Parametric Curve Command

Curve

Curve[Expression e1, Expression e2, Parameter t, Number a, Number b]: Yields the Cartesian parametric curve for the given x-expression e1 and y-expression e2 (using parameter t) within the given interval [a, b].       
Example: Input of c = Curve[2 cos(t), 2 sin(t), t, 0, 2 pi] creates a circle with radius 2 around the origin of the coordinate system.

 

Note: Parametric curves can be used with pre-defined functions and arithmetic operations.

Example: Input c(3) returns the point at parameter position 3 on curve c.

 

Note: Using the mouse you can also place a point on a curve using tool mode_point_16 New Point or command Point. Since the parameters a and b are dynamic you could use slider variables as well (see tool mode_slider_32.gif Slider).

Commands for Parametric Curves

Curvature[Point, Curve]: Calculates the curvature of the curve in the given point.

CurvatureVector[Point, Curve]: Yields the curvature vector of the curve in the given point.

Derivative[Curve]: Returns the derivative of the parametric curve.

Derivative[Curve, Number n]: Returns the nth derivative of the parametric curve.

Length[Curve, Number t1, Number t2]: Yields the length of the curve between the parameter values t1 and t2.

Length[Curve c, Point A, Point B]: Yields the length of curve c between two points A and B that lie on the curve.

OsculatingCircle[Point, Curve]: Yields the osculating circle of the curve in the given point.

Tangent[Point, Curve]: Creates the tangent to the curve in the given point.


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