Where On the World Am I?
Our little school doesn't have a gym to practice in. We practice outside (remember we live in southern California, we've only missed one practice this winter on account of rain.) Without a gym every game is an away game so we have to travel. I've discovered that people have definite differences in the way they communicate driving directions. Some give directions solely relative to street names and turns (left and right). Others use cardinal directions (North, South...) street names and landmarks, and I suppose many other variations and different combinations are also used. I suffer from an unofficial form of dyslexia where I don't know my left from my right! I seriously have to think every time. In my brain left and right are completely relative. I have to mentally perform the pledge of allegiance to know, which is my right hand, that I'm placing over my heart (a genetic defect that I fear I have passed along to my daughter.)
In CAD the universe is a cube, a big Cartesian coordinate system (x', y' and z'). In GIS the world is a coordinate fabric. GIS still stores it's coordinates in a Cartesian coordinate system of x', y', and z'. However, it also includes a definition of the shape of the fabric. The fabric itself has defining geometry. The two parts of the coordinate system the (x',y',z') and the fabric projection, allow GIS to map accurately the spheroid that we live on, and to convert data in one or another flat map approximations of our globe.
When you survey our world and record the coordinates into your survey data collector or into a CAD program you may be accurately measuring, but your encoding of the coordinates is based on an approximation of a flat surface on a round globe. In a small area the approximation is relatively accurate. Over a large area the approximation gets worse toward the edges. The only accurate way to measure on a spheroid would be to use polar coordinates. However this is generally impractical for the work we do.
Think of a triangle. We know from trigonometry class that the sum of the included angles of a triangle always equals 180 degrees. Pick up a schoolroom globe. With your finger draw a triangle from the North Pole down the international dateline to the equator near the Phoenix Islands then across the equator to the 90 W Meridian, near San Cristobol Island, then back up to the North Pole. You notice the sum total of the angles is 90 degrees + 90 degrees + 90 degrees or 270 degrees (not 180!). Were Euclid and Pythagoras wrong, or is this not a triangle?
If you were to survey road features with a local coordinate system to the 10,000th of an inch one square mile at a time, for the entire state of Texas and then wanted to paste those drawings together edge to edge, what do you think would happen when you view the data within the existing State boundary? Are those drawings accurate? Are they precise?
When laying out a large radius highway curve, should it be mapped and stored as an elliptical curve based on its true geometric reality (including the curvature of the earth), or should it be stored with an approximation as a circular curve?
In ArcGIS you can provide the missing coordinate projection information of a CAD file using a companion ESRI projection file to identify which flat map approximation the CAD data was encoded with. ArcGIS looks for projection files when it reads a CAD file. In this way CAD files from one coordinate projection can be accurately viewed with data from other coordinate projections.