The window "Domain" displays a domain and a point
(u_{0},
v_{0}) in the domain.

The window "Surface: X(u, v)" shows the torus X(u, v) = ((2 + cos(v))cos(u), (2 +
cos(v))sin(u), sin(v)), the point X(u_{0}, v_{0}), the
tangent
vectors X_{u}(u_{0}, v_{0}) and X_{v}(u_{0},
v_{0}) with their
tails at X(u_{0}, v_{0}), the
normal vector N(u_{0}, v_{0}), also with its tail at X(u_{0},
v_{0}), and the
osculating paraboloid to X(u, v) at X(u_{0}, v_{0}).

The window "Projection" displays an alternate view of the display in the "Surface X(u, v)"
window with X(u_{0}, v_{0}) as the origin, X_{u}(u_{0},
v_{0})
giving the direction of
the x-axis, N(u_{0}, v_{0}) giving the direction of the
z-axis,
and N(u_{0}, v_{0})
× X_{u}(u_{0}, v_{0}) giving the direction of
the y-axis.

The control
window
displays L_{11}, L_{12}, L_{21}, L_{22},
and L_{11}L_{22} – L_{12}L_{21}. When L_{11}L_{22}
– L_{12}L_{21} is positive, negative, or zero, the
point X(u_{0}, v_{0}) will be elliptic, hyperbolic, or
either
parabolic or
planar, respectively. The point X(u_{0}, v_{0}) will be
planar if
and only if
all coefficients of the second fundamental form are 0. It is possible
to change u_{0} and v_{0}.