VISUALIZATION OF MULTI DIMENSIONAL FUNCTIONS
CURRENT APPROACH IN DETAIL
The main objective is to enable the user to comprehend the functional space very easily. So we use a very different approach, namely the focus + context approach which has not been attempted so far. First the user chooses a point in the functional space which is called the "focus point". This forms the region which the user is interested in knowing about in more detail. We imagine rays to emanate in all directions from the focal point. The focal rays consist of a number of points and we attempt to represent the functional values of these points around the focal point.
In order to represent all the functional values of the points surrounding the focal point we consider a hypercube surrounding the focal point. For example if the functional space was three dimensional then the focal point will be surrounded by a cube at varying distances from the focal point. We use the hypercube to aggregate the points and represent them on the screen. There are two methods in which this representation can be done
Each face of the hypercube could be divided into a grid. All the focal rays which pass through a particular grid square on a face are considered, the functional values on the rays passing through that grid can be aggregated and represented in the visualization.
A path can be considered on the face of the hypercube. Points can be selected on this path and their functional values can be represented in the visualization.
I have worked on both the approaches. The first one seems probable but a lot of computations are required during runtime which could make the visualization less responsive during runtime. The second one is what I am currently working on. It seems to be more promising and I am trying to find out a function which would enable the points on the screen to the path on the hypercube.
I will keep updating this page as I make more progress in this project. So keep checking this page often.
Updated on Sept 2nd 2001