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.

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