables u, v and w. This allows, for example, plane families or overlapping three-dimensional figures to be generated. text/html 2026-03-03T17:27:14+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:about&rev=1772558834&do=diff About CGRAPH CGRAPH originated in 1989 from a small programme originally written for an hp-28c pocket calculator. With the help of this programme, complex calculations could be performed on the small LCD screen of the hp28c – at the time, it served as a (permitted) means of checking answers in a Higher Mathematics III exam for electrical engineering students. text/html 2026-03-03T17:21:48+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:advanced_options&rev=1772558508&do=diff Settings: Advanced Options CGRAPH offers a few additional settings that are intended for testing purposes and may change from version to version. We recommend that you do not change these options. Changes made here are not saved when you exit the programme. text/html 2026-03-08T09:05:39+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:area_mappings&rev=1772960739&do=diff Complex layer: Area mappings After mapping edges, individual parts of the area can be marked in colour to enable a correlation between the graphic and the original image. To do this, CGRAPH maps individual points within the area, from which the area is filled. Such an assignment does not have to be unique; it depends on the function used. text/html 2026-03-03T11:37:15+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:axes_parameters_2d&rev=1772537835&do=diff Axis parameters (2D) Here you can define the display and labelling of the axes. The dialogue box opens when you double-click on the text of the main node of the Axes. In the Display area, you can set which parts of the axes should be visible. In addition, there are options for setting the text/html 2026-03-03T11:35:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:axes2d&rev=1772537741&do=diff Coordinate system (2D) The 2D coordinate system used in the illustrations consists of several elements that can be displayed and modified in the tree view. Element Description Axes Main node in the tree - double-clicking opens the settings for the text/html 2026-03-24T09:42:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:axes3d&rev=1774345345&do=diff Coordinate system (3D) The 3D coordinate system used in the illustrations consists of several elements that can be displayed and modified in the tree view. Element Description Axes Main node in the tree - double-clicking opens the settings for the text/html 2026-03-24T09:38:05+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:axisparameters3d&rev=1774345085&do=diff Axis parameters (3D) Here you can define the display and labelling of the axes. The dialogue box opens when you double-click on the text of the main node of the Axes. In the Graphics section, you can set which parts of the axes should be visible: grid, markers, axes and labelling. Visibility can also be switched on and off by clicking on the respective coloured symbol. text/html 2026-03-03T11:10:24+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:basics&rev=1772536224&do=diff Basics In this section, you will find all the information you need to get started with CGRAPH Interface layout Here you will find everything you need to know about working with CGRAPH – a description of the interface, the menu, the function bar and the essential functions for modifying a 2D and 3D graphic representation text/html 2026-03-03T17:00:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:bedienunggrafik3dduo&rev=1772557201&do=diff Functions of the graphic display with two windows (3D) CGRAPH displays 3D objects in a view where the origin (0/0/0) always remains in the centre of the image. The origin therefore always remains part of the image; for example, you cannot zoom out beyond it to get to ‘the other side’ of the image. In addition, the z-axis is always oriented upwards in the default setting for a better overview. The text/html 2026-03-03T11:51:58+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:bedienungparameterc&rev=1772538718&do=diff Graphical modification of complex parameters CGRAPH offers an interactive method for modifying a complex parameter that has been entered. Each modification is immediately reflected graphically. To change a parameter in the graphic, proceed as follows: text/html 2026-03-03T16:32:16+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:bedienungparameterm&rev=1772555536&do=diff Graphical modification of the starting value or parameter for fractals CGRAPH offers an interactive method for modifying an entered starting point (Mandelbrot set) or parameter (Julia set). Each modification is immediately reflected graphically. For a better overview, the fractal was created here in monochrome view. text/html 2026-03-03T15:22:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:bedienungparameterr&rev=1772551321&do=diff Changing real parameters CGRAPH offers an interactive method for changing an entered parameter. Each change is immediately reflected in the graph. To change a parameter in the graphic, proceed as follows: * Click on the desired parameter in the tree view (red arrow). A field will then appear below the graphic, which can be used to change the parameter. text/html 2026-03-23T18:34:56+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:beta-versions&rev=1774290896&do=diff Beta versions The links below contain builds from 23 March 2026, 18:30. Version for macOS ARM Version for macOS Intel Version for Windows 11 Installation: Simply unzip. The Windows version should