arctan

Jonathan Holle

Hi all !

I'am doing an hexapod controlled by a basic stamp 2 and two PSC. So, in order to do inverse kinematic I have to use inverse trig functions (arcsin, arccos and arctan).
The only way I found is this :

' {$STAMP BS2}
' {$PBASIC 2.5}

X VAR Byte ' input value 0 to 99 (0.00 to 0.99)
Y VAR Byte
arccos VAR Byte ' angle in brads, 0<=A<=64.
arcsin VAR Byte
arctan VAR Byte
Z VAR Byte ' helper variable

X=


Z = X */ 983 / 3 ' renormalize to 127
arccos=63-(Z/2) ' first approx, to minimize iterations
boucle:
IF COS arccos <= Z THEN done
Arccos = Arccos+1
GOTO boucle
done:
Arccos = Arccos */ 360 ' convert brads to degrees using */ operator

arcsin = 90 - arccos

'For a negative X :
'Arccos = 180 - Arccos
'arcsin = -arsin

DEBUG "arccos 0.", DEC2 X," = ",DEC Arccos, CR
DEBUG ?arcsin, CR


But how could I get the arctan function, is there any relation with arcsin or arccos.
I know that a better way is to use a table ... But being completely beginner in BS2 programming, I don't know how to do it ...
Could you please help me :-D

many thanks !

Mike Green

There is an arctangent function (operator) in PBasic (ATN). Look in the help files for the Stamp Editor or in the Stamp Syntax and Reference Manual if you have that.

Jonathan Holle

But this function just returns the angle to a vector specified by X and Y coordinate values ; Am I wrong ?

Martin_H

At one time I was awesome with trig functions, but I'm really rusty now. But when I get to the programming phase of my robot arm I'll need to work all this out in PBASIC. But it looks like arcsin and arccos can be defined in terms of arctan and the use of the half angle formula. Have a look here: http://en.wikipedia.org/wiki/Inverse_trigonometric_functions

Tracy Allen

Jonathan, the Stamp ATN operator (x ATN y) does take the coordinates x and y, but the answer depends only on the ratio y/x (within quadrants 1 and 4). So (1000,1000) and (7,7) should give the same angle, 45°, or 32 brads in Stampese. If you are given a ratio, you can translate that into coordinates to plug into x and y. The related function, (x HYP y), returns the length of the vector, and that of course is different for those two points.

I have a computation of the ARCTAN (using CORDIC math) posted at
emesystems.com/programs/cordic-atn.bpe
emesystems.com/BS2mathC.htm
It is more accurate than the Stamp ATN operator, but slower.

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Tracy Allen
www.emesystems.com