• x does not need to be an integer

Fit a polynomial of degree up to 5 to the points (x,y). Calculate the polynomial at the x values specified by nodes.

• The x nodes do not need to be equally spaced.
• If nodes is a single value n rather than an array of values then nodes is taken to be range(x,n).
• If nodes is not specified then the default value is 33
• If degree is not specified then the default value is 1

This function is described in the section: How do I fit a line?

Interpolate 2D scattered data onto a grid using triangulation based point gridding.

The method:

1. The input points are arranged in triangles such that the vertices of each triangle is an input point and each input point is the vertex of a triangle. The area outside the input points, but within the grid is divided into further triangles and quadrilaterals.
2. For each polygon, a bivariate polynomial is determined in such a way that the surface which results is continuously differentiable. To accomplish this estimates of certain partial derivatives at input points are required. The derivatives are estimated by the weighted averages of difference quotients and involve the point for which the estimates are computed and its closest neighbours. The number of neighbouring points can be set using smoothing. The default is 4.
3. The bivariate function is then evaluated at the grid nodes.

This method is fully described in A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points by Akima, H. (1978).

• The x location of the grid is defined like so:
  • If xGrid is an array then xGrid is used.
  • If xGrid is a single value, range(x,xGrid) is used
  • If xGrid is not specified, range(x,33) is used.
    
    
• The y location is determined in a similar way.

• The current page can be selected with scope

• The current printer can be selected with hardcopy.XuNdevice e.g.

  set hardcopy
   ( XuNdevice = 'hcposta4',
     XuNplotFileName = "bob.ps",
     XuNplotCommand = "lpr -laser bob.ps"
   );
  

• The list of available printers is defined in the file $UNIDIR/base/Gsharprc.gsl. Edit this file for more details. Extra printers can be added with the function define_device().

• The function make_image() in $UNIDIR/lib/libio.gsl can be used to make GIFs, JPEGs, TIFFs and Encapsulated PostScript files.

function PrintAllPages()
  string PAGE;
  for PAGE in all("Page")
    scope $PAGE;
    print;
  endfor
endfunction

define_device, scope

• printf returns the number of characters output

• If any of the parameters is an array then a line is output from every element in the array. e.g. printf("%g - %d", pi, 1:3) will output:

  3.14159 - 1
  3.14159 - 2
  3.14159 - 3

For those unfamiliar with C format strings - a format string is a string containing a number of variables. The percentage character (%) is used to donate that a variable should be inserted into the string. The character following the % shows how the variable should be formatted. The first parameter after the format string is used for the first variable, the second parameter for the second variable and so on.

For example %d means insert an integer, %s a string and %f a float.

printf("x = %d", 3.0) outputs "x = 3"

You can also include modifiers - for example %6.3f means use six digits with three decimal places. %-3d means left align the integer within three character spaces. See below for some examples.

fprintf, sprintf

The projection functions transforms latitude/longitude co-ordinates to and from a projected co-ordinate system (x,y). proj_coord is used to modify the origin of the projected (x,y) co-ordinate system.

• xorigin, yorigin specifies the location of the desired origin in the co-ordinates of the default co-ordinate system.
• angle is the number of degrees anticlockwise from the x-axis that the desired co-ordinate system is from the default co-ordinate system.

If proj_transform would have transformed (lat,long) into (x,y) it will now transform it into:

(newx,newy) = (x-xorigin,y-yorigin)

if angle<>0 then it will also be rotated about the new origin.

• xorigin, yorigin and angle are all zero by default.
• If a valid dataset is passed as a parameter and has the value undef, then the dataset is set to the current value of the parameter.

proj_transform, proj_false

This function can be used to avoid negative values of longitude and latitude by setting a false easting and a false northing. For example:

proj_false(-180,-90);

• longOrigin and latOrigin are zero by default.
• If a valid dataset is passed as a parameter and has the value undef, then the dataset is set to the current value of the parameter.

proj_transform, proj_coord

Cartographic projections are most accurate in the area about the origin of the projection.

• longOrigin and latOrigin are zero by default.
• If a valid dataset is passed as a parameter and has the value undef, then the dataset is set to the current value of the parameter.

proj_transform, proj_coord

A conic projection maps parallels onto concentric circles and is usually true-scale along one or two parallels called standard parallels.

• The default value for the first parallel is 33. The default for the second parallel is 45.
• If a valid dataset is passed as a parameter and has the value undef, then the dataset is set to the current value of the parameter.

proj_transform

Cartographic projections always involve some form of distortion and the central scale factor can be used to compensate for this. The central scale factor is normally 1 or very close to 1.

• The default value for the central scale factor is 1.
• If a valid dataset is passed as sfactor and has the value undef, then the dataset is set to the current central scale factor.

proj_transform, proj_unit

• If major equals minor the earth is assumed to be spherical.
• If the major axis is less than the minor axis the values are interchanged.
• Predefined projection spheroids can be selected using proj_spheroid_select
• If a valid dataset is passed as a parameter and has the value undef, then the dataset is set to the current value of the parameter.

proj_transform, proj_spheroid_select

The earth is an ellipsoid of revolution. The radius along the polar axis is approximately 3% less than the equatorial radius. This function sets the definition of this spheroid to one of the common international standards:

• "sphere" (default)
• "clarke_1866"
• "hayford_1909"
• "grs_1980"
• "bessel_1841"
• "krasovsky_1940"
• "wgs_1972"
• "australian_1965"
• "airy_1849"
• "everest_1830"
• "hough_1956"
• "fischer_1960"

proj_transform, proj_spheroid

The various projection functions such as proj_type and proj_spheroid_select are used to define the transformation between a (longitude/latitude) co-ordinate system and a projected (x,y) co-ordinate system.

Once this projection has been defined proj_transform can be used to perform the transformation in either direction.

• If the direction is "latlong_to_xy" (the default) then xin is the longitude values and yin is the latitude values
• If the direction is "xy_to_latlong" then xin is the x co-ordinates and yin - the y co-ordinates.

For example to go from one to the other and back again:

proj_transform(xin, yin, "xout", "yout","xy_to_latlong");
proj_transform(xout, yout, "xin2", "yin2");

proj_coord, proj_spheroid, proj_false, proj_origin, proj_parallels, proj_scale_factor, proj_spheroid_select, proj_type, proj_unit, proj_utm_zome

The following projections are available:

• "transverse mercator" (default)
• "utm"
• "mercator"
• "lambert_conformal"
• "azimut_stereo"
• "gnomonic"

proj_transform

proj_unit can be used to scale the (x,y) co-ordinates into different units:

• proj_unit(1000) - kilometres
• proj_unit(1609.3) - miles
• proj_unit(1/39.37) - inches
• proj_unit(.3048) - feet

proj_transform

• There are 60 zones numbered from 1 to 60. Zone 1 is from -180 to -174, zone 2 from -174 to -168 etc. You can use the following formula to calculate a zone based on your desired central meridian (cm):

  zone = nint((cm+183)/6);

• The hemisphere can be either "northern" or "southern".

Calling proj_utm_zone will also set the following:

• proj_scale_factor(0.9996)
• A false easting of 500 km
• A false northing of 0.0 in the northern hemisphere and 10,000 km in the southern.

proj_transform

• putenv returns true (1.0) on success and false (0.0) on failure.

getenv, system