NAME
    super_ellipse

FUNCTION
    super_ellipse(slices, rx, ry, p)

NOTES
    Creates 2D super ellipse line.

    Based on the equations
    
        x = rx * cos(phi)^p
        y = ry * sin(phi)^p
        
    of Paul Bourke' home page (http://astronomy.swin.edu.au/~pbourke/surfaces/mobius/).
    Where 0 <= phi <= pi / 2 and 0 < p < infinite.
    
    Example:
        require("plot_simple")
        plot = plot_simple.new()
        plot:add_static(zeGrf.new("light"))
        require("super_ellipse")
        xyz, nor = super_ellipse(36, 100, 100, .5)
        line = zeGrf.new("line")
        line:set{type = "strip", vertex = xyz, vertex_normal = nor, color = {0, .5, .5, 1}}
        plot:add(line)
        plot:animate()    
 NPUTS
    slices - slices between 0 and  pi/2
    rx     - size parameter in x-direction
    ry     - size parameter in y-direction
    p      - shape parameter

OUTPUTS
    Two zeArray objects containing coordinates and normals.
    The z-component is zero.

SOURCE

require("curve_generator")

function super_ellipse(slices, rx, ry, p)
    assert(slices >= 16)
    assert(rx > 0)
    assert(ry > 0)
    assert(p > 0)

    local function cfunc(t)
        return rx * math.cos(t)^p, ry * math.sin(t)^p
    end

    local function nfunc(t)
        local cos, sin = math.cos(t), math.sin(t)
        local x, y, d
        x = ry * cos * sin^p / sin
        y = rx * sin * cos^p / cos
        d = math.sqrt(x * x + y * y)
        return x/d, y/d
    end

    local T = zeUtl.new("double")
    T:range(1.e-12, 1.5707963/slices, slices+1)
    
    xyz = curve_generator(T, cfunc)
    nor = curve_generator(T, nfunc)
        
    return xyz, nor
end