Basic Coordinate Systems & VR Babu 2011

Changing between coordinate systems z1 y2 x1 z2 Coordinate Systems 1 x2 Coordinate Systems 2 Babu 2011

What information do we need? Distance between origins: [x,y,z] and rotations of coordinate system axes of coordinate system 2 to line them up with coordinate system 1 axes Transformation matrix between the two coordinate systems Babu 2011

Coordinate Systems in VEs Tfrom Chair’s coordinate system to Room’s coordinate system Room Door Table Chair Vase We usually deal with multiple coordinate systems in a virtual environment Scene is collection of geometric objects Geometries are usually defined relative to a local coordinate system Coordinate System Graph is used to relate all geometries to the virtual world that we are presenting Babu 2011

Where is the “eyepoint” in a HMD Sensor x y z Tracker gives position and orientation of Sensor’s coordinate system relative to the Source Y Z X Your eye is not on the top of your head! (0,0,0) Electromagnetic Tracker Source Babu 2011

Where is the “eyepoint” in a HMD Sensor x y z Your right eye is a fixed distance and orientation from the sensor (which you must measure based on the configuration of the HMD and sensor). Y Z X (0,0,0) Electromagnetic Tracker Source Babu 2011

The eyepoint also has a coordinate system! Sensor x y z Y Z X The image source and the optics of the HMD define a “screen” that is located a fixed distance from the eye (projection plane in graphics terminology) and moves with the head. (0,0,0) Electromagnetic Tracker Source Babu 2011

Coordinate System Graph Each node represents a coordinate system, each edge linking the nodes represents a transformation between those coordinate systems Babu 2011

Coordinate System Graph User Model Modified when user uses joystick or other virtual method to walk or fly in the world World Constant orientation and translation Workspace Tracker Source Measured by Tracker Constant orientation and translation Head (Sensor) Right Eye Left eye Projection Plane Projection Plane Babu 2011

Coordinate System Graph User Model Modified when user uses joystick or other virtual method to walk or fly in the world World Constant orientation and translation Workspace Tracker Source Measured by Tracker Constant orientation and translation Head (Sensor) Right Eye Left eye Projection Plane Projection Plane Babu 2011

Tracker allows the user to move through a small subset of the world Babu 2011

Coordinate System Graph User Model Modified when user uses joystick or other virtual method to walk or fly in the world World Constant orientation and translation Workspace Tracker Source Measured by Tracker Constant orientation and translation Head (Sensor) Right Eye Left eye Projection Plane Projection Plane Babu 2011

Virtual walking changes relative position of user and tracker to the world. Babu 2011