then be copied to \Program Files\x64. The macOS programmes belong in the Applications folder, but will also run from other locations. text/html 2026-03-24T10:28:42+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:cgraph&rev=1774348122&do=diff CGRAPH - Mathematical Graphics CGRAPH is a universal tool for the graphical representation of mathematical equations. It offers a complete library of functions defined in complex space, which can be used to execute important drawing routines in the realm of real or complex numbers. The range of graphics types offered extends from the representation of functions in two- or three-dimensional space, interpolation of unknown functions using input values, curve discussion, the mapping of simply conn… text/html 2026-03-06T16:12:00+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:circle_sections&rev=1772813520&do=diff Complex plane : Circle sections In CGRAPH, a circle section is defined as a chord of a circle, whereby the starting and ending angles as well as the centre point and radius of the circle can be freely adjusted. The function is defined uniformly above the default values for all types of area mappings, as common mappings only make sense if the same function is used. The variable names z and param (as complex numbers) as well as x and y (as the real and imaginary parts of the variable z) are perm… text/html 2026-03-03T15:50:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:color3d&rev=1772553055&do=diff Colour and transparency settings For some elements, only the colour can be selected. To do this, double-click on the text next to the coloured symbol for the graph or axes in the tree view. In addition to the colour, you can also set the transparency text/html 2026-03-03T11:38:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:colour_2d&rev=1772537910&do=diff Colour and pattern settings For some elements, only the colour can be selected. To do this, double-click on the text next to the coloured symbol for the graph or axes in the tree view. In addition to the colour, patterns can also be selected. Depending on the graphic, however, these may look different in the display than in the selection box in this dialogue box. text/html 2026-03-03T16:27:51+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:complex_functions&rev=1772555271&do=diff System Functions : Complex Functions Unlike trajecvtory Curves, this graph considers the course of complex functions on real and imaginary axes. Unlike other graphs, the settings and graph are located in the same window. Only functions containing the variables z and param are permitted. Alternatively, the variables x and y can be used as shorthand for the real and imaginary parts. Enter the desired function in the input field for the function, or select one of the existing functions by cl… text/html 2026-03-03T11:54:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:complex_plane&rev=1772538897&do=diff Complex plane This section contains graphics that can be used to map areas and regions in complex space. Both the original image (i.e. the direct representation of the boundaries without functional influence) and the corresponding image (i.e. the values of the elements calculated using the function f(z)) are displayed in two separate graphics windows. text/html 2026-03-03T12:35:47+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:complex_space&rev=1772541347&do=diff Settings: Complex Space Here you can set the initial size of the complex graphics window. Here, you can use the mouse to zoom in or out, or use the three buttons above the graphics window to set the size of the initial section that CGRAPH should display in complex 2D graphics. This section does not have to be centred on the centre point. text/html 2026-03-03T16:05:39+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:complexspace3d&rev=1772553939&do=diff Complex space This section contains graphics that include a z-dimension above the complex plane to enable three-dimensional representations of complex functions. SymbolGraphicDescriptionSurfaces in complex spaceRepresents surface curves of the real part, the imaginary part or the absolute value of complex functions in the z-plane. text/html 2026-03-03T16:29:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:convergences&rev=1772555374&do=diff Convergences In contrast to the set of real numbers, the complex plane often exhibits unexpected behaviour, for example when applying integral and differential calculus to complex functions. Another example is iterations. Here, it becomes apparent that – in contrast to real space – iterations for points that are close together in the complex plane can lead to completely different results. If we plot the divergence rate, i.e. the number of iterations until a maximum difference from the previous… text/html 2026-03-03T17:11:14+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:coordinate_transformations&rev=1772557874&do=diff Coordinate transformations This section contains graphics in which the 2D or 3D coordinate system is first transformed using mapping functions and then calculated function or curve curves can also be transformed into the new coordinate system. Symbol text/html 2026-03-03T11:50:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:createcirclecluster&rev=1772538657&do=diff Circle segments: Add circle family If several circles are to be plotted simultaneously, the corresponding values can be entered more easily by defining circle families. Circle families share the same centre point and have evenly increasing radii. Therefore, the text/html 