What is the difference between a geographic coordinate system and a projected coordinate system?

What are the three components of a projected coordinate system?

What is the correct method to do that?

To calculate the transformation between 2 coordinate systems, we need to express an object with a coordinate system (the object). We can imagine the object like a black box with a specific orientation and position and dimensions. The position of the point where the coordinate system starts (origin) and the dimension where the coordinates range are given.

A position is simply the angle of inclination from the x axis. There is one in our head - the up. The y axis is orthogonal to the x. It points to the left. The z-axis is the right-up (3rd dimension). This orientation must always be in the same place of the object. We define the object's position on 3D world space and the location in all directions is then calculated based on this coordinate system. If the camera looks at the left side of the object, we have only x, y and z values left: x = 0, y = 0, z = 1. However, a rotation about the y-axis results in: x = 0.5, y = 0, z = 0.7. That's why it's called projective geometry.

For simplicity, we assume that a camera's focal length does not change. Also, we assume that the origin remains fixed at the start point of the coordinate system and the X-axis is horizontal (that's why x and z is always positive). The z-axis is vertical and points towards the ground. That's why y is positive for a left and negative for a right turning side of the camera. All this should give the feeling of being in 3D world space.

The transformation for converting x, y and z values of an object from one coordinate system to another is called the perspective projection matrix. The projection matrix is applied to the vector from camera to the object to transform the object in the image plane.

Here is a simple example for a rotation about the y-axis of an object. By rotating y through, the object rotates y degrees clockwise around the new y axis.

However, the problem with the projection matrix is, that even though it's applied to the vector as a whole, it breaks down into three components: Object Coordinate. Projection into X and Y components.

What is the difference between a geographic coordinate system and a projected coordinate system?

What purpose do they serve in GIS?

I've looked around for information, but haven't found much.

First of all, what you might call geographic coordinate systems (GCSs) are called spatial reference systems (SRSs). An example of a GCS would be latitude/longitude. This would give us the ability to use a set of coordinates to describe where a place is located on the globe - that could be useful if we had to travel there. However, a more practical approach in modern times is to use a projected coordinate system. That is, if I wanted to give a coordinate to the city of New York, I'd give it the longitude and latitude of 42. These coordinates don't really make sense because they look out into space, so when plotting the city on a map, I need to scale it according to the projection I chose (usually the Mercator projection, but not always). Projection means the way the Earth's surface is scaled onto a plane (it's a process, not an object) - it will stretch and compress the distances according to how far from the equator it is.

Projected coordinate systems are very practical because you can easily see what scale your city/country/etc is on, while GCSs need to be adjusted for a number of different purposes.

What are the two types of coordinate systems used in GIS?

There are two types of coordinate systems used in GIS: the orthogonal coordinate system (x,y,z) and the non-orthogonal coordinate system (lat,lon,h). Orthogonal coordinate system (x,y,z) is usually used for terrestrial applications. In this system, the x, y, and z axes are defined as right-handed Cartesian coordinates where the origin is at the Earth's surface and points up toward the North Pole. The positive x axis is oriented to the east of the true north, and positive y axis is oriented to the north of the east. Positive z axis points up. These coordinate axes are perpendicular to each other. For example, a positive x coordinate along with a positive y coordinate and a positive z coordinate will be considered to be the same location.

Non-orthogonal coordinate system (lat,lon,h) is usually used for the ocean and coastal areas. In this system, the x, y, and z axes are defined as true geographic coordinates where the origin is at the Earth's center and points out of the Earth in the general direction of the geodetic North Pole. The positive x axis is oriented in the direction of increasing longitude, and positive y axis is oriented in the direction of increasing latitude. Positive z axis points to the top of the sphere. These coordinate axes are not perpendicular to each other. For example, a positive x coordinate along with a positive y coordinate and a positive z coordinate will be considered to be different locations.

What is the difference between a map coordinate system and a location coordinate system? The difference between a map coordinate system and a location coordinate system can be explained in two ways: the projection of the location coordinate system onto the map coordinate system. The orientation of the location coordinate system relative to the Earth's surface. A location coordinate system defines a 3D point on the Earth's surface. Map coordinate system projects the location coordinate system onto a 2D plane. Map coordinate system uses Mercator projection for any location on Earth except Antarctica. Map coordinate system has only one degree of freedom: latitude.

The map coordinate system is called cartographic coordinate system because the Mercator projection used in it resembles the appearance of the landscape when the map is viewed from above. The location coordinate system represents an actual geographic point and has both latitude and longitude components.