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Class Line

class Line
The Line class defines a new object type for a line. It is in a sense a "point-slope" definition of a line. A Line has a base point and a direction, the direction being a unit vector. This is an effective way of defining a line in a way that does not limit it to any specific segment and allows for Affine Transformations to be applied.
Defined in Line.js

Variable Summary
mathnetics.point3D base
The "anchor" point.
mathnetics.point3D direction
The direction of the line; will be a unit vector.
public static Line x
The x-axis.
public static Line y
The y-axis.
public static Line z
The z-axis.

Constructor Summary
Line (Vector base, Vector direction)
Line (Line line)
The constructor function for a new Line.

Function Summary
public boolean contains (mathnetics.point3D point)
Tests to see if a point lies on the line.
public Number distanceFrom (Line line)
public Number distanceFrom (Plane plane)
public Number distanceFrom (mathnetics.point3D point)
Gets the distance between a line and another line, plane, or a point.
public boolean equalTo (Line line)
Tests two lines for equality.
public mathnetics.point3D intersection (Plane plane)
public mathnetics.point3D intersection (Line line)
Finds the UNIQUE intersection of a line and another Line or Plane.
public boolean intersects (Plane plane)
public boolean intersects (Line line)
Tests if this line intersects with a given line or plane.
public boolean isParallel (Line line)
public boolean isParallel (Plane plane)
Tests to see if a line is parallel to another line or plane.
public boolean liesIn (Plane plane)
Tests if a Line lies in a given Plane.
public mathnetics.point3D pointAt (Number t)
Returns the point on the line at a given value of t.
public mathnetics.point3D pointClosestTo (Line line)
public mathnetics.point3D pointClosestTo (Vector point)
Finds the point on this line closest to a given line or point.
public Line reflectionIn (Plane plane)
public Line reflectionIn (Line line)
public Line reflectionIn (mathnetics.point3D point)
Returns the line's reflection in the given point, line, or plane.
public Line rotate (Number deg, Line line)
Rotates a line through an angle about an arbitrary line.
public String toString()
Returns a string representation of the Line.
public Line translate (Number dx, Number dy, Number dz)
Returns a new Line that is the old one translated by dx, dy, and dz.

Variable Details

variable mathnetics.point3D base

The "anchor" point.

variable mathnetics.point3D direction

The direction of the line; will be a unit vector. Use mathnetics.point3D object for this to allow Affine Transformations.

variable public static Line x

The x-axis. Base: (0,0,0), Direction: Vector.i

variable public static Line y

The y-axis. Base: (0,0,0), Direction: Vector.j

variable public static Line z

The z-axis. Base: (0,0,0), Direction: Vector.k

Constructor Details

constructor Line

Line(Vector base, Vector direction)
Line(Line line)
The constructor function for a new Line. If only a Line object is supplied as a parameter, a duplicate of that Line will be created.
Parameters:
standard
base - the base point of the Line; can be a mathnetics.point2D, mathnetics.point3D or Vector (of dimension 2 or 3) object. The actual base point of the Line will be a point3D object.
direction the direction of the Line; can be a mathnetics.point2D, mathnetics.point3D or Vector. Actual direction will be a normalized point3D object.
clone
line - the line to clone as a new one

Function Details

function contains

public boolean contains(mathnetics.point3D point)
Tests to see if a point lies on the line.
Parameters:
point - the point to test
Returns:
true iff point is on line, false otherwise

function distanceFrom

public Number distanceFrom(Line line)
public Number distanceFrom(Plane plane)
public Number distanceFrom(mathnetics.point3D point)
Gets the distance between a line and another line, plane, or a point.
Parameters:
Line
line
Plane
plane - not implemented yet!
Point
point - can also be a mathnetics.point2D
Returns:
the distance between object and the line; 0 if two lines have same base or one contains the base of the other

function equalTo

public boolean equalTo(Line line)
Tests two lines for equality. Will return true if line is parallel or antiparallel.
Parameters:
line - the line to compare
Returns:
true if line has same base point and is parallel or antiparallel

function intersection

public mathnetics.point3D intersection(Plane plane)
public mathnetics.point3D intersection(Line line)
Finds the UNIQUE intersection of a line and another Line or Plane.
Parameters:
Plane
plane - not implemented yet!
Line
line
Returns:
the intersection point (null if obj does not intersect with line)

function intersects

public boolean intersects(Plane plane)
public boolean intersects(Line line)
Tests if this line intersects with a given line or plane.
Parameters:
Plane
plane
Line
line - to test for intersection with the line
Returns:
true if there is a unique intersection point between the line and the given line or plane, false otherwise

function isParallel

public boolean isParallel(Line line)
public boolean isParallel(Plane plane)
Tests to see if a line is parallel to another line or plane.
Parameters:
Line
line - Line with which to test parallelity
Plane
plane - a Plane, with which to test parallelity
Returns:
true if parallel or anti-parallel, false otherwise

function liesIn

public boolean liesIn(Plane plane)
Tests if a Line lies in a given Plane.
Parameters:
plane - the plane which may or may not contain this Line
Returns:
true iff Line lies in plane, false otherwise

function pointAt

public mathnetics.point3D pointAt(Number t)
Returns the point on the line at a given value of t.
Parameters:
t - the time value at which to find the point on the line
Returns:
this.base + t*this.direction

function pointClosestTo

public mathnetics.point3D pointClosestTo(Line line)
public mathnetics.point3D pointClosestTo(Vector point)
Finds the point on this line closest to a given line or point.
Parameters:
Line
line - the line from which to find the closest point on this line
Point
point - a mathnetics.point2D/3D (or Vector)
Returns:
the point on the original line closes to obj

function reflectionIn

public Line reflectionIn(Plane plane)
public Line reflectionIn(Line line)
public Line reflectionIn(mathnetics.point3D point)
Returns the line's reflection in the given point, line, or plane.
Parameters:
Plane
plane - the plane in which to reflect
Line
line
point
point - can also be a point2D or Vector
Returns:
a new line, the old one reflected in obj

function rotate

public Line rotate(Number deg, Line line)
Rotates a line through an angle about an arbitrary line. Be careful, rotation axis' direction affects the outcome!
Parameters:
deg - the degrees, in radians, to rotate the line
line - the line about which to rotate this line
Returns:
a new line that is the old one rotated

function toString

public String toString()
Returns a string representation of the Line.
Returns:
the string representation of the line, containing all relevant info

function translate

public Line translate(Number dx, Number dy, Number dz)
Returns a new Line that is the old one translated by dx, dy, and dz. Note that direction does not change in a translation, only the base point.
Parameters:
dx - the x translation
dy - the y translation
dz - the z translation
Returns:
a new Line, the old one translated