Update AngleBetweenVectors.jl

src/AngleBetweenVectors.jl

@@ -13,6 +13,38 @@ function arc(point1::NTuple{2,T}, point2::NTuple{2,T}) where {T<:Real}
     return atan(point1[2], point1[1]) - atan(point2[2], point2[1])
 end
 
+function arc(pt1::NTuple{3,T}, pt2::NTuple{3,T}) where {T<:Real}
+    n1 = ab_minus_cd(pt1[2],pt2[3],pt1[3],pt2[2])
+    n2 = ab_minus_cd(pt1[3],pt2[1],pt1[1],pt2[3])
+    n3 = ab_minus_cd(pt1[1],pt2[2],pt1[2],pt2[1])
+    h = hypot(n1,n2,n3)
+    n1 = n1 / h; n2 = n2 / h; n3 = n3 / h
+    h = hypot(n1,n2,n3)
+    return atan(h)
+end
+
+
+# from Kahan
+function ad_minus_bc(a,b,c,d)
+    w = b*c
+    e = fma(-b, c, w)
+    f = fma(a, d, -w)
+    return f+e
+end
+
+
+function area_lo2hi(a,b,c)
+    p = (c + (b + a))*(a - (c - b))*(a + (c - b))*(c + (b - a))
+    return sqrt(p)/4
+end
+
+function tantheta(pt1::NTuple{3,T}, pt2::NTuple{3,T}) where {T<:Real}
+    h1, h2 = minmax(hypot(pt1...), hypot(pt2...))
+    h3 = hypot((pt2 .- pt1)...)
+    a  = 2*area_lo2hi(h1, h2, h3)
+    return a/dot(p1,p2)
+end
+
 """
     angle(point1::T, point2::T) where {T}