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67 | 68 | 80 |A library of two- and three-dimensional vector operations. All vectors 68 | are represented as tuples with either two or three elements.
69 |iex> # Vector Tripple Product Identity
75 | ...> a = {2, 3, 1}
76 | ...> b = {1, 4, -2}
77 | ...> c = {-1, 2, 1}
78 | ...> Vector.equal?(
79 | ...> Vector.cross(Vector.cross(a, b), c),
80 | ...> Vector.subtract(Vector.multiply(b, Vector.dot(a, c)), Vector.multiply(a, Vector.dot(b, c))))
81 | trueAdds two vectors
116 |Returns the basis vector for the given axis
123 |Returns the scalar component for the axis given
130 |Returns the cross product of two vectors A⨯B
137 |Returns the norm (magnitude) of the cross product of two vectors A⨯B
144 |Divide a vector by scalar value s
Returns the dot product of two vectors A⨯B
158 |Compares two vectors for euqality, with an optional tolerance
165 |Multiply a vector by scalar value s
Returns the norm (magnitude) of a vector
179 |Returns the square of the norm norm (magnitude) of a vector
186 |Returns a new coordinate by projecting a given length distance from
193 | coordinate start along vector
Reverses a vector
201 |Subtract vector B from vector A. Equivalent to Vector.add(A, Vector.revers(B))
Returns the unit vector parallel ot the given vector.
215 | This will raise an ArithmeticError if a zero-magnitude vector is given.
216 | Use unit_safe if there is a chance that a zero-magnitude vector
217 | will be sent
Returns the unit vector parallel ot the given vector, but will handle
225 | the vectors {0, 0} and {0, 0, 0} by returning the same vector
Adds two vectors
293 |iex> Vector.add({3, -4}, {2, 1})
299 | {5,-3}
300 | iex> Vector.add({-2, 0, 5}, {0, 0, 0})
301 | {-2, 0, 5}
302 | iex> Vector.add({2, 1, -2}, Vector.reverse({2, 1, -2}))
303 | {0, 0, 0}Returns the basis vector for the given axis
320 |iex> Vector.basis(:x)
326 | {1, 0, 0}
327 | iex> Vector.basis(:y)
328 | {0, 1, 0}
329 | iex> Vector.component(Vector.basis(:y), :y)
330 | 1Returns the scalar component for the axis given
347 |iex> Vector.component({3, -4}, :y)
353 | -4
354 | iex> Vector.component({-6, 0, 8}, :z)
355 | 8
356 | iex> Vector.component({1, -2}, :z)
357 | 0
358 | iex> Vector.component(Vector.basis(:x), :z)
359 | 0Returns the cross product of two vectors A⨯B
376 |iex> Vector.cross({2, 3}, {1, 4})
382 | {0, 0, 5}
383 | iex> Vector.cross({2, 2, -1}, {1, 4, 2})
384 | {8, -5, 6}
385 | iex> Vector.cross({3, -3, 1}, {4, 9, 2})
386 | {-15, -2, 39}Returns the norm (magnitude) of the cross product of two vectors A⨯B
403 |iex> Vector.cross_norm({2, 3}, {1, 4})
409 | 5
410 | iex> Vector.cross_norm({1, 4}, {2, 2})
411 | 6
412 | iex> Vector.cross_norm({2, 0, -1}, {0, 3, 3})
413 | 9.0
414 | iex> Float.floor(:math.pow(Vector.cross_norm({2, 2, -1}, {1, 4, 2}), 2))
415 | 125.0Divide a vector by scalar value s
iex> Vector.divide({3, -4}, 2.5)
438 | {1.2, -1.6}
439 | iex> Vector.divide({-2, 0, 5}, -2)
440 | {1.0, 0.0, -2.5}Returns the dot product of two vectors A⨯B
457 |iex> Vector.dot({2, 3}, {1, 4})
463 | 14
464 | iex> Vector.dot({1, 4}, {2, 2})
465 | 10
466 | iex> Vector.dot({2, 0, -1}, {0, 3, 3})
467 | -3Compares two vectors for euqality, with an optional tolerance
486 |iex> Vector.equal?({3, -4}, {3, -4})
492 | true
493 | iex> Vector.equal?({3, -4}, {3.0001, -3.9999})
494 | false
495 | iex> Vector.equal?({3, -4}, {3.0001, -3.9999}, 0.001)
496 | true
497 | iex> Vector.equal?({3, -4, 1}, {3.0001, -3.9999, 1.0}, 0.001)
498 | trueMultiply a vector by scalar value s
iex> Vector.multiply({3, -4}, 2.5)
521 | {7.5, -10.0}
522 | iex> Vector.multiply({-2, 0, 5}, -2)
523 | {4, 0, -10}Returns the norm (magnitude) of a vector
540 |iex> Vector.norm({3, 4})
546 | 5.0
547 | iex> Vector.norm({-1, 0})
548 | 1
549 | iex> Vector.norm({0, -2, 0})
550 | 2Returns the square of the norm norm (magnitude) of a vector
567 |iex> Vector.norm_squared({3, 4})
573 | 25
574 | iex> Vector.norm_squared({1, 0})
575 | 1
576 | iex> Vector.norm_squared({2, 0, -1})
577 | 5
578 | iex> Vector.norm_squared({-2, 3, 1})
579 | 14Returns a new coordinate by projecting a given length distance from
596 | coordinate start along vector
iex> Vector.project({3, -4}, {-1, 1}, 4)
603 | {1.4, -2.2}
604 | iex> Vector.project({-6, 0, 8}, {1, -2, 0.4}, 2.5)
605 | {-0.5, -2.0, 2.4}
606 | iex> Vector.project({-2, 1, 3}, {0, 0, 0}, 2.5) |> Vector.norm()
607 | 2.5Reverses a vector
624 |iex> Vector.reverse({3, -4})
630 | {-3, 4}
631 | iex> Vector.reverse({-2, 0, 5})
632 | {2, 0, -5}
633 | iex> Vector.cross_norm({-2, 3, 5}, Vector.reverse({-2, 3, 5}))
634 | 0Subtract vector B from vector A. Equivalent to Vector.add(A, Vector.revers(B))
iex> Vector.subtract({3, -4}, {2, 1})
657 | {1,-5}
658 | iex> Vector.subtract({-2, 0, 5}, {-3, 1, 2})
659 | {1, -1, 3}Returns the unit vector parallel ot the given vector.
676 | This will raise an ArithmeticError if a zero-magnitude vector is given.
677 | Use unit_safe if there is a chance that a zero-magnitude vector
678 | will be sent.
iex> Vector.unit({3, 4})
685 | {0.6, 0.8}
686 | iex> Vector.unit({8, 0, 6})
687 | {0.8, 0.0, 0.6}
688 | iex> Vector.unit({-2, 0, 0})
689 | {-1.0, 0.0, 0.0}
690 | iex> Vector.unit({0, 0, 0})
691 | ** (ArithmeticError) bad argument in arithmetic expressionReturns the unit vector parallel ot the given vector, but will handle
708 | the vectors {0, 0} and {0, 0, 0} by returning the same vector
iex> Vector.unit_safe({3, 4})
715 | {0.6, 0.8}
716 | iex> Vector.unit_safe({0, 0})
717 | {0, 0}
718 | iex> Vector.unit_safe({0, 0, 0})
719 | {0, 0, 0}A library of two- and three-dimensional vector operations. All vectors 78 | are represented as tuples with either two or three elements
79 |