Move intersectparameters utility to utils/intersect.jl

Author: juliohm

src/utils/intersect.jl

@@ -2,6 +2,58 @@
 # Licensed under the MIT License. See LICENSE in the project root.
 # ------------------------------------------------------------------
 
+"""
+    intersectparameters(a, b, c, d)
+
+Compute the parameters `λ₁` and `λ₂` of the lines 
+`a + λ₁ ⋅ v⃗₁`, with `v⃗₁ = b - a` and
+`c + λ₂ ⋅ v⃗₂`, with `v⃗₂ = d - c` spanned by the input
+points `a`, `b` resp. `c`, `d` such that to yield line
+points with minimal distance or the intersection point
+(if lines intersect).
+
+Furthermore, the ranks `r` of the matrix of the linear
+system `A ⋅ λ⃗ = y⃗`, with `A = [v⃗₁ -v⃗₂], y⃗ = c - a`
+and the rank `rₐ` of the augmented matrix `[A y⃗]` are
+calculated in order to identify the intersection type:
+
+- Intersection: r == rₐ == 2
+- Collinear: r == rₐ == 1
+- No intersection: r != rₐ
+  - No intersection and parallel:  r == 1, rₐ == 2
+  - No intersection, skew lines: r == 2, rₐ == 3
+"""
+function intersectparameters(a::Point, b::Point, c::Point, d::Point)
+  # augmented linear system
+  A = ustrip.([(b - a) (c - d) (c - a)])
+
+  # normalize by maximum absolute coordinate
+  A = A / maximum(abs, A)
+
+  # numerical tolerance
+  T = eltype(A)
+  τ = atol(T)
+
+  # check if a vector is non zero
+  isnonzero(v) = !isapprox(v, zero(v), atol=τ)
+
+  # calculate ranks by checking the zero rows of
+  # the factor R in the QR matrix factorization
+  _, R = qr(A)
+  r = sum(isnonzero, eachrow(R[:, SVector(1, 2)]))
+  rₐ = sum(isnonzero, eachrow(R))
+
+  # calculate parameters of intersection
+  if r ≥ 2
+    λ = A[:, SVector(1, 2)] \ A[:, 3]
+    λ₁, λ₂ = λ[1], λ[2]
+  else # parallel or collinear
+    λ₁, λ₂ = zero(T), zero(T)
+  end
+
+  λ₁, λ₂, r, rₐ
+end
+
 """
     pairwiseintersect(segments; [digits])
 

src/utils/misc.jl

@@ -55,55 +55,3 @@ function svdbasis(p::AbstractVector{<:Point})
   n = Vec(zero(ℒ), zero(ℒ), oneunit(ℒ))
   isnegative((u × v) ⋅ n) ? (v, u) : (u, v)
 end
-
-"""
-    intersectparameters(a, b, c, d)
-
-Compute the parameters `λ₁` and `λ₂` of the lines 
-`a + λ₁ ⋅ v⃗₁`, with `v⃗₁ = b - a` and
-`c + λ₂ ⋅ v⃗₂`, with `v⃗₂ = d - c` spanned by the input
-points `a`, `b` resp. `c`, `d` such that to yield line
-points with minimal distance or the intersection point
-(if lines intersect).
-
-Furthermore, the ranks `r` of the matrix of the linear
-system `A ⋅ λ⃗ = y⃗`, with `A = [v⃗₁ -v⃗₂], y⃗ = c - a`
-and the rank `rₐ` of the augmented matrix `[A y⃗]` are
-calculated in order to identify the intersection type:
-
-- Intersection: r == rₐ == 2
-- Collinear: r == rₐ == 1
-- No intersection: r != rₐ
-  - No intersection and parallel:  r == 1, rₐ == 2
-  - No intersection, skew lines: r == 2, rₐ == 3
-"""
-function intersectparameters(a::Point, b::Point, c::Point, d::Point)
-  # augmented linear system
-  A = ustrip.([(b - a) (c - d) (c - a)])
-
-  # normalize by maximum absolute coordinate
-  A = A / maximum(abs, A)
-
-  # numerical tolerance
-  T = eltype(A)
-  τ = atol(T)
-
-  # check if a vector is non zero
-  isnonzero(v) = !isapprox(v, zero(v), atol=τ)
-
-  # calculate ranks by checking the zero rows of
-  # the factor R in the QR matrix factorization
-  _, R = qr(A)
-  r = sum(isnonzero, eachrow(R[:, SVector(1, 2)]))
-  rₐ = sum(isnonzero, eachrow(R))
-
-  # calculate parameters of intersection
-  if r ≥ 2
-    λ = A[:, SVector(1, 2)] \ A[:, 3]
-    λ₁, λ₂ = λ[1], λ[2]
-  else # parallel or collinear
-    λ₁, λ₂ = zero(T), zero(T)
-  end
-
-  λ₁, λ₂, r, rₐ
-end