Transformations

 

Besides the coordinate system support, a linear transformation can be applied to the local coordinate for further flexibility. When importing, the transformation is applied prior to the inverse projection. When exporting, the transformation is applied after the projection.

 

Transformations can also be used to convert from local coordinates to longitude and latitude, if neither the projection nor coordinate system is known.

 

The transformation is specified with the Transform option, which can be:

• Explicit, by providing the scaling factors and offsets in local units

• Implicit, by providing local and world coordinates for two or more control points

The following table describes the three formats of the Transform option:

 

Transform

Format

Description

Scale and Offset	{x_mult, y_mult, x_offset, y_offset}	X and y multipliers and offsets
Center and Extent	{c1_x, c1_y, width_1, c2_x, c2_y, width_2}	Shift the center from c1 to c2 and scale based on the ratio of width_2 divided by width_1
N-Point	{{local x, local y, world lon, world lat},...}	One or more subarrays containing the local X and Y values and the equivalent longitude and latitude values. One subarray will just translate (shift), two or more will gives a linear transformation based on least squares

 

Note that when you use any transformation, the result must be in decimal degrees for longitude and latitude coordinates. If you do not use a transformation, integer longitude and latitude coordinates with six implied decimal places can be imported without transformation. For example, the coordinate (-78123456, 43654321) would be imported correctly as (-78.123456, 43.654321), but if you need to convert the (78123456, 43654321) to make the longitude negative you must multiply the longitude by -.000001 and the latitude by .000001.

 

Examples

// Multiply the X values by 10 and add 1,000,000 to the Y values

...

{"Transform", {10, 1, 0, 1000000}}

...

// Shift the center from (0,0) to (1250000,510000) and double the scale

...

{"Transform", {0, 0, 1, 1250000, 510000, 2}}

...

// Define three control points in local and world (longitude and latitude) coordinates

...

{"Transform", {{12943,37494,-77,43.25}, {12439, 49437,-77,43.5}, {1423,34974,-77.5,43.25}}}

...