The perspective transformation

* Can convert 3D positions to 2D screen locations using PerspectiveMap

Author: Andy Ferris

src/CoordinateTransformations.jl

@@ -28,10 +28,12 @@ export SphericalFromCartesian, CartesianFromSpherical,
 # Common transformations
 export AbstractAffineMap
 export AffineMap, LinearMap, Translation
+export PerspectiveMap
 
 include("core.jl")
 include("coordinatesystems.jl")
 include("affine.jl")
+include("perspective.jl")
 
 # Deprecations
 export transform

src/perspective.jl

@@ -0,0 +1,26 @@
+"""
+    PerspectiveMap()
+
+Construct a perspective transformation. The persepective transformation takes,
+e.g., a point in 3D space and "projects" it onto a 2D virtual screen of an ideal
+pinhole camera (at distance `1` away from the camera). The camera is oriented
+towards the positive-Z axis (or in general, along the final dimension).
+
+This transformation is designed to be used in composition with other coordinate
+transformations, defining e.g. the position and orientation of the camera. For
+example:
+
+    cam_transform = PerspectiveMap() ∘ AffineMap(cam_rotation, -cam_position)
+    screen_points = map(cam_transform, points)
+"""
+immutable PerspectiveMap <: Transformation
+end
+
+function (::PerspectiveMap)(v::AbstractVector)
+    scale =  1/v[end]
+    return [v[i] * scale for i in 1:length(v)-1]
+end
+
+@inline function (::PerspectiveMap)(v::StaticVector)
+    return pop(v) * inv(v[end])
+end