Need help creating parabola

[nmz787]

I tried converting the example here:
https://github.com/pboyer/verb/blob/master/example/threeMeshIntersectExample.html#L345

to be a parabolic concave surface but am totally new to NURBS. I thought this would work but it doesn't, and I can't seem to find any help online :/

var degree = 2
    , knots = [0, 0, 1, 1]
    , pts = [   [ [0, 0, 0],    [10, 0, 10], [20, 0, 10] , [30, 0, 0] ],
                [ [0, 10, 0],   [10, 10, 10], [20, 10, 10] , [30, 10, 0] ]
            ]

    , wts = [   [ 1, 1, 1, 1],
                [ 1, 1, 1, 1]
            ];

srf1 = new verb.NurbsSurface( degree, knots, degree, knots, pts, wts );

Do you think you provide a parabolic surface example, and also an example of a few cycles of a sine wave? Is there some way I can specify a curve using math operators like sin and cos, without computing a bunch of polylines myself?

[nmz787]

OK, here's what I figured out. Seems to look like a parabola, though I am not sure how to confirm this:

function parabolic_channel(length, width, depth){
  var half_width = width/2;
  var half_length = length/2;
  var degree = 2
    , knots = [0, 0, 0, 1, 1, 1]
    , pts = [   [ [-half_width, -half_length,    0], [0, -half_length, depth], [half_width, -half_length, 0] ],
                [ [-half_width, 0           ,    0], [0,  0          , depth], [half_width, 0           , 0] ],
                [ [-half_width, half_length ,    0], [0, half_length , depth], [half_width, half_length , 0] ]
        ]

    , wts = [   [ 1, 1, 1],
          [ 1, 1, 1],
          [ 1, 1, 1]
        ];

  srf1 = new verb.NurbsSurface( degree, knots, degree, knots, pts, wts );