Help!!....I need some sort of a formula!!

Question

My application displays graphs from given data and I need to somehow get it to show between 8 and 12 tick marks on the x and y axis. They also have to be rational values i.e. 120.0 130.0 140.0, etc not like 120.25432 or 132.5363 or 143.94. The program can put the tick marks at regular intervals already but not rational values. I seem to need a tick mark everytime the integer part changes by 1, 2, 2.5, 5, 10, 20, 25 or 50. This sequence would repeat for hundreds: 100, 200, 250, 500, 1000, 2000, 2500, 5000 and so on for hundreds of thousands. I don't need ticks at 40, 60, 3500, etc unless these numbers fall naturally into the above sequence. This requirement also repeats for the fractional part as well: a tick every 0.1, 0.2, 0.25 or 0.5 units.
I need to find a formula for "every XXX" depending on the level of the sequence.
I would need between 8 and 12 ticks on a "normal" screen 800 x 600 pixels. E.g. if the graph runs horizontally between 0 and 841ms then the 1000-scale would be too rare. Same for 500, 250 and 200 scales. The 100 scale would be ok as this would display 8 ticks, but the 50, 25, 20, 10 scales, etc, would be too dense. I need a formula to automatically make the decision that the 100 scale would be the one to use.
The program also knows how to adjust the "base number" of ticks on the axis so that the labels don't run into each other. Possibly assume that base number of regular ticks plus/minus 20% of that number. E.g. 8 to 12 ticks become 10 ticks +/- (20% of 10 == 2) == 10 +/- 2 ticks. If user reduces the window, the base number may become 5 or 4. In that case the scale will be 5 +/- 1 tick or 4 +/- 1 tick (20% of 4 == 0.8 approx 1).
Your help would be really, really appreciated as this needs to be sorted in the next week or two and I'm really stuck with this one!!
Thanks!!

Answer 1

To determine which scale to use first find the span of your axis Sx = Xmax-Xmin. You need to find which increment, when multiplied by the number of ticks N you wish to display, will cover this span.
The pattern of numbers that you specify (1,2,2.5...) is not a regular pattern and therefore cannot be elegantly implemented with a simple formula. You need to create a lookup array that contains these values, then create your series by scaling that array by powers of ten.
Start at an arbitrary scale, say, dx = 1 and find out if N * dx > Sx. If so, reduce dx to the next lowest increment in your series and repeat until N * dx > Sx is no longer true.
If N * dx < Sx you need to increase dx and repeat until you achieve N * dx > Sx. Your previous value of dx will be your "magic increment".
Hope this helps. Good luck!