# scotttd/RhinoScriptSamples

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 ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ' ParametricEllipsoid.rvb -- February 2012 ' If this code works, it was written by Dale Fugier. ' If not, I don't know who wrote it. ' Works with Rhino 4.0. ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ' The surface of the ellipsoid may be parameterized in several ways. ' One possible choice which singles out the 'z'-axis is: ' x = a * Cos(u) * Cos(v) ' y = b * Cos(u) * Sin(v) ' z = c * Sin(u) ' where: ' -pi/2 <= u <= pi/2, And -pi <= v <= pi ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Option Explicit ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ' ParametricEllipsoid ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Sub ParametricEllipsoid() ' Variables Dim a, b, c Dim dom_u(1), dom_v(1), num_u(1), num_v(1) Dim i, j, st(1), uv(1), pts(), crvs() ' Prompt for coefficents a = Rhino.GetInteger("A Coefficient", 1, 1) If IsNull(a) Then Exit Sub b = Rhino.GetInteger("B Coefficient", 1, 1) If IsNull(b) Then Exit Sub c = Rhino.GetInteger("C Coefficient", 1, 1) If IsNull(c) Then Exit Sub ' Define domain of ellipsoid dom_u(0) = -(Rhino.PI / 2.0) dom_u(1) = Rhino.PI / 2.0 dom_v(0) = -(Rhino.PI) dom_v(1) = Rhino.PI ' Define a domain of point samples ' To sample more points, increase num_u(1) and num_v(1) num_u(0) = 0 num_u(1) = 20 num_v(0) = 0 num_v(1) = 20 ' Storate for calculated point and temporary curves ReDim pts(num_u(1)) ReDim crvs(num_v(1)) ' Calculate ellipsoid points and interpolate For j = num_v(0) To num_v(1) For i = num_u(0) To num_u(1) st(0) = NormalizedAt(num_u(0), num_u(1), i) st(1) = NormalizedAt(num_v(0), num_v(1), j) uv(0) = ParameterAt(dom_u(0), dom_u(1), st(0)) uv(1) = ParameterAt(dom_v(0), dom_v(1), st(1)) pts(i) = PointAt(a, b, c, uv(0), uv(1)) Next crvs(j) = Rhino.AddInterpCurve(pts) Next ' Loft the results Call Rhino.AddLoftSrf(crvs) ' Delete the temporary curves 'Call Rhino.DeleteObjects(crvs) End Sub ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ' PointAt ' Evaluates an ellipsoid at a parameter ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Function PointAt(a, b, c, u, v) Dim pt(2) pt(0) = a * Cos(u) * Cos(v) pt(1) = b * Cos(u) * Sin(v) pt(2) = c * Sin(u) PointAt = pt End Function ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ' ParameterAt ' Converts a normalized parameter to a domain value ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Function ParameterAt(t0, t1, x) ParameterAt = (1.0 - x) * t0 + x * t1 End Function ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' ' NormalizedAt ' Converts a domain value to a normalized parameter ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Function NormalizedAt(t0, t1, t) Dim x : x = t0 If (t0 <> t1) Then If (t = t1) Then x = 1.0 Else x = (t - t0)/(t1 - t0) End If End If NormalizedAt = x End Function