Class Line

constructor

• new Line(...values: unknown[]): Line

  Parameters

  • ...values: unknown[]

  Returns Line

StaticPARALLEL

StaticPERPENDICULAR

a

• get a(): Fraction

  Coefficient of x in ax + by + c = 0. Setting it does not update the reference point OA.

  Returns Fraction

• set a(value: Fraction): void

  Parameters

  • value: Fraction

  Returns void

asCanonical

• get asCanonical(): this

  Output option for the next tex or display: ax+by+c=0 (default). Chainable.

  Returns this

asCartesian

• get asCartesian(): this

  Output option for the next tex or display: ax+by=-c. Chainable.

  Returns this

asMxh

• get asMxh(): this

  Output option for the next tex or display: y=mx+h, or x=k for a vertical line. Chainable.

  Returns this

asParametric

• get asParametric(): this

  Output option for the next tex or display: a point and a direction vector. Chainable.

  Returns this

asSystem

• get asSystem(): this

  Output option for the next tex or display: the parametric system of x and y. Chainable.

  Returns this

b

• get b(): Fraction

  Coefficient of y in ax + by + c = 0. Setting it does not update the reference point OA.

  Returns Fraction

• set b(value: Fraction): void

  Parameters

  • value: Fraction

  Returns void

c

• get c(): Fraction

  Constant term in ax + by + c = 0. Setting it does not update the reference point OA.

  Returns Fraction

• set c(value: Fraction): void

  Parameters

  • value: Fraction

  Returns void

d

• get d(): Vector

  Direction vector (b, -a), oriented to the right unless the line was built from a direction pointing to the left. Setting it keeps the point OA and changes the direction.

  Returns Vector

• set d(value: Vector): void

  Parameters

  • value: Vector

  Returns void

director

• get director(): Vector

  Same as d.

  Returns Vector

display

• get display(): string

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

  Returns string

height

• get height(): Fraction

  Intercept h of y = mx + h: -c/b. Infinite for a vertical line.

  Returns Fraction

n

• get n(): Vector

  Normal vector computed from the direction (the direction turned by 90 degrees). It can be the opposite of normal.

  Returns Vector

normal

• get normal(): Vector

  Normal vector (a, b).

  Returns Vector

OA

• get OA(): Vector

  A point of the line, as a vector. Setting it moves the line through that point and keeps its direction.

  Returns Vector

• set OA(value: Point | Vector): void

  Parameters

  • value: Point | Vector

  Returns void

slope

• get slope(): Fraction

  Slope m of y = mx + h: -a/b. Infinite for a vertical line.

  Returns Fraction

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(value: Line): 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

  • value: Line

  Returns this

distanceTo

• distanceTo(pt: Point): Root

  Distance from a point to the line, as an exact reduced Root.

  Parameters

  • pt: Point

  Returns Root

getEquation

• getEquation(): Equation

  The equation ax + by + c = 0 with integer coefficients, as an Equation.

  Returns Equation

getValueAtX

• getValueAtX(value: number | Fraction): Fraction

  Returns an invalid (NaN) Fraction if the line is vertical (no y term).

  Parameters

  • value: number | Fraction

  Returns Fraction

getValueAtY

• getValueAtY(value: number | Fraction): Fraction

  Returns an invalid (NaN) Fraction if the line is horizontal (no x term).

  Parameters

  • value: number | Fraction

  Returns Fraction

hitSegment

• hitSegment(A: Point, B: Point): boolean

  True when the line crosses the segment [AB], ends included.

  Parameters

  • A: Point
  • B: Point

  Returns boolean

intersection

• intersection(line: Line): LineIntersection

  Intersection with another line, as {point, hasIntersection, isParallel, isSame}. The point is null when the lines are parallel or the same.

  Parameters

  • line: Line

  Returns LineIntersection

isEqual

• isEqual(line: Line): boolean

  True when both lines are the same line, whatever their coefficients.

  Parameters

  • line: Line

  Returns boolean

isHorizontal

• isHorizontal(): boolean

  True when the slope is zero.

