The table below shows a few other examples of contour maps for common 3D surfaces: Below is a contour map of the above hemisphere, using planes z = 3, z = 5, and others (there are infinitely many contours for the hemisphere). Translating these level curves onto the xy-axis creates a contour map of the hemisphere. Also, note that these contours are level curves that are parallel to the xy-plane. The intersections of the planes with the hemisphere form two contours, both of which are circles with centers about the z-axis the circle formed by plane z = 3 has radius of 3√3 and the circle formed by z = 5 has radius of √11. The graph of the hemisphere, is intersected by planes z = 3 and z = 5. These curves are also referred to as level curves since their distance from the xy-plane is k for any point on the plane. If a plane z = k, where k is some constant, intersects the surface, a contour with the equation k = f(x, y) is formed. Let z = f(x,y) be a function of two variables that forms a curved surface in the 3D coordinate plane. Each curve in the figure above represents an increase in elevation of 100 ft. The curves of a topographic map, referred to as contours or contour lines, are used to depict the varying elevation of the terrain. A topographic map is a two-dimensional (2D) representation of the three-dimensional features of the Earth's surface, such as hills. The figure depicts a representation of some hilly physical terrain along with its topographic map. Home / calculus / vector / contour ContourĬontour plots are used to depict functions that have a two-dimensional input with a one-dimensional output.
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