Coordinate Conversions: Rectangular, Cylindrical, Spherical

[Eddie W. Shore]

PLEASE SCROLL TO THE END OF THIS THREAD, the most recent version is there. Thanks,

Eddie

Code:

EXPORT COORDCONV()
BEGIN
// 2014-02-03 EWS
// 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*√(-1)),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*√(-1)),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+√(-1)*√(X²+Y²)),ARG(X+√(-1)*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;

Note: Sqrt(-1) is that "I" character (Shift+3).

Eddie

[Eddie W. Shore]

(02-04-2014 04:48 AM)Eddie W. Shore Wrote:  

Code:

EXPORT COORDCONV()
BEGIN
// 2014-02-03 EWS
// 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*√(-1)),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*√(-1)),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+√(-1)*√(X²+Y²)),ARG(X+√(-1)*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;

Note: Sqrt(-1) is that "I" character (Shift+3).

Eddie

** PLEASE IGNORE THIS PROGRAM - There is a problem with one of the commands (ARG) - apologizes for any inconvenience. Hope to have a working solution soon. Eddie

[Han]

Change sqrt(-1) to lower-case i (and ensure lower-case i is not declared as a local variable); or use the "i" character [Shift][3]. This will work around the possibility that users may not have enabled complex output from real input (page 1 in the Home settings).

[Eddie W. Shore]

(12-16-2014 02:11 PM)Han Wrote:  Change sqrt(-1) to lower-case i (and ensure lower-case i is not declared as a local variable); or use the "i" character [Shift][3]. This will work around the possibility that users may not have enabled complex output from real input (page 1 in the Home settings).

Thanks, Han. I works better now.

Code:

OK try this, use the lowercase "i" instead of the "i" from [Shift]+[3] or sqrt(-1). Seems to work. Please let me know. Thanks Luigi. 

EXPORT COORDCONV()
BEGIN
// 2014-02-03 EWS
// 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;

[BERNARD MICHAUD]

I notice that in the section below "ρ*COS(θ)];" should theta be replaced with 'phi'.
I tried X=8, Y=6, Z=4 it returns 10.77, 68.2, 36.87. Working it in reverse = 8, 6, 8.62.
That's 8.62 instead of 4.

IF ch==6 THEN
INPUT({ρ,θ,φ});
RETURN [ρ*COS(θ)*SIN(φ),ρ*SIN(θ)*SIN(φ),
ρ*COS(θ)];
END;

[Eddie W. Shore]

Thank you Bernard.

The corrected program below:

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;

[BERNARD MICHAUD]

Sorry Eddie if I misled you. What I mean is this. You have the first section below, but should be the second section. ρ*COS(θ)]; should be ρ*COS(φ)];

First section
IF ch==6 THEN
INPUT({ρ,θ,φ});
RETURN [ρ*COS(θ)*SIN(φ),ρ*SIN(θ)*SIN(φ),
ρ*COS(θ)]; error
END;

Second section
IF ch==6 THEN
INPUT({ρ,θ,φ});
RETURN [ρ*COS(θ)*SIN(φ),ρ*SIN(θ)*SIN(φ),
ρ*COS(φ)]; correct
END;