Examples of Curves
Section 5.1 starts from the basic notion of a regular curve. Then we investigate cycloidal curves and other remarkable parametric curves, as well as curves given implicitly as level curves of functions in two variables. The level sets are useful in solving problems with conditional extrema. We study the variational calculus for functions of one variable and employ it to derive Euler’s spiral. In Section 5.2 we study some fractal curves. Section 5.3 discusses the basic MATLAB® capabilities for plotting space curves, surveys the parallel and perspective projections, and presents curves with shadows on planar, cylindrical, or spherical displays. Section 5.4 introduces helix-type curves on surfaces of revolution and studies curves obtained by the intersection of pairs of surfaces.