Merge pull request #21 from timholy/pull-request/7e99e237

Add `recenter` convenience function

Author: andyferris

README.md

@@ -56,6 +56,13 @@ composed_inv = inv(composed)
 composed_inv(z) == x
 ```
 
+For any transformation, we can shift the origin to a new point using `recenter`:
+```julia
+rot_around_x = recenter(rot, x)
+```
+Now `rot_around_x` is a rotation around the point `x = SVector(1.0, 2.0, 3.0)`.
+
+
 Finally, we can construct a matrix describing how the components of `z`
 differentiates with respect to components of `x`:
 ```julia

src/CoordinateTransformations.jl

@@ -12,7 +12,7 @@ export RotMatrix, Quat, SpQuat, AngleAxis, RodriguesVec,
        RotXYZ, RotYXZ, RotZXY, RotXZY, RotYZX, RotZYX
 
 # Core methods
-export compose, ∘, transform_deriv, transform_deriv_params
+export compose, ∘, transform_deriv, transform_deriv_params, recenter
 export Transformation, IdentityTransformation
 
 # 2D coordinate systems and their transformations

src/affine.jl

@@ -202,5 +202,7 @@ function Base.:(==)(t1::LinearMap, t2::AffineMap)
         0 == vecnorm(t2.v)
 end
 
+recenter(trans::AbstractMatrix, origin::AbstractVector) = recenter(LinearMap(trans), origin)
+
 transform_deriv(trans::AffineMap, x) = trans.m
 # TODO transform_deriv_params

src/core.jl

@@ -70,6 +70,17 @@ end
 Base.inv(trans::ComposedTransformation) = inv(trans.t2) ∘ inv(trans.t1)
 Base.inv(trans::IdentityTransformation) = trans
 
+"""
+    recenter(trans::Union{AbstractMatrix,Transformation}, origin::AbstractVector) -> ctrans
+
+Return a new transformation `ctrans` such that point `origin` serves
+as the origin-of-coordinates for `trans`. For example, if `trans` is a
+rotation matrix, then `ctrans` is a rotation around `origin`.
+"""
+function recenter(trans::Transformation, origin::AbstractVector)
+    Translation(origin) ∘ trans ∘ Translation(-origin)
+end
+
 
 """
     transform_deriv(trans::Transformation, x)

test/affine.jl

@@ -88,6 +88,15 @@ CoordinateTransformations.transform_deriv(::SquareMe, x0) = diagm(2*x0)
         @test m2 == eye(2)
     end
 
+    @testset "Recenter" begin
+        M = [1 2; 3 4]
+        for origin in ([5,-3], @SVector([5,-3]))
+            c = recenter(M, origin)
+            @test c(origin) == origin
+            @test c(zero(origin)) == [6,-6]
+        end
+    end
+
 #=
     @testset "Rotation2D on Polar" begin
         p = Polar(2.0, 1.0)