Coordinate Conversions: Rectangular, Cylindrical, Spherical

Code:
EXPORT COORDCONV()

BEGIN

// 2014-02-03 EWS

// updated 2016-05-01

// Source: CRC



LOCAL ch,X,Y,Z,R;

LOCAL θ,ρ,φ;



CHOOSE(ch,"Coord. Conv.","Cart→Cyl",

"Cyl→Cart","Cyl→Sph","Sph→Cyl",

"Cart→Sph","Sph→Cart");



CASE



IF ch==1 THEN 

INPUT({X,Y,Z});

RETURN [√(X²+Y²),ARG(X+Y*i),Z];

END;



IF ch==2 THEN 

INPUT({R,θ,Z});

RETURN [R*COS(θ),R*SIN(θ),Z]; END;



IF ch==3 THEN

INPUT({R,θ,Z});

RETURN [√(R²+Z²),ARG(Z+R*i),θ];

END;



IF ch==4 THEN

INPUT({ρ,φ,θ});

RETURN [ρ*SIN(φ),θ,ρ*COS(φ)];

END;



IF ch==5 THEN

INPUT({X,Y,Z});

RETURN [√(X²+Y²+Z²),

ARG(Z+*√(X²+Y²)),ARG(X+i*Y)];

END;



IF ch==6 THEN

INPUT({ρ,θ,φ});

RETURN [ρ*COS(θ)*SIN(φ),ρ*SIN(θ)*SIN(φ),

ρ*COS(θ)];

END;



DEFAULT

RETURN "CANCELLED";

END;



END;