## Wednesday, April 13, 2011

### doodler formulas

Here are some of the formulas I use to calculate where to draw.

doodler formulas

I need to figure out where the pen is.
I keep track of how long each string is with each step it takes.
I also know the distance between the cuphooks the strings go over.
That defines a triangle.
There is a neat formula for calculating the area of a triangle.
Add up all three sides, that is the perimeter. Half of that is the semi-perimeter.
Find the difference between each side and the semi-perimeter.
Multiply those three differences times each other and times the semi-perimeter.
Take the square root of that and you have the area.
Once you have the area you can figure out the height of the triangle, (area*2)/base=height.

WBPLEFT is the length of the left string.
WBPRIGHT is the length of the right string.
WBPBASE is the distance between the cuphooks.
WBPS is the semi-perimeter.
WBPS = (WBPLEFT + WBPRIGHT + WBPBASE) / 2
WBPAREA = SQR(WBPS * (WBPS - WBPLEFT) * (WBPS - WBPRIGHT) * (WBPS - WBPBASE))
WBPHEIGHT is the distance down from the cuphooks to the pen.
WBPHEIGHT = (WBPAREA * 2) / WBPBASE
WBPWIDTH is the distance from the left hook to the pen.
WBPWIDTH = SQR((WBPLEFT * WBPLEFT) - (WBPHEIGHT * WBPHEIGHT))
The center of my board is 0,0 so this calculates X and Y for where the pen is.
Units is inches.
WBPXNOW = WBPWIDTH - WBPCENTERWIDTH
WBPYNOW = WBPCENTERHEIGHT - WBPHEIGHT
WBPCENTERWIDTH is the distance from the left hook to the center of the board.
WBPHEIGHT is the distance from the hooks down to the center of the board.