I am trying to calculate the quality of a triangle. Parameters are skewness, aspect ratio, and size. Skewness ranges between 0 and 1. Aspect ratio is the ratio of longest edge to shortest edge. Likewise size is the ratio of area of triangle to that of certain ideal triangle. I would like to get a score over 100 such as:
score = skewness*coefSkew
+ ar*coefAR
+ size*coefSize
where, coefficients are set as (20,60,20). The problem is with aspect ratio and size since they have no upper limits so I can't grade them over something whereas skewness can be graded over 1. What would you suggest?
There are a variety of functions that map $(0,+\infty)$ to a finite interval. For example, $\tan^{-1} x$ maps $(0,+\infty)$ to $(0,\frac{\pi}{2})$.