2026-03-05T09:16:02+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:data_tree&rev=1772702162&do=diff Data tree The data tree displays all relevant information about the graphics created. The information is arranged chronologically according to when the graphics were created. Axes This area displays all elements that serve as orientation within the graphic representation. text/html 2026-03-03T17:17:39+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:default_values&rev=1772558259&do=diff Settings: Default values The input fields for real and complex numbers offer an additional feature besides direct input. Right-clicking in an input field opens a pop-up menu from which you can select predefined default values for easy entry of frequently used values such as pi. These values can be set here. text/html 2026-03-11T12:09:56+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:export&rev=1773230996&do=diff Export CGRAPH supports two types of export: * Data can be saved as a CSV file and is then available outside the programme for further processing. Within CGRAPH, all CSV files created can also be re-imported into Linear Algebra for 2D and 3D. * Graphics can be saved in various formats. text/html 2026-03-06T16:11:00+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:exportformat&rev=1772813460&do=diff Export formats CGRAPH allows calculated values or data to be exported at various points. The format used for this is a semicolon-separated text format with the extension CSV, which is understood by spreadsheet programmes such as Microsoft Excel. The format has multiple columns. The first column always contains an identifier to describe the type of the object, while the other columns contain the object's data, such as coordinates in the x, y and z directions and, in the case of circles and sphe… text/html 2026-03-03T16:23:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:fft&rev=1772555018&do=diff System Functions : One-dimensional FFT In CGRAPH, the Fourier transforms of any functions can be displayed. Any intervals of the functions can be transformed. The transformation is performed in a complex manner; the real part of the Fourier spectrum is always displayed in an interval from -* to +*. Since the transformation only yields discrete values, no continuous curve is produced. Only the calculated support values are displayed. text/html 2026-03-24T10:23:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:flaechenimraum&rev=1774347808&do=diff Real space: 3D Surfaces In addition to 3D Curves, CGRAPH can also display surfaces in three-dimensional space where the x, y and z coordinates are functions of two variables. With this definition, any surfaces or closed objects can be drawn in three-dimensional space. text/html 2026-03-08T09:38:42+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:flaechenkomplexerraum&rev=1772962722&do=diff Complex space: Areas in complex space This graphic allows the real part, the imaginary part or the absolute value of complex functions to be displayed in three dimensions above the complex plane. This makes it easy to identify the poles or zero points of a function. text/html 2026-03-03T11:39:56+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:font&rev=1772537996&do=diff Font and colour settings The font and colour can be adjusted for the axis labels. In addition to the colour, you can also select the font and font size. The font can also be displayed in bold, italics or underlined. The example shows the approximate appearance that can be expected later in the graphical representation. In 3D representations, the font size shown in the graphic also depends on how close the text is to the window section. Texts that are further away are displayed smaller. text/html 2026-03-08T10:40:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:frequency_response&rev=1772966428&do=diff System functions: Frequency response This summarises the amplitude and phase response as well as the attenuation curve. The graphs are plotted on a logarithmic frequency axis. Unlike other graphs, the settings and graph are located in the same window. The lower section contains three graphs: the amplitude response, the attenuation and the phase response. text/html 2026-03-08T11:04:44+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:function_convergence&rev=1772967884&do=diff Convergences: Function convergence In CGRAPH, complex functions can be examined for convergence or divergence through iteration. A graph shows the course of the iteration. After each iteration, the programme checks whether the absolute value of the function is moving further away from or closer to the starting point. Each function value is plotted in the graph. text/html 2026-03-05T16:19:51+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:function_families&rev=1772727591&do=diff Real plane : Function families A function can be superimposed multiple times by varying a parameter using the Functions graphic. This is easier with function sets, which vary the parameter with a single call and can thus display several function curves at once. text/html 2026-03-03T17:24:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:function_syntax&rev=1772558672&do=diff Definition and notation of functions CGRAPH is a tool for creating graphical representations. In CGRAPH, functions can therefore be defined simply by typing them in on the keyboard – without the considerable effort that learning a programming language, for example, would entail. In order for CGRAPH to recognise the functions entered as such, certain conditions must be met. text/html 