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- - -A library of two- and three-dimensional vector operations. All vectors -are represented as tuples with either two or three elements.
-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))))
-trueAdds 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 euqality, 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
Adds two vectors
-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}Returns the basis vector for the given axis
-iex> Vector.basis(:x)
-{1, 0, 0}
-iex> Vector.basis(:y)
-{0, 1, 0}
-iex> Vector.component(Vector.basis(:y), :y)
-1Returns the scalar component for the axis given
-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)
-0Returns the cross product of two vectors A⨯B
-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}Returns the norm (magnitude) of the cross product of two vectors A⨯B
-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 a vector by scalar value s
iex> Vector.divide({3, -4}, 2.5)
-{1.2, -1.6}
-iex> Vector.divide({-2, 0, 5}, -2)
-{1.0, 0.0, -2.5}Returns the dot product of two vectors A⨯B
-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})
--3Compares two vectors for euqality, with an optional tolerance
-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 a vector by scalar value s
iex> Vector.multiply({3, -4}, 2.5)
-{7.5, -10.0}
-iex> Vector.multiply({-2, 0, 5}, -2)
-{4, 0, -10}Returns the norm (magnitude) of a vector
-iex> Vector.norm({3, 4})
-5.0
-iex> Vector.norm({-1, 0})
-1
-iex> Vector.norm({0, -2, 0})
-2Returns the square of the norm norm (magnitude) of a vector
-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})
-14Returns a new coordinate by projecting a given length distance from
-coordinate start along vector
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()
-2.5Reverses a vector
-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 vector B from vector A. Equivalent to Vector.add(A, Vector.revers(B))
iex> Vector.subtract({3, -4}, {2, 1})
-{1,-5}
-iex> Vector.subtract({-2, 0, 5}, {-3, 1, 2})
-{1, -1, 3}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.
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 expressionReturns the unit vector parallel ot the given vector, but will handle
-the vectors {0, 0} and {0, 0, 0} by returning the same vector
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}A library of two- and three-dimensional vector operations. All vectors -are represented as tuples with either two or three elements
-