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import std/math, std/sequtils, std/sugar
import types
const dim_mismatch = "Dimensional mismatch - check your vectors"
## Vector addition
func `+`*(a, b: Vector): Vector =
assert a.len() == b.len(), dim_mismatch
result.setLen(a.len)
for i in 0 ..< a.len():
result[i] = (a[i] + b[i])
## Vector subtraction
func `-`*(a, b: Vector): Vector =
assert a.len() == b.len(), dim_mismatch
result.setLen(a.len)
for i in 0 ..< a.len():
result[i] = (a[i] - b[i])
## Vector dot product
func `*`*(a, b: Vector): float =
assert a.len() == b.len(), dim_mismatch
for i in 0 ..< a.len():
result += a[i] * b[i]
func dot*(a, b: Vector): float =
return a * b
## Scalar-Vector multiplication
func `*`*(a: float, b: Vector): Vector =
return map(b, (x) => (a*x))
## Produce the length (in space) of a vector
func length*(a: Vector): float =
return sqrt(a * a)
## Produce the number of elements in a vector
func size*(a: Vector): int =
return len(a)
## Returns whether two vectors are orthagonal
func ortho*(a, b: Vector): bool =
return a * b == 0
## Produce the angle between two vectors, in radians
func angle*(a, b: Vector): Radian =
return arccos((a * b) / (a.length * b.length))
## Produce the cross product between two 3D vectors
func cross*(a, b: Vector): Vector =
assert a.len() == 3, "The first vector is not three-dimensional"
assert b.len() == 3, "The second vector is not three-dimensional"
return @[
(a[1]*b[2]) - (b[1]*a[2]),
(a[2]*b[0]) - (b[2]*a[0]),
(a[0]*b[1]) - (b[0]*a[1])
]
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