2026-03-03T15:10:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:function_terms&rev=1772550631&do=diff Settings: Function terms Functions are stored separately for each graphic in CGRAPH. Once you have entered functions, you can select them by clicking on the arrow to the right of the respective input field for functions. This tab in the settings allows you to remove unnecessary entries from the list of stored functions. text/html 2026-03-08T12:03:48+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:functionmappings2d&rev=1772971428&do=diff 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 d… text/html 2026-03-24T10:49:44+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:functions&rev=1774349384&do=diff Real plane : Functions The representation of functions in two-dimensional space is the oldest area within the mathematical application of computer graphics. CGRAPH provides the routines required for curve discussion. By definition, functions in two-dimensional space (R²) can only depend on one variable. Therefore, only functions containing the variables x and param are permitted. Enter the desired function in the input field for the function, or select one of the existing functions by clicki… text/html 2026-03-03T17:10:52+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:functionsmappings3d&rev=1772557852&do=diff Coordinate transformations : Function mappings (3D) In addition to the graphical representation of spatial curves, their graphs can also be coordinate-transformed. CGRAPH maps the Cartesian representation in the transformed 3D coordinate system. To do this, in addition to the transformation functions for the coordinate system, the mapping functions for the graphic must be selected. For better differentiation, only functions that contain the variables t and param are permitted. Enter the des… text/html 2026-03-24T10:39:44+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:general&rev=1774348784&do=diff Settings: General Here you will find settings for the general operating behaviour of CGRAPH. In the Save entered values section, you can specify whether these values should be saved once when exiting or every time graphics are created. Every change to the input values for the graphics is saved. If both switches are deactivated, CGRAPH permanently retains the numerical values that are loaded at start-up. text/html 2026-03-03T17:09:39+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:graphic_types&rev=1772557779&do=diff Graphic types in CGRAPH CGRAPH categorises graphics according to how they can be used together. There are eight types: Graphic type Description Real plane A 2D space in which functions, plane curves, Polar curves, Function Families and linear algebra can be represented. It is also possible to calculate intersection points and represent text/html 2026-03-03T17:25:20+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:hint&rev=1772558720&do=diff Floating windows (hints) Some input fields, buttons, or lists provide a small hint that is displayed when you hover the mouse pointer over them. These hints may include input formats, permitted variable names, or information about advanced functions. text/html 2026-03-05T16:37:56+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:implicitcurves&rev=1772728676&do=diff 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. text/html 2026-03-06T09:41:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:impliziteflaechen&rev=1772790097&do=diff 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. text/html 2026-03-03T17:31:24+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:impressum&rev=1772559084&do=diff Impressum Allgemeines Betreiber dieser Seite und verantwortlich für die Inhalte ist: Dipl-Ing. Frank Brennecke, Großbeerenstraße 24, 10963 Berlin, E-Mail: frank — at — brennecke — punkt— org Dies ist eine rein private Homepage, die keinerlei kommerzielle oder geschäftliche Interessen verfolgt. text/html 2026-03-03T17:31:12+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:imprint&rev=1772559072&do=diff Imprint General information The operator of this website and responsible for its content is: Dipl-Ing. Frank Brennecke, Großbeerenstraße 24, 10963 Berlin, email: frank — at — brennecke — dot— org This is a purely private website that does not pursue any commercial or business interests. text/html 2026-03-05T11:53:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:interface_layout&rev=1772711611&do=diff Interface Structure Start View When CGRAPH is launched, it displays the following image. On the left-hand side is the function bar, which can be used to create graphics. The menu can also be used for this purpose. In Windows, it is located at the top of the CGRAPH window; in macOS, it is displayed at the top of the screen. text/html 2026-03-08T11:50:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:interpolations&rev=1772970630&do=diff Interpolations CGRAPH can create interpolated graphs for a list of values and, in classic cases, also determine the underlying function. Value pairs can be entered as values or graphically, or they can be imported as a CSV file and also saved. Types of interpolation text/html 2026-03-05T16:29:21+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:intersections&rev=1772728161&do=diff Real plane : Intersections CGRAPH can graphically determine intersections of functions and curves. To use this function, at least two graphs must first be displayed in the view. All previously created graphs are displayed in the tree on the left – for functions, this also includes their derivatives and integrals. To select a graph, click on the checkbox next to