# Coordinate Systems

Geometry undergoes a series of transformations before being rendered to the screen. This conversion process is used to move objects through various coordinate systems in the projection pipeline which starts with world space at one end, and culminates in pixel space (the picture on the screen) at the other. The pipeline is as follows:

```Object -> World (-> Viewpoint) -> Outer Window -> Pixel
```

## Object Coordinates

After graphics primitives are inserted into the HOOPS/3dGS database, they reside in a unitless infinite 3D Cartesian coordination system called ‘object coordinates’. Each segment has its own local object coordinate system. Objects are then transformed from object coordinates into another coordinate system called world coordinates using the local modelling matrix contained set in the segment concatenated with any transforms from the parent segment. Modelling matrices will be discussed here.

## World Coordinates

This is another unitless infinite 3D Cartesian coordinate system where objects reside after having been transformed through their local modelling matrices. There is a single, global world coordinate system in the HOOPS/3dGS database. (This is sometimes referred to as camera coordinates.) This is the space viewed by cameras in the scene. A camera defines a particular view of the world coordinate system. This is the coordinate system where objects exist after local modeling transformations have been applied.

## Viewpoint Coordinates

The viewpoint coordinate system is orthogonal to the current view plane.

• The Z-axis is in the direction of the viewing vector

• Y-axis is in the direction of the up vector

• The origin is at the camera position

This system enables you to easily construct geometry in your current viewplane.

## Window Coordinates

Each camera projects its field of view into it’s containing window. The window coordinate system is a 2D coordinate system which corresponds to the HOOPS window drawn on the screen. In window space, the top right of the window is 1,1 and the bottom left is -1, -1, and it’s z-range is also -1, 1 (World space is normalized into the window coordinate system’s z-range).

## Pixel Coordinates

After an object has been transformed based on the viewing transform defined by a camera and drawn on the screen, it ultimately resides in a 2D coordinate system called screen coordinates. This is also called pixel coordinates, since it corresponds with the physical pixels on the screen. This is also the coordinate system where GUI events are typically returned.

## Converting Between Coordinate Systems

The function `Compute_Coordinates` provides support for converting between different coordinate systems. Typical uses include:

• Converting input from a GUI toolkit to actual position in scene; this involves converting from pixel coordinates to world coordinates

• Building geometry in construction plane; this involves converting from world coordinates to viewpoint coordinates, and then back to world coordinates