Most graphing programs that are available today do what I would call statistical graphing. The user gives the program a series of data that he has calculated or measured, and the program can produce a variety of graphs (say a pie chart, or a scatter plot).
However, when you want to graph a mathematical equation, such a graphing program is cumbersome to use (you have to first generate the data using the formula), and often doesn't produce the desired layout.
MathiGraph would take a completely different approach to graphing by working entirely with mathematical equations rather than with data. This would address the needs of a different class of users, namely mathematics teachers, researchers, and students.
MathiGraph would need to:
I know of no program that satisfies all three of these needs. There is a popular graphing calculator on the Macintosh which is easy to use, but is not at all flexible. The high-end programs Maple and Mathematica are more flexible, but are hard to use because the settings must be changed using text commands. I know of no program that, with minimal effort, produces a picture of good enough quality to be published in a book.
Solution:
Here are some features that MathiGraph would have, in order to cater for the above needs:
This program would take mathematical graphing software to a completely new level. The program would not just plot a graph dot by dot, but would use a sophisticated algorithm to determine the best way to plot an equation.