Curves

The use of this tool is exemplified in The Spiral and Parabolic Motion.

The configuration panel of CURVES may have as many lines as desired. Each line defines a curve and looks like this:

[f(t),g(t)]:parameter=t[a,b]N:colour=red

where f and g are expressions that define, for every value of  t in the interval [a,b], the coordinates of a point, and  N is the number de subintervals in which [a,b] is divided to draw the curve.

The functions f and g may be expressions that depend on the parameters of the applet, the variables, the functions and the most common mathematical functions. They should be written as functions of the curve's parameter (in this case t). Afterwards, and separated by  : , the expression parameter=t[a,b]N should follow. This expression defines the name and properties of the parameter of the curve. It starts with the name of the parameter of the curve,  t in this case, which is the name of the variable used in the definition of f and g. Next comes the interval spanned by the parameter of the curve, that is, its initial and final values, in square brackets, followed by the number N of segments to be used in drawing the curve. The curve is aproximated by drawing the N segments joining the consecutive points [f(t),g(t)] for the N+1 values of t that result from dividing [a,b] into N equal subintervals. An expression color=blue may be used to define the colour of the curve (blue in this case).

The following example shows the curves called cycloid, epicycloid and hipocycloid. The reader can modify the parameter r , which corresponds to the radius of the rotating circle, and the parameter a which corresponds to the distance from the center of this circle to the point that generates the curve when the circle rotates without sliding over the x axis. If a=r, the curve is called a cycloid, if a>r the curve is an epicycloid and if a<r it is a hipocycloid.

In the example the number N of segments used to draw the curve was included as a parameter of the applet so the user can change it. For small values of N the graph looks like a polygon but for large values of N the graph looks like an authentic curve.

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	Ministerio de Educación, Cultura y Deporte. Aņo 2000