## DESCRIPTION
## Parametric equations: graphing a parametric surface in space
## ENDDESCRIPTION

## KEYWORDS('parametric', 'graphing a surface in space')

## DBsubject('WeBWorK')
## DBchapter('WeBWorK Tutorial')
## DBsection('Fort Lewis Tutorial 2011')
## Date('01/30/2011')
## Author('Paul Pearson')
## Institution('Fort Lewis College')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')


###########################
#  Initialization

DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"LiveGraphicsParametricSurface3D.pl",
);

TEXT(beginproblem());


##########################
#  Setup

Context("Numeric");

Context()->variables->are(x=>"Real",y=>"Real",z=>"Real",u=>"Real",v=>"Real");

$plot = ParametricSurface3D(
Fx => Formula("3*cos(u)*sin(v)"),
Fy => Formula("3*sin(u)*sin(v)"),
Fz => Formula("3*cos(v)"),
uvar => 'u', # theta
vvar => 'v', # phi
umin => 0,
umax =>  2*pi,
vmin =>  0,
vmax =>  pi,
usamples => 15,
vsamples => 15,
axesframed => 1,
xaxislabel => "X",
yaxislabel => "Y",
zaxislabel => "Z",
mesh => 0,
outputtype => 4,
);


##########################
#  Main Text 

Context()->texStrings;
BEGIN_TEXT
\{ 
Live3Ddata(
$plot,
image => "sphere.png", 
size => [400,400],
tex_size => 600,
tex_center => 1,
scale => 1.1,
);
\}
END_TEXT
Context()->normalStrings;


########################
#  Answer Evaluation

$showPartialCorrectAnswers = 1;


############################
#  Solution

Context()->texStrings;
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.');

ENDDOCUMENT();