<p><b>Abstract</b>—Given a three-dimensional (3D) array of function values <it>F</it><sub><it>i</it>, <it>j</it>,<it>k</it></sub> on a rectilinear grid, the marching cubes (MC) method is the most common technique used for computing a surface triangulation <tmath>${\cal T}$</tmath> approximating a contour (isosurface) <it>F</it>(<it>x</it>, <it>y</it>, <it>z</it>) = <it>T</it>. We describe the construction of a <it>C</it><super>0</super>-continuous surface consisting of rational-quadratic surface patches interpolating the triangles in <tmath>${\cal T}.$</tmath> We determine the Bézier control points of a single rational-quadratic surface patch based on the coordinates of the vertices of the underlying triangle and the gradients and Hessians associated with the vertices.</p>