Lemniscate curve; a 'figure eight' path.

Equation in polar coords is:

r^2  =  2 a^2  cos(2t)
r = (+/-) a Sqrt(2 cos(2t))

where a=constant, t=angle from -Pi/4 to Pi/4, and r=radius

To get both lobes with the direction of travel increasing across the origin, define

T = -t + Pi/2

Then

r = a Sqrt(2 cos(2t))   for -Pi/4 < t < Pi/4
r = -a Sqrt(2 cos(2T))   for Pi/4 < t < 3 Pi/4

To get into Cartesian coords, we use

x = r cos(t)
y = r sin(t)

Hierarchy (view full)

Implements

Constructors

Methods

  • Name of this object, either the language-independent name for scripting purposes or the localized name for display to user.

    The language-independent name should be the same as the English version but capitalized and with spaces and dashes replaced by underscore, see Util.toName and nameEquals.

    Parameters

    • Optional opt_localized: boolean

      true means return the localized version of the name; default is false which means return the language independent name.

    Returns string

    name of this object

  • Whether this ParametricPath has the given name, adjusting for the transformation to a language-independent form of the name, as is done by Util.toName.

    Parameters

    • name: string

      the English or language-independent version of the name

    Returns boolean

    whether this ParametricPath has the given name (adjusted to language-independent form)

  • Returns the x value for the given value of t in the parametric equation.

    Parameters

    • t: number

      the value of t in the parametric equation

    Returns number

    the x value for the given value of t

  • Returns the y value for the given value of t in the parametric equation.

    Parameters

    • t: number

      the value of t in the parametric equation

    Returns number

    the y value for the given value of t

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