# Class LemniscatePath

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)
``````

## 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)

• Sets whether the path is a closed loop, ending at the same point it starts.

#### Parameters

• ##### value: boolean

whether the path is a closed loop

#### Returns void

• Sets the ending value for `t` in the parameteric equation defining the path.

#### Parameters

• ##### value: number

ending value for `t`

#### Returns void

• Sets the starting value for `t` in the parameteric equation defining the path.

#### Parameters

• ##### value: number

starting value for `t`

#### Returns void

• 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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