VISUALIZATION OF MULTI DIMENSIONAL FUNCTIONS
EVOLUTION
The project has been through several pages. This page just reflects the various approaches that I have tried so far.
STAGE 1 : SPRING 2001
The project started as a semester project for the InfoViz class during the Spring semester, the participants of the project being Ashwini, Vijay, Prasunna and Ravikiran Vatrapu. At this stage in the project the functional values of the points on the focal rays were mapped onto straight vertical lines. The project was implemented in OpenGL (click here to see the figure).
STAGE 2 : MAPPING OF THE FACES OF THE HYPERCUBE
The project took a major turn in terms of idea and implementation at this stage. In this stage the hypercube around the focal point was represented as a rectangle on the screen. The rectangle was appropriately divided to represent the faces of the hypercube. This method had the major disadvantage that any point on a rectangle found at a greater distance from the focal point was not aligned accurately with a point lying on the same focal ray represented on any of the inner rectangles. I started implementing the project in Java (click here to see the figure).
STAGE 3 : MAPPING FOUR FACES OF THE HYPERCUBE
At this phase I attempted to map pixel points on the screen to functional values. To test the feasibility and practicality of this approach I first attempted to map only four faces of the hypercube on to the screen. After implementing this stage I found that this method actually was a much more intuitive method and I was able to overcome a lot of disadvantages and drawbacks when I went from the function to its representation. The visualization at this stage was square in shape (click here to see the figure).
STAGE 4 : MAPPING ALL FACES OF THE HYPERCUBE
At this stage I took the idea of going from the pixel points to the functional value a step further. I mapped all the faces of the hypercube and the visualization was circular. The circle was divided equally depending on the number of faces of the hypercube. I also added the mouse over labeling feature (click here to see the figure).
And now I am still working on this visualization to make it much more intuitive and useful.......
Updated on Sept 2nd 2001