it. Only one graph can be selected as a reference for intersections. text/html 2026-03-03T16:33:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:julia_sets&rev=1772555618&do=diff Convergences: Julia sets Julia sets belong to the group of fractals. This requires a function zn+1 = f(zn) that contains a parameter. After each iteration, a check is performed to see whether the result lies outside the specified decision limit. If this is the case, the result is plotted at the position of the initial value z text/html 2026-03-03T15:32:21+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:linearalgebra2d&rev=1772551941&do=diff Real plane : Linear algebra 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 straight lines and circles in 2D space and can calculate intersections. text/html 2026-03-06T09:31:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:linearealgebra3d&rev=1772789485&do=diff Real space : Linear algebra 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. text/html 2026-03-08T10:52:11+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:mandelbrot_sets&rev=1772967131&do=diff Convergences: Mandelbrot sets Mandelbrot sets belong to the group of fractals. This requires a function zn+1 = f(zn) that contains a parameter. After each iteration, a check is performed to see whether the result lies outside the specified decision limit. If this is the case, the result is plotted at the location of the initial value z text/html 2026-03-08T10:30:18+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:mappingscomplexspace&rev=1772965818&do=diff Complex space: Mappings in complex space This graphic is the most versatile and comprehensive mapping option in GGRAPH. For each of the coordinate axes x, y and z, a separate complex mapping function can be defined, which depends on three equally complex variables u, v and w. For each of the functions, it can be specified whether their real part, imaginary part or magnitude is used as a reference for the coordinate axis. This allows even the most complex mappings and three-dimensional figures t… text/html 2026-03-03T16:40:45+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:mathematical_basics&rev=1772556045&do=diff Mathematical Basics This section explains the mathematical routines used in CGRAPH and the principles underlying them. It also contains a brief introduction to the theory of complex numbers and explains the complex functions that form the basis of all calculations in CGRAPH. text/html 2026-03-03T11:30:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:mathematics&rev=1772537433&do=diff Settings: Mathematics Here you will find settings for how CGRAPH handles mathematical specifications and conditions. In the Imaginary Unit section, you can specify whether CGRAPH should use the mathematical i or the electrical j to represent imaginary numbers. Both options are always permitted for input. text/html 2026-03-24T10:34:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:menu&rev=1774348441&do=diff Menu In CGRAPH, all functions can also be accessed via the menu. In Windows, the menu is located at the top of the programme window; in macOS, it is located at the top of the screen. The menus for graphic functions also display the corresponding icon to the left of the menu text. text/html 2026-03-03T17:16:56+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:number_formats_and_value_ranges&rev=1772558216&do=diff Number formats and value ranges CGRAPH expects numerical values to be entered in many input fields. The formats and possible value ranges for such entries are explained below. Default values in input fields CGRAPH enters a default value in each input field. When you first start the programme, these are predefined values, but any changes to these values are saved as soon as a graph is created. The last values entered are then displayed the next time the graph is called up. text/html 2026-03-24T10:15:11+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:operating_the_graphics&rev=1774347311&do=diff Functions of the graphic display (2D) The display of graphics offers several options for modification Element Description Tree view (red arrow) In this view, to the left of the actual graphic display, you will find all the important parameters for the individual graphics as well as settings for text/html 2026-03-24T10:08:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:operatinggraphics3d&rev=1774346910&do=diff Graphics display functions (3D) CGRAPH displays 3D objects in a view where the origin (0/0/0) always remains in the centre of the image. The origin therefore always remains part of the image; for example, you cannot zoom out beyond it to get to ‘the other side’ of the image. In addition, the z-axis is always oriented upwards in the default setting for a better overview. The text/html 2026-03-03T15:05:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:operationparameters&rev=1772550357&do=diff Changing real parameters CGRAPH offers an interactive method for changing an entered parameter. Each change is immediately reflected in the graph. To change a parameter in the graphic, proceed as follows: * Click on the desired parameter in the tree view (red arrow). A field will then appear below the graphic, which can be used to change the parameter. text/html 2026-03-08T10:33:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:ortskurve&rev=1772966009&do=diff System functions : Nyquist Plot The Nyquist Plot shows the course of the system function on the imaginary axis. Its course provides information about the stability behaviour of the system. Unlike other graphics, the