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A scalar cannot 'point' in any direction. You were asked to decompose the Cartesian basis vectors into the spherical ones in post #4 and to make the drawing with the position vector relative to a point in spherical coordinates twice in posts #6 and #8. I suggest that you follow either or both of these suggestions. The terminal coordinates program may be used to find the coordinates on the Earth at some distance, given an azimuth and the starting coordinates. The shortest distance between two points on the surface of a sphere is an arc, not a line. (Try this with a string on a globe.) In addition, the azimuth looking from Point B to Point A will not be the converse (90 degrees minus the.

This document was published with and applies to ArcGIS 9.3. A version also exists. A version also exists. Summary Every dataset has a coordinate system, which is used to integrate it with other geographic datasets within a common coordinate framework. Coordinate systems enable you to integrate datasets to perform various integrated analytical operations, such as overlaying data layers from disparate sources and coordinate systems. Geographic, projected, and vertical coordinate systems, as well as geographic (datum) transformations, are discussed in this topic.

Types of coordinate systemsThe following are two common types of coordinate systems used in a geographic information system (GIS): • A global or spherical coordinate system such as latitude-longitude. These are often referred to as geographic coordinate systems. • A projected coordinate system such as universal transverse Mercator (UTM), Albers Equal Area, or Robinson, all of which (along with numerous other map projection models) provide various mechanisms to project maps of the earth's spherical surface onto a two-dimensional Cartesian coordinate plane.

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Projected coordinate systems are referred to as map projections. Latitude and longitude values are traditionally measured either in decimal degrees or in degrees, minutes, and seconds (DMS).

Latitude values are measured relative to the equator and range from –90° at the south pole to +90° at the north pole. Longitude values are measured relative to the prime meridian. They range from –180° when traveling west to 180° when traveling east. If the prime meridian is at Greenwich, then Australia, which is south of the equator and east of Greenwich, has positive longitude values and negative latitude values. If two datasets are not referenced to the same geographic coordinate system, you may need to perform a geographic (datum) transformation. This is a well-defined mathematical method to convert coordinates between two geographic coordinate systems.

As with the coordinate systems, there are several hundred predefined geographic transformations that you can access. It is very important to correctly use a geographic transformation if it is required. When neglected, coordinates can be in the wrong location by up to a few hundred meters. Sometimes no transformation exists, or you have to use a third GCS like the World Geodetic System 1984 (WGS84) and combine two transformations.

Whether you treat the earth as a sphere or a spheroid, you must transform its three-dimensional surface to create a flat map sheet. This mathematical transformation is commonly referred to as a map projection. One easy way to understand how map projections alter spatial properties is to visualize shining a light through the earth onto a surface, called the projection surface. Imagine the earth's surface is clear with the graticule drawn on it. Wrap a piece of paper around the earth.

A light at the center of the earth will cast the shadows of the graticule onto the piece of paper. You can now unwrap the paper and lay it flat. The shape of the graticule on the flat paper is different from that on the earth. The map projection has distorted the graticule. A spheroid cannot be flattened to a plane any more easily than a piece of orange peel can be flattened—it will tear. Representing the earth's surface in two dimensions causes distortion in the shape, area, distance, or direction of the data. A map projection uses mathematical formulas to relate spherical coordinates on the globe to flat, planar coordinates.