# Coordinate Systems

## GKS Coordinate Systems

In addition to its own user coordinate space, NCAR Graphics uses two GKS coordinate systems: world coordinates (WC) and normalized device coordinates (NDC). Both are defined in terms of floating point numbers.

### World Coordinates

A world coordinate system is a Cartesian coordinate system that is linear along both axes. A world coordinate system can have units of feet, meters, millibars, or whatever engineering units apply to the calculations. World coordinates are expressed as real numbers. You can select a rectangular subspace of world coordinates for output.

### Normalized Device Coordinates

This is a device-independent coordinate system used by GKS as an addressing system for a virtual plotting device; it is a two dimensional Cartesian space that has horizontal and vertical ranges of 0. to 1. inclusive. In GKS, a transformation is performed from a subrectangle of world coordinates (called a "window" ) to a subrectangle of the normalized device coordinates (NDC). The rectangular subspace of NDC is called a "viewport.". To ensure that squares in world coordinates are mapped onto squares on the output plotting device, the maximum display surface on that device will be the largest square which will fit on the plotting device. The NCAR Graphics CGM interpreter, ctrans, centers the maximum viewport on an output plotting device. X11 output is centered in the output window. PostScript output is centered on the page by default, but options exist for positioning PostScript output anywhere on the page.

In NCAR Graphics, Normalized Device Coordinates are sometimes referred to as "Fractional Coordinates".

### Normalization Transformations

The linear transformation between the world coordinate window and the NDC viewport is called a normalization transformation. For example, the horizontal coordinates of the window might be from 100. to 1000. meters. The horizontal coordinates of the viewport might be.15 to.95. Diagram 1 shows a typical GKS normalization transformation.

### Diagram 1 - A typical GKS normalization transformation ## NCAR Graphics Coordinate Systems

### User Coordinates

A user coordinate system is any coordinate system in which user calculations are performed. This may be polar coordinates, log scaled coordinates, or any other such coordinate system. If you are working in a user coordinate space that is a Cartesian space with no log scaling or mirror imaging of an axis, then world coordinates and user coordinates are equivalent.

GKS requires that both windows and viewports have linear scaling. GKS also requires that the horizontal coordinate increase from left to right, and that the vertical coordinate increase from bottom to top. Thus, the viewport coordinate (0.,0.) references the lower left corner of a plotting surface. NCAR Graphics provides extensions to GKS world coordinates to allow for mirror imaging of an axis, and log scaling of an axis. If you are using any other coordinate system, then you will have to map it into one of the coordinate systems supported by NCAR Graphics before making GKS calls.

In order to use the log scaling or mirror-imaging features of the NCAR Graphics user coordinate spaces, you must establish your coordinate mapping transformations. The easiest way to do this to by using a SET call. In user coordinates, windows can be defined in which the horizontal coordinate of the window might be meters ranging from 1000. at the left to 100. at the right (mirror imaging), and the vertical coordinate might vary from 10**2 at the bottom to 10**3 at the top in logarithmic scaling.

For a detailed description of the relationship between the GKS coordinate systems and User Coordinates, see NCAR Graphics Fundamentals, UNIX Version, Appendix A.

### Diagram 2 - A normalization transformation with mirror imaging and log scaling ### Plotter Address Units as Absolute Lengths

In certain places in the documentation for LLUs, reference is made to Plotter Address Units (PAUs). PAUs are integers defined in the range 1 to 1024 and map linearly to normalized device coordinate space. For example, if you wanted a length of .01 in normalized device coordinate space, but were required to specify this as a PAU, then you would use the integer value 102 (.01*1024).

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