NAME
    hyperbolic_paraboloid 

FUNCTION
    hyperbolic_paraboloid(n, r, a, b)

NOTES
    Generate hyperbolic paraboloid (z = x^2/a^2 - y^2/b^2) surface.

    Example:
        require("plot_simple")
        plot = plot_simple.new()
        plot:add_static(zeGrf.new("light"))
        require("hyperbolic_paraboloid")
        xyz, nor = hyperbolic_paraboloid(32, 1, 1, 1)
        xyz:scale(100, 100, 100)
        shape = zeGrf.new("polygon")
        shape:set{type = "quads", vertex = xyz,
                  vertex_normal = nor, color = {0, .7, .7, 1}}
        plot:add(shape)
        plot:animate()
NPUTS
    n    - slices between -r and r
    r    - range
    a, b - hyperbolic parameters

OUTPUTS
    Two zeVertex objects containing coordinates and normals of quads.

SOURCE

require("surface_generator")

function hyperbolic_paraboloid(n, r, a, b)
    assert(n >= 8)
    assert(r > 0)
    assert(a ~= 0)
    assert(b ~= 0)

    a, b = a*a, b*b

    local function sfunc(u, v)
        return u, v, u*u/a - v*v/b
    end

    local function nfunc(u, v)
        return zeMake.normal2(0, 0, 0,   1, 0, 2*u/a,   0, 1, -2*v/b)
    end

    local U, V = zeUtl.new("double", "double")
    U:range(-r, r/n, 2*n+1)
    U:copy(V)
    
    local xyz = surface_generator(U, V, sfunc)
    local nor = surface_generator(U, V, nfunc)

    return xyz, nor
end