Class Sphere3

constructor

• new Sphere3(): Sphere3

  Returns Sphere3

• new Sphere3(equation: string | Equation): Sphere3

  Parameters

  • equation: string | Equation

  Returns Sphere3

• new Sphere3(sphere: Sphere3): Sphere3

  Parameters

  • sphere: Sphere3

  Returns Sphere3

• new Sphere3(
      center: Point,
      radius: InputValue<Fraction>,
      square?: boolean,
  ): Sphere3

  Parameters

  • center: Point
  • radius: InputValue<Fraction>
  • Optionalsquare: boolean

  Returns Sphere3

StaticRELATIVE_POSITION

asCenterRadius

• get asCenterRadius(): this

  Output option: the form (x-a)^2+(y-b)^2+(z-c)^2=r^2 (default). Chainable, persistent.

  Returns this

asDeveloped

• get asDeveloped(): this

  Output option: the developed equation. Chainable, persistent.

  Returns this

center

• get center(): Point

  The center, as a point.

  Returns Point

  Throws

  if the sphere is not defined.

display

• get display(): string

  ASCIIMath rendering of the current state (terminal output, not chainable).

  Returns string

equation

• get equation(): Equation

  The equation (x-a)^2+(y-b)^2+(z-c)^2-r^2=0, as an Equation.

  Returns Equation

  Throws

  if the sphere is not defined.

radius

• get radius(): { display: string; tex: string; value: number }

  The radius, as an object with its tex, its display and its decimal value. It is written as a number when the square of the radius is a perfect square, and as a root otherwise.

  Returns { display: string; tex: string; value: number }

  Throws

  if the sphere is not defined.

squareRadius

• get squareRadius(): Fraction

  The square of the radius, as an exact fraction.

  Returns Fraction

  Throws

  if the sphere is not defined.

tex

• get tex(): string

  LaTeX rendering of the current state (terminal output, not chainable).

  Returns string

clone

• clone(): this

  Full duplicate of this instance, including display state (selected form and options set via as*** / with***). Distinct from copy.

  Returns this

copy

• copy(sphere: Sphere3): this

  Copy the mathematical state of another instance into this (display state is NOT transferred — the receiver keeps its own formatting). Entry point used when constructing/parsing from a same-type input. Distinct from clone. Classes without a real implementation throw NotImplementedError.

  Parameters

  • sphere: Sphere3

  Returns this

isEqual

• isEqual(S: Sphere3): boolean

  True when both spheres have the same center and the same radius.

  Parameters

  • S: Sphere3

  Returns boolean

isPointOnSphere

• isPointOnSphere(P: Point): boolean

  True when the point satisfies the equation of the sphere.

  Parameters

  • P: Point

  Returns boolean

parse

• parse(...values: unknown[]): this

  Replace the sphere with an equation, another sphere, or a center and a radius. Arguments that do not match any form leave the sphere unchanged.

  Parameters

  • ...values: unknown[]

  Returns this

relativePosition

• relativePosition(S: Sphere3): Sphere3RelativePosition

  The relative position of two spheres, as a Sphere3.RELATIVE_POSITION value: interior, exterior, secant, tangent inside or outside, superposed, or concentric.

  Parameters

  • S: Sphere3

  Returns Sphere3RelativePosition

withDigits

• withDigits(digits: number | null): this

  Parameters

  • digits: number | null

  Returns this

  See

  IDisplayDigits.withDigits

StaticfromCenterRadius

• fromCenterRadius(
      center: Point,
      radius: InputValue<Fraction>,
      square?: boolean,
  ): Sphere3

  The sphere with the given center and radius.

  Parameters

  • center: Point
  • radius: InputValue<Fraction>
  • Optionalsquare: boolean

    when true, radius is already the square of the radius.

  Returns Sphere3

StaticfromEquation

• fromEquation(value: InputAlgebra<Equation>): Sphere3

  Does not mutate the input.

  Parameters

  • value: InputAlgebra<Equation>

  Returns Sphere3

  Throws

  if the input is not a valid sphere equation (degree ≠ 2 in x/y/z, or unequal leading coefficients)

StaticfromString

• fromString(str: string): Sphere3

  The sphere of an equation written in a string.

  Parameters

  • str: string

  Returns Sphere3

  Throws

  if the equation is not the one of a sphere.