Sketching Surfaces (Examples)

Example 1: Circular Cylinder

Example 2: Parabolic Cylinder

For sketching the graph of a function

z = f(x, y),

a topographic map, or contour map, can often be used as a first step. It is a method of representing a surface which is often found in atlases. In a topographic map, the curves

f(x, y) = z₀

are sketched in the (x, y) plane for several different constants z₀, and each curve is labeled (Figure 11.1.14). These curves are called level curves, or contours.

Figure 11.1.14

Example 3: Elliptic Paraboloid

Example 4: Hyperbolic Paraboloid

Example 5: Hyperboloid of Two Sheets

Example 6: Plane

Example 7: Saddle Shaped Surface

Example 8: 'Beaker Spout' Shaped Curve