%% POSTSCRIPT ASIN AND ACOS OPERATORS
%% ==================================

%% Copyright c 2001 by Don Lancaster and Synergetics, Box 809, Thatcher, AZ
%% 85552. (520) 428-4073. mailto:don@tinaja.com

%% All commercial and all media rights ~fully~ reserved. Additional support at
%% http://www.tinaja.com/post01.asp and http://www.tinaja.com/info01.asp

%% These four PostScript utilities generate arcsine and arccos capabilities,
%% both in traditional "atan" and more convenient formats. Predefine them before
%% use in your PostScript code.

%% "arc" or "inverse" operators are used in trig to get from a sine, cosine,
%% tangent, or other function value to the underlying primary angle in degrees.

%% For instance, arcsine (0.5) would be 30 degrees. Only the atan operator is
%% initially defined in PostScript.

%% These utilities work by "completing the triangle" of sides x and y and
%% hypoteneuse (x^2 + y^2)^0.5 and then calling PS atan given x and y.

%% The first two utilities are in the same format as the existing PostScript
%% atan operator. Input TWO triangle sides as noted...

/acos {2 copy dup mul exch dup mul sub sqrt exch pop
exch atan} def      % arccosine use  - xside hypotenuse acos -

/asin {2 copy dup mul exch dup mul sub sqrt exch pop
atan} def           % arcsine use  - yside hypotenuse asin -


%% These two utilities are in a more convenient "input trig, get degrees" format.
%% They call the above two procs..

/trig.acos {1 acos} def  % arcosine from input of trig value

/trig.asin {1 asin} def  % arcosine from input of trig value


%% Demo -- Send to Distiller. Remove or alter before reuse --


1 2 acos ==                 
1 2 asin ==

0 1 acos ==
0 1 asin ==


0.5 trig.acos ==
1 trig.acos ==
0 trig.acos ==
 
0.5 trig.asin ==
1 trig.asin ==
0 trig.asin ==

%% results should be 60.0 30.0 90.0 0.0 60.0 0.0 90.0 30.0 90.0 0.0