Class point3D

Object
   |
   +--Vector
         |
         +--point3D

class point3D

extends Vector

The point3D class defines a point in 3-dimensional Euclidean space via homogeneous coordinates (i.e. as a 4-vector (x,y,z,1)). This allows affine transformations to be applied to 3-D points via matrix multiplication.
Defined in point3D.js

Requires:

- Vector

Field Detail

components

Array components

The components of the 3D point. This allows multiplication by affine transformation matrices and other useful Vector operations.

n

<final> Integer n

The "dimension" of the point; ALWAYS 3. Important that this.n != 3; gives "illusion" of 3-D vector while allowing multiplication by matrices with 3 columns for transformations

See Also:

Constant Field Values

x

Number x

The x-value of the 3D point.

y

Number y

The y-value of the 3D point.

z

Number z

The z-value of the 3D point.

zero

<static> Object zero

point3D

point3D(<Number> x, <Number> y, <Number> z)

Constructor function. Makes a new 3D point (x,y,z,1).

Parameters:
x - the x component
y - the y component
z - the z component

Requires:
- Vector

map

point3D map(func)

Maps this point to a new 3D point according to a given function. Overwrites the map function of the Vector class. Used internally for things like addition, multiplication, dot products, etc.

Parameters:
func - {Object} the mapping function

Returns:
the new, mapped point

rotate

Object rotate(<Number> theta, <Object> axis)

Rotates a point3D object through an angle theta about an arbitrary axis.

Parameters:
theta - the degree (in radians) to rotate the point
axis - the axis about which to rotate; either a point3D, 3-D Vector or 3D Array

rotateX

point3D rotateX(<Number> phi)

Rotates a 3D point through an angle phi about the x axis and returns a new 3D point.

Parameters:
phi - the angle in radians to rotate the point

Returns:
a new point3D object that has been rotated an angle phi around the x axis

rotateY

point3D rotateY(<Number> theta)

Rotates a 3D point through an angle theta about the y axis and returns a new 3D point.

Parameters:
theta - the angle in radians to rotate the point

Returns:
a new point3D object that has been rotated an angle theta around the y axis

rotateZ

point3D rotateZ(<Number> psi)

Rotates a 3D point through an angle psi about the y axis and returns a new 3D point.

Parameters:
psi - the angle in radians to rotate the point

Returns:
a new point3D object that has been rotated an angle psi around the z axis

toSpherical

point3D toSpherical()

Converts a point in Cartesian coordinates to spherical coordinates (r, psi, theta).

Returns:
a new point3D (x,y,z,1) = (r (length), arctan(sqrt(x^2+y^2)/z), arctan(y/x))

toString

String toString()

Produces a string representation of the point. Overwrites the toString function of the Vector class.

Returns:
the string (x,y,z)

toVector

Vector toVector()

Converts point3D object back to a Vector. Will no longer be homogeneous coordinates.

Returns:
the vector [x,y,z]

translate

point3D translate(<Number> dx,<Number> dy,<Number> dz)

Returns a new 3D point (x',y',z',1) = (x+dx,y+dy,z+dz,1).

Parameters:
dx - the x translation
dy - the y translation
dz - the z translation

Returns:
a new point3D object that is the original point translated