Vector (vector v1.1.0)
A library of two- and three-dimensional vector operations. All vectors are represented as tuples with either two or three elements.
examples
Examples
iex> # Vector Tripple Product Identity
...> a = {2, 3, 1}
...> b = {1, 4, -2}
...> c = {-1, 2, 1}
...> Vector.equal?(
...> Vector.cross(Vector.cross(a, b), c),
...> Vector.subtract(Vector.multiply(b, Vector.dot(a, c)), Vector.multiply(a, Vector.dot(b, c))))
trueLink to this section Summary
Functions
Adds two vectors
Returns the basis vector for the given axis
Returns the scalar component for the axis given
Returns the cross product of two vectors A⨯B
Returns the norm (magnitude) of the cross product of two vectors A⨯B
Divide a vector by scalar value s
Returns the dot product of two vectors A⨯B
Compares two vectors for equality, with an optional tolerance
Multiply a vector by scalar value s
Returns the norm (magnitude) of a vector
Returns the square of the norm norm (magnitude) of a vector
Returns a new coordinate by projecting a given length distance from
coordinate start along vector
Reverses a vector
Subtract vector B from vector A. Equivalent to Vector.add(A, Vector.revers(B))
Returns the unit vector parallel ot the given vector.
This will raise an ArithmeticError if a zero-magnitude vector is given.
Use unit_safe if there is a chance that a zero-magnitude vector
will be sent.
Returns the unit vector parallel ot the given vector, but will handle
the vectors {0, 0} and {0, 0, 0} by returning the same vector
Link to this section Types
Link to this section Functions
add(arg1, arg2)
Adds two vectors
examples
Examples
iex> Vector.add({3, -4}, {2, 1})
{5,-3}
iex> Vector.add({-2, 0, 5}, {0, 0, 0})
{-2, 0, 5}
iex> Vector.add({2, 1, -2}, Vector.reverse({2, 1, -2}))
{0, 0, 0}basis(atom)
Returns the basis vector for the given axis
examples
Examples
iex> Vector.basis(:x)
{1, 0, 0}
iex> Vector.basis(:y)
{0, 1, 0}
iex> Vector.component(Vector.basis(:y), :y)
1component(arg, atom)
Returns the scalar component for the axis given
examples
Examples
iex> Vector.component({3, -4}, :y)
-4
iex> Vector.component({-6, 0, 8}, :z)
8
iex> Vector.component({1, -2}, :z)
0
iex> Vector.component(Vector.basis(:x), :z)
0cross(arg1, arg2)
Returns the cross product of two vectors A⨯B
examples
Examples
iex> Vector.cross({2, 3}, {1, 4})
{0, 0, 5}
iex> Vector.cross({2, 2, -1}, {1, 4, 2})
{8, -5, 6}
iex> Vector.cross({3, -3, 1}, {4, 9, 2})
{-15, -2, 39}cross_norm(arg1, arg2)
Returns the norm (magnitude) of the cross product of two vectors A⨯B
examples
Examples
iex> Vector.cross_norm({2, 3}, {1, 4})
5
iex> Vector.cross_norm({1, 4}, {2, 2})
6
iex> Vector.cross_norm({2, 0, -1}, {0, 3, 3})
9.0
iex> Float.floor(:math.pow(Vector.cross_norm({2, 2, -1}, {1, 4, 2}), 2))
125.0divide(arg, s)
Divide a vector by scalar value s
examples
Examples
iex> Vector.divide({3, -4}, 2.5)
{1.2, -1.6}
iex> Vector.divide({-2, 0, 5}, -2)
{1.0, 0.0, -2.5}dot(arg1, arg2)
Returns the dot product of two vectors A⨯B
examples
Examples
iex> Vector.dot({2, 3}, {1, 4})
14
iex> Vector.dot({1, 4}, {2, 2})
10
iex> Vector.dot({2, 0, -1}, {0, 3, 3})
-3equal?(a, b, tolerance \\ 0.0)
Compares two vectors for equality, with an optional tolerance
examples
Examples
iex> Vector.equal?({3, -4}, {3, -4})
true
iex> Vector.equal?({3, -4}, {3.0001, -3.9999})
false
iex> Vector.equal?({3, -4}, {3.0001, -3.9999}, 0.001)
true
iex> Vector.equal?({3, -4, 1}, {3.0001, -3.9999, 1.0}, 0.001)
truemultiply(arg, s)
Multiply a vector by scalar value s
examples
Examples
iex> Vector.multiply({3, -4}, 2.5)
{7.5, -10.0}
iex> Vector.multiply({-2, 0, 5}, -2)
{4, 0, -10}norm(arg)
Returns the norm (magnitude) of a vector
examples
Examples
iex> Vector.norm({3, 4})
5.0
iex> Vector.norm({-1, 0})
1
iex> Vector.norm({0, -2, 0})
2norm_squared(arg)
Returns the square of the norm norm (magnitude) of a vector
examples
Examples
iex> Vector.norm_squared({3, 4})
25
iex> Vector.norm_squared({1, 0})
1
iex> Vector.norm_squared({2, 0, -1})
5
iex> Vector.norm_squared({-2, 3, 1})
14project(vector, start, distance)
Returns a new coordinate by projecting a given length distance from
coordinate start along vector
examples
Examples
iex> Vector.project({3, -4}, {-1, 1}, 4)
{1.4, -2.2}
iex> Vector.project({-6, 0, 8}, {1, -2, 0.4}, 2.5)
{-0.5, -2.0, 2.4}
iex> Vector.project({-2, 1, 3}, {0, 0, 0}, 2.5) |> Vector.norm()
2.5reverse(arg)
Reverses a vector
examples
Examples
iex> Vector.reverse({3, -4})
{-3, 4}
iex> Vector.reverse({-2, 0, 5})
{2, 0, -5}
iex> Vector.cross_norm({-2, 3, 5}, Vector.reverse({-2, 3, 5}))
0subtract(a, b)
Subtract vector B from vector A. Equivalent to Vector.add(A, Vector.revers(B))
examples
Examples
iex> Vector.subtract({3, -4}, {2, 1})
{1,-5}
iex> Vector.subtract({-2, 0, 5}, {-3, 1, 2})
{1, -1, 3}unit(v)
Returns the unit vector parallel ot the given vector.
This will raise an ArithmeticError if a zero-magnitude vector is given.
Use unit_safe if there is a chance that a zero-magnitude vector
will be sent.
examples
Examples
iex> Vector.unit({3, 4})
{0.6, 0.8}
iex> Vector.unit({8, 0, 6})
{0.8, 0.0, 0.6}
iex> Vector.unit({-2, 0, 0})
{-1.0, 0.0, 0.0}
iex> Vector.unit({0, 0, 0})
** (ArithmeticError) bad argument in arithmetic expressionunit_safe(v)
Returns the unit vector parallel ot the given vector, but will handle
the vectors {0, 0} and {0, 0, 0} by returning the same vector
examples
Examples
iex> Vector.unit_safe({3, 4})
{0.6, 0.8}
iex> Vector.unit_safe({0, 0})
{0, 0}
iex> Vector.unit_safe({0, 0, 0})
{0, 0, 0}