settings and graphics are located in the same window. text/html 2026-03-05T16:16:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:planecurves&rev=1772727398&do=diff Real plane: Plane curves In addition to functions of the type y = f(x), which assign exactly one abscissa value to each ordinate value, CGRAPH can also display curves in which both the x and y coordinates are functions of a parameter. With this definition, any shape can be drawn in two-dimensional space. text/html 2026-03-03T15:25:00+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:polarkurven&rev=1772551500&do=diff Real plane: Polar curves Polar curves are a special class of plane curves. While in plane curves the x- and y-axes are functions of a parameter, polar curves represent the dependence of the radius curve on the corresponding angle or vice versa. Such curves are often needed when representing directional characteristics. text/html 2026-03-08T08:57:18+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:polylines&rev=1772960238&do=diff Complex plane: polylines CGRAPH offers a description using a polyline to represent more complicated borders. This also allows extensive images to be displayed. The line can also be a closed border, in which case it is referred to as a polygon. The function is defined uniformly here above the default values for all types of area images, because common images only make sense if the same function is used. The variable names z and param (as complex numbers) as well as x and y (as the real and imag… text/html 2026-03-08T12:55:10+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:printing_and_exporting&rev=1772974510&do=diff Settings: Printing and Export Graphics can be printed or saved as high-resolution bitmaps. These settings define the basic parameters. In the Settings for printout section, you can specify whether the printout should show exactly what is visible in the graphics window – in most cases, this will not make optimal use of the paper format because the graphics window has a different page-to-height ratio. If this field is not selected, the printout will show more than is visible in the graphics wi… text/html 2026-03-03T17:22:50+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:printing&rev=1772558570&do=diff Printing CGRAPH uses the standard print settings of the operating system and printer for printouts. Therefore, the print dialogues and the settings available in them vary depending on the printer and operating system. A preview is not available in CGRAPH, but both Windows and macOS offer the option of redirecting printouts to a PDF document, thus enabling a preview. text/html 2026-03-23T11:01:04+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:quickstart&rev=1774263664&do=diff Quick Start CGRAPH allows you to create mathematical graphs quickly and easily. All graphing functions are structured in the same way. The following example shows how to plot a sine function in CGRAPH. Selecting the Graph On the left-hand side is a toolbar from which all graphing functions can be accessed. If you hover the mouse pointer over one of the buttons, a text/html 2026-03-03T11:33:19+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:real_space&rev=1772537599&do=diff Settings: Real Space Here you can set the initial size of the real graphics window. Here, you can use the mouse to zoom in or out, or use the three buttons above the graphics window to set the size of the initial section that CGRAPH should display in real 2D graphics. This section does not have to be centred. text/html 2026-03-03T15:35:45+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:realplane&rev=1772552145&do=diff Real plane This section contains graphics that can be plotted in a 2D Cartesian coordinate system. SymbolGraphicDescriptionFunctionsRepresents functions of the type y=f(x). In addition, within the framework of functional analysis, the first and second derivatives, the definite integral, zero points, poles and inflection points can be represented. text/html 2026-03-05T16:44:04+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:realspace3d&rev=1772729044&do=diff Real space This section contains graphics that can be plotted in a Cartesian 3D coordinate system. SymbolGraphicDescription3D CurvesRepresents curve trajectories in the x-, y- and z-directions using three functions that depend on a parameter.3D AreasDisplays open surfaces or closed objects in the x, y and z directions using three functions that depend on two parameters. text/html 2026-03-06T09:20:50+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:sections3d&rev=1772788850&do=diff Real space : Sections CGRAPH can graphically determine sections of functions and curves. To use this function, at least two graphics (or two graphic elements) must first be displayed in the representation. Depending on the element, intersections can be intersection points, intersection lines, intersection curves or intersection circles. text/html 2026-03-03T11:57:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:set_of_straight_lines&rev=1772539050&do=diff Straight line segments: Add straight line sets Straight line sets share the same length, while their start and end points are offset in parallel. You can specify the start and end points of the first straight line segment, as well as the increment per section text/html 2026-03-24T10:36:46+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:settings&rev=1774348606&do=diff Settings CGRAPH offers a wide range of settings for customising graphical and mathematical representations. The settings are organised into tabs, Tab Description