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Vectors.md

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Vectors

Design choices are still being made over the Vec3 and Vec4 classes. Mostly due to graphical rotation matrices supporting both Vec3 and Vec4 classes. Currently a large number of function are unimplemented for the Vec4 class.

The vector classes contain parameters x, y, z and w depending on the class, as follows,

Vec2 (x, y)
Vec3 (x, y, z)
Vec4 (x, y, z, w)

Functions

  1. Initalisation
  2. Standard
  3. Comparison
    • Equal
    • [Not Equal](#Not Equal)
  4. [Extra functionality](#Extra Functionality)
    • Zero
    • [Distance Between Vectors](#Distance Between Vectors)
    • Magnitude
    • Normalize
    • [Cross Product](#Cross Product)
    • [Dot Product](#Dot Product)
    • [Angle Between Vectors](#Angle Between Vectors)
    • [Midpoint Between Vectors](#Midpoint Between Vectors)
    • [Rotate Vector](#Rotate Vector)
    • [Set Vector Rotation](#Set Vector Rotation)
    • [Scalar Triple Product](#Scalar Triple Product)
    • [Vector Triple Product](#Vector Triple Product)

Initalisation

Calling the vector with out parameters will initalise a vector to zero

>>> import pyclid
>>> pyclid.Vec2()
<0, 0>
>>> pyclid.Vec3()
<0, 0, 0>
>>> pyclid.Vec4()
<0, 0, 0, 0>

Or vectors can be initalised with parameters

>>> pyclid.Vec2(1, 2)
<1, 2>
>>> pyclid.Vec3(1, 2, 3)
<1, 2, 3>
>>> pyclid.Vec4(1, 2, 3, 4)
<1, 2, 3, 4>

Standard

Addition

Requires two Vec2 objects,
Returns a Vec2 object

>>> v1 = pyclid.Vec2(1, 2)
>>> v2 = pyclid.Vec2(3, 4)
>>> v3 = v1 + v2
>>> print v3
<4, 6>

Subtraction

>>> v1 = pyclid.Vec2(6, 2)
>>> v2 = pyclid.Vec2(1, 2)
>>> v3 = v1-v2
>>> print v3
<5, 0>

Multiplication

Must be used with a scalar value

>>> v = pyclid.Vec2(2, 4)
>>> print v*2
<4, 8>

Division

Must be used with a scalar value

>>> v = pyclid.Vec2(2, 4)
>>> print a/2
<1, 2>

Comparison

Comparison is performed on the same parameters between two vector objects or the same type

Equal

>>> v1 = pyclid.Vec2(1, 2)
>>> v2 = pyclid.Vec2(1, 2)
>>> v1 == v2
True

>>> v1 = pyclid.Vec2(1, 2)
>>> v2 = pyclid.Vec2(1, 3)
>>> v1 == v2
False

Not Equal

>>> v1 = pyclid.Vec2(1, 1)
>>> v2 = pyclid.Vec2(1, 2)
>>> v1 != v2
True

Extra functionality

Zero

Sets the vector parameters to zero

>>> v = pyclid.Vec2(1, 2)
>>> v.zero()
<0, 0>

Distance Between Vectors

Find the distance between two vectors using the following equation,

distance = sqrt((u.x**2 - v.x**2) + (u.y**2 - v.y**2))

>>> a = pyclid.Vec2(0, 0)
>>> b = pyclid.Vec2(1, 1)
>>> a.distance_between(b)
1.4142135623730951

Magnitude

Returns a float of the magnitue of the vector. Note, the abs() operator can be used in place of magnitude

>>> v = pyclid.Vec2(3, 4)
>>> v.magnitude()
5.0
>>> abs(v)
5.0

Normalize

Scales the current vector so that its magnitude is equal to 1.0

>>> v = pyclid.Vec2(3, 4)
>>> v.normalize()
<0.6, 0.8>

Cross Product

Vector cross Product

>>> v = pyclid.Vec2(1, 2)
>>> u = pyclid.Vec2(3, 4)
>>> v.cross(u)
-2

Dot Product

Vector dot product

>>> v = pyclid.Vec2(1, 2)
>>> u = pyclid.Vec2(3, 4)
>>> v.cross(u)
11

Angle Between Vectors

Returns the angle between two vectors using <0, 0> as root

>>> v = pyclid.Vec2(0, 1)
>>> u = pyclid.Vec2(1, 0)
>>> v.angle(u)
1.57079632679
(0, 1)
      |
      |
(0, 0)|_____(1, 0)

Midpoint Between Vectors

Finds the midpoint between two vectors

>>> v = pyclid.Vec2(0, 0)
>>> u = pyclid.Vec2(2, 2)
>>> v.mid_point(u)
<1.0, 1.0>

Rotate Vector (Currently only Vec2)

Rotates a vector about <0, 0> Accepts an angle or a rotation matrix

If a rotation matrix is used it must be of the form pyclid.Mat2()

Matrix
|x1, y1|
|x2, y2|

Vector.x = x1*Vector.x + y1*Vector.y
Vector.y = x2*Vector.x + y2*Vector.y

If a float is supplied the roation is calculated based on

Vector.x = cos(angle)*Vector.x - sin(angle)*Vector.y
Vector.y = sin(angle)*Vector.x + cos(angle)*Vector.y

>>> # Rotate by 90 deg, note floating point error
>>> v = Vec2(1, 0)
>>> v.rotate(math.pi/2.0)
<6.12323399574e-17, 1.0>
>>> v.rotate(math.pi/2.0)
<-1.0, 1.22464679915e-16>

DO NOT USE - Set Vector Rotation

Similar to rotate, however sets the vector to the applied angle (does not apply a rotation ontop of the current rotation)

Currently a bug in this function

Scalar Triple Product (Vec3 only)

Requires three Vec3 vectors, result is the dot product of one of the vectors with the cross product of the other two

a · (b × c)

>>> a = pyclid.Vec3(1, 0, 0)
>>> b = pyclid.Vec3(0, 1, 0)
>>> c = pyclid.Vec3(0, 0, 1)
>>> a.triple_s(b, c)
1

Vector Triple Product (Vec3 only)

Requires three Vec3 vectors, result is the cross product of one of the vectors with the cross product of the other two vectors

a × (b × c)

>>> a = Vec3(1, 2, 3)
>>> b = Vec3(2, 3, 1)
>>> c = Vec3(1, 1, 2)
>>> a.triple_v(b, c)
<7, 16, -13>