  Returns boolean

isParallelTo

• isParallelTo(line: Line): boolean

  True when the lines have the same direction but are not the same line.

  Parameters

  • line: Line

  Returns boolean

isPerpendicularTo

• isPerpendicularTo(line: Line): boolean

  True when the directions are perpendicular.

  Parameters

  • line: Line

  Returns boolean

isPointOnLine

• isPointOnLine(pt: Point): boolean

  True when the point satisfies the equation of the line.

  Parameters

  • pt: Point

  Returns boolean

isVertical

• isVertical(): boolean

  True when the slope is infinite.

  Returns boolean

parse

• parse(...values: unknown[]): this

  Replace the line with an equation, another line, two points, a point and a vector, or three coefficients.

  Parameters

  • ...values: unknown[]

  Returns this

  Throws

  if the arguments do not describe a line.

project

• project(pt: Point): Point

  Orthogonal projection of pt onto this line.

  Parameters

  • pt: Point

  Returns Point

randomNearPoint

• randomNearPoint(k?: number): Point

  A random point close to the line but not on it.

  Parameters

  • Optionalk: number

    same as in randomPoint.

  Returns Point

randomPoint

• randomPoint(k?: number): Point

  A random point of the line: the point OA moved along the direction vector by a non-zero integer between -k and k.

  Parameters

  • Optionalk: number

    largest multiple of the direction vector (default 3).

  Returns Point

reflect

• reflect(pt: Point): Point

  Reflection of pt through this line (proj is the midpoint of [pt, reflect(pt)]).

  Parameters

  • pt: Point

  Returns Point

simplify

• simplify(): this

  Give the equation the smallest integer coefficients with no common divisor.

  Returns this

withDigits

• withDigits(digits: number | null): this

  Show the coefficients as decimals with digits digits, in every output mode. Persistent (copied by clone()); null goes back to the exact output.

  Parameters

  • digits: number | null

  Returns this

  Throws

  if digits is neither null nor an integer from 0 to 100.

StaticfromCoefficient

• fromCoefficient(
      a: InputValue<Fraction>,
      b: InputValue<Fraction>,
      c: InputValue<Fraction>,
  ): Line

  Build the line ax + by + c = 0. Fractional coefficients are multiplied to become integers.

  Parameters

  • a: InputValue<Fraction>
  • b: InputValue<Fraction>
  • c: InputValue<Fraction>

  Returns Line

StaticfromEquation

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

  Build a line from an equation in x and y of the first degree.

  Parameters

  • value: InputAlgebra<Equation>

  Returns Line

  Throws

  if the equation has no x or y, has another variable, or is not linear.

StaticfromParallel

• fromParallel(parallel: Line, point: Point): Line

  The line through point parallel to parallel.

  Parameters

  • parallel: Line
  • point: Point

  Returns Line

StaticfromPerpendicular

• fromPerpendicular(perpendicular: Line, point: Point): Line

  The line through point perpendicular to perpendicular.

  Parameters

  • perpendicular: Line
  • point: Point

  Returns Line

StaticfromPointAndDirection

• fromPointAndDirection(P: Point | Vector, d: Vector): Line

  The line through a point with a direction vector.

  Parameters

  • P: Point | Vector
  • d: Vector

  Returns Line

  Throws

  if the vector is zero.

StaticfromPointAndLine

• fromPointAndLine(P: Point | Vector, L: Line, orientation?: LineProperty): Line

  The line through a point, parallel (default) or perpendicular to a line.

  Parameters

  • P: Point | Vector
  • L: Line
  • orientation: LineProperty = LineProperty.Parallel

    Line.PARALLEL or Line.PERPENDICULAR.

  Returns Line

StaticfromPointAndNormal

• fromPointAndNormal(P: Point | Vector, n: Vector): Line

  The line through a point with a normal vector.

  Parameters

  • P: Point | Vector
  • n: Vector

  Returns Line

  Throws

  if the normal vector is zero.

StaticfromPoints

• fromPoints(A: Point, B: Point): Line

  The line through two points.

  Parameters

  • A: Point
  • B: Point

  Returns Line

  Throws

  if the points are the same.