GeneralContains settings for the general operating behaviour of CGRAPHMathematicsAllows settings for number representation and termination conditions text/html 2026-03-05T16:42:10+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:spatial_curves&rev=1772728930&do=diff 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… text/html 2026-03-03T17:21:20+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:speed_bar&rev=1772558480&do=diff Settings: Speed bar All graphic functions in CGRAPH can be accessed either via the menu or the speed bar on the left side of the main window. The buttons displayed there can be defined here. The list on the right shows all possible entries. All selected entries are displayed in the function bar. Regardless of this, all graphics functions can still be accessed via the text/html 2026-03-08T08:51:16+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:straight_lines&rev=1772959876&do=diff Complex plane : Line segments In CGRAPH, line segments, i.e. lines with defined start and end points, can be mapped onto the complex plane. Either the end point or the length and angle of the line segment can be specified. The function is defined uniformly above the default values for all types of area mappings, because common mappings only make sense if the same function is used. The variable names z and param (as complex numbers) as well as x and y (as the real and imaginary parts of the var… text/html 2026-03-24T09:32:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:stroke2d&rev=1774344761&do=diff Colour and pen type settings For most graphics, the colour and appearance can be freely selected. To do this, double-click on the text next to the coloured symbol for the graph in the tree view. In addition to the colour, pen styles can also be selected. Depending on the graph, however, these may look different in the display than in the selection box in this dialogue box. The text/html 2026-03-03T15:52:45+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:stroke3d&rev=1772553165&do=diff Line colour settings (3D) For most graphics, the colour and appearance of lines can be freely selected. To do this, double-click on the text next to the coloured symbol for the graph in the tree view. The example shows the approximate appearance that can be expected later in the graphical representation. text/html 2026-03-03T16:01:51+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:stroke3dcube&rev=1772553711&do=diff Colour and appearance settings for implicit surfaces CGRAPH displays implicitly defined surfaces as a point cloud formed from individual small cubes. In addition to the colour, the size of the cubes can also be specified. However, this size is relative – the actual display depends on the position of a cube in 3D space. Cubes that are closer to the front are displayed larger than those in the background. text/html 2026-03-03T15:42:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:stroke3dext&rev=1772552558&do=diff Colour and pattern settings (3D) For most graphics, the colour and pattern can be freely selected. To do this, double-click on the text next to the coloured symbol for the graph in the tree view. In addition to the colour, a fill pattern can be selected. This pattern allows the graphics to appear either fully filled or partially filled, giving them a transparent effect. text/html 2026-03-03T11:32:19+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:sumproddefinition&rev=1772537539&do=diff Sums and products CGRAPH offers the sum() and prod() functions for calculating sums and products. These are defined as follows: The use of the two functions sum() and prod () is subject to the condition that they must always be placed in brackets around the function. Nothing may appear outside of sum() and prod (). The following function terms are therefore permitted: text/html 2026-03-03T17:10:08+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:surfaceplots3d&rev=1772557808&do=diff Coordinate transformations: Surface mappings (3D) In addition to the graphical representation of surfaces in space, their graphs can also be coordinate-transformed. CGRAPH displays the Cartesian representation in the transformed 3D 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 x, y and param are permitted. Enter the des… text/html 2026-03-08T10:32:46+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:system_functions&rev=1772965966&do=diff System functions This graphing function allows you to display the different parameters of system functions. System functions are functions that represent the output value of a mechanical or electrical system as a complex function of the input value. Such functions can be obtained, for example, by Fourier or Laplace transformation from the differential equation of a system. text/html 2026-03-08T11:59:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:transformation_basis_2d&rev=1772971171&do=diff Coordinate transformations : Transformation basis (2D) CGRAPH enables the mapping of 2D coordinate systems using coordinate-based mapping functions Only functions containing the variables x, y 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. text/html 2026-03-08T12:19:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://cgraph.de/doku.php?id=en:transformationbasis3d&rev=1772972341&do=diff Coordinate transformations : Transformation basis (3D) CGRAPH enables the mapping of 3D coordinate systems using coordinate-based mapping functions. To assist users and improve the classification of the transformation, CGRAPH displays a rectangular cube grid that is transformed using the mapping functions.