Question

in GIS, we can use cartesian cordinate system, 3 D cordinate system. how do we fit that 3D system to the actual earth ( mountains, Vales) then how do we get that back to 2D system screen.

Answer 1

Coordinate System: It is a particular kind of reference system or frame that use location of points to determine the relative location of other point in reference to a fixed reference or point.

Cartesian Coordinate System: It is system to specify each point uniquely. In this system two perpendicular lines or three mutually perpendicular lines are chosen and coordinates of a point are taken to determine the distance from the fixed perpendicular lines. It can be one dimensional, two dimensional, three dimensional or higher dimensional.

3 D Coordinate System: Here three mutually perpendicular axis are used to determine the distance of a point from the lines. Here a formula is used to find out the distance between two points,

Point A (x₁, y₁, z₁) and B (x₂, y₂ ,z₂)

Distance (D) = [(x_{2 -} x₁)² + (y₂ - y₁)² + (z_2-z₁)² ]^1/2

3 D Coordinate System to Actual Earth:

It includes latitude, longitude and altitude of an earth feature i.e. mountain (elevation), vales (depth) etc. There are two types of systems to represent earth features in a 3 D coordinate system

1. Earth Centered, Earth Fixed System
2. Local Tangent Plane

There are some models to fit actual into Global Information System. These are

DEM: Digital Elevation Model

It is a mosaic system of grids or Discrete Global Grid which represents the entire earth's surface. It generally used for landscape mapping. The mountains and elevated places are best fitted here. It can be represented as a contoured topographical map or pseudo-colored map for better understanding. It can be

1. TIN (Triangulated Irregular Network) DEM: It is suitable for triangular surfaces features, also known as primary DEM. It uses vector data.
2. Raster DEM: It is also known as the secondary DEM. It used to represent 'Heightmap'. Here the elevated parts are best represented like mountains.

DSM: Digital Surface Model

It use for landscape modelling. It is actually the primary data source for DEM modelling.

DTM: Digital Terrain Model

It basically for land use studies, flood or drainage modelling etc. It use for contour generation, ortho reflection of remotely sensed images for making direct measurements of geographic locations, distances, angles, area etc in 3 D space.

3 D to 2 D:

• We use suitable projections for the representation of 3 D surface in to a 2 D screen or piece of paper. Only two coordinates are used here.
• Here the distance between two points are calculated based on the following formula,

Point A, (x₁, y₁) and B (x₂, y₂)

Distance (D): [(x₂ - x₁)² + (y₂ - y₁)]^1/2

• Here some distortion also arises, like shape, size, direction etc. Considering the above factors the 2 D representation has been done. For an example we represent a cylindrical form of object (3 D) into a rectangular form in the 2 D screen. If you cover a cylinder made up of wire by a piece of paper and draw the graticules into the paper and unfold after drawing it will look like a rectangular coordinate system.
• Here the nearest point from the elevated point is represented to maintain the angular measurement
• The steps are
  1. 3 D object coordinates (x,y,z): the Geometric primitives
  2. Modeling transformation: transform into World Coordinate System or Cartesian Coordinate System
  3. Viewing transformation: use lighting and reflectance
  4. Projection transformation: transform into 2 D camera coordinate
  5. Window to Viewport transformation: clipping of primitives outside the camera's view
  6. 2 D image coordinates (x,y): draw pixels including hidden surface, texturing etc. to convert into a image