TLCalc offers the unique feature of being able to find intersections between functions, polar plots, parametric plots and even between plots of different types, but there are some limitations. These limitations are that:
- it runs fairly slowly (the search is done in the background so it's less noticeable)
- it has medium accuracy (expect 5-9 significant figures)
- it has low stability (if you move the plots around, you will notice that some intersections get missed out, even if they were found earlier) and
- plots which come very close together (closer than 0.00001) may be mistaken as intersections.
The limitations are due to algorithm which must optimise two independent and non-linear variables and I haven't found a good way to do this yet. Despite these limitations, the current one does reasonably well and you can find pretty much any intersection between different plots if you don't need super high accuracy and if you spend a second panning the plot around until the intersection you want gets picked up.
In V1.19.0, an intersection finder was added specifically for functions. This finder was the old finder from V1.15.1 which was much faster, more accurate and had much better stability than the generic finder (expect at least 9 significant figures of accuracy and zero misses). This finder replaces the generic finder when the intersection is between two functions which are in terms of the same variables. I.e. finding the intersections between f(x) and f(y) will use the generic finder with less accuracy. The obvious limitation is that the finder from V1.15.1 only works for functions.
You may be wondering whether implicit plots and statistical plots will be included in the future. Intersection of statistical plots is useless for all but the line and scatter plot, but even then, it doesn't really make any sense (intersection between discrete and continuous data is not something that is normally required). The implicit plot is also not available because I haven't found a way to do this yet. I haven't even implemented a way to do tracing of implicit plots (this is another 2 variable optimisation problem except this time I don't have a slope that is dependent on a single variable to work with which means my current algorithm is useless for this task).
