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Table of Contents
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 connected areas in the complex plane, as used for the transformation of inaccessible geometries, to the consideration of dynamic systems and the representation of fractals, which are still the subject of mathematical research today.
This wiki explains how to use the individual functions of CGRAPH. The individual pages can also be accessed from within the app by pressing the F1 key.
Here you will find the following explanations about CGRAPH:
Basics
In the Basics section, you will find explanations about the structure of the CGRAPH interface, number formats, the syntax of function terms and the mathematical basics.
Graph types
The individual graphic types that can be created in CGRAPH are organised by content. CGRAPH recognises the following graph 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 intersections and display implicit equations. |
| Real space | A 3D space in which space curves, surfaces and objects of linear algebra can be represented. The calculation of sections and the representation of implicit equations are also possible. |
| Complex plane | Two 2D representations of real and imaginary axes in which circle segments, line segments and polylines can be represented in their original form and as images. Individual areas can then be plotted and coloured |
| Complex space | A 3D space in which the curves of the real part, imaginary part or magnitude of complex functions can be represented in the z-plane as surfaces in complex space or as mappings in complex space. |
| System functions | A summary of functions in which the location curve, the frequency response, the FFT and the functional behaviour of complex system functions can be represented. |
| Convergences | Here, the iterative behaviour of complex functions can be examined. Mandelbrot sets, Julia sets and the influence of individual parameters on the convergence curve can be examined. |
| Interpolations | CGRAPH offers the possibility of performing various interpolations with existing value pairs and even recovering the probable underlying function. The value pairs can also be converted beforehand for this purpose. |
| Coordinate transformations | Here, the coordinate system can be transformed by functions in two-dimensional or three-dimensional space. In addition, curves in two-dimensional space as well as curves and surfaces in three-dimensional space can then also be mapped and transformed. |
For each graphic, you will find explanations of the input fields and an example.
Settings
In the Settings, you will find all the options that CGRAPH offers for presetting the initial parameters of graphics, the function bar and the screen display. All basic settings are carried out in a register that can be accessed via the Settings menu and is divided into individual tabs.
About CGRAPH
Some information and images on the history of CGRAPH
CGRAPH is available in the Mac App Store and the Windows App Store.