A contour line (also isoline, isopleth, or isarithm) of a
function of two variables is a curve along which the function
has a constant value. In cartography, a contour line (often just
called a "contour") joins points of equal elevation (height)
above a given level, such as mean sea level. A contour map is a
map illustrated with contour lines, for example a topographic
map, which thus shows valleys and hills, and the steepness of
slopes. The contour interval of a contour map is the difference
in elevation between successive contour lines. More generally, a
contour line for a function of two variables is a curve
connecting points where the function has the same particular
value. The gradient of the function is always perpendicular to
the contour lines. When the lines are close together the
magnitude of the gradient is large: the variation is steep. A
level set is a generalization of a contour line for functions of
any number of variables. Contour lines are curved or straight
lines on a map describing the inter