add slerp

.travis.yml

@@ -1,16 +1,11 @@
-language: cpp
-compiler:
-    - gcc
+language: julia
+os:
+  - linux
+  - osx
+julia:
+  - 0.3
+  - 0.4
+  - nightly
 notifications:
-    email: false
-before_install:
-    - sudo add-apt-repository ppa:staticfloat/julia-deps -y
-    - sudo add-apt-repository ppa:staticfloat/julianightlies -y
-    - sudo apt-get update -qq -y
-    - sudo apt-get install git libpcre3-dev julia -y
-    - git config --global user.name "Travis User"
-    - git config --global user.email "travis@example.net"
-    - if [[ -a .git/shallow ]]; then git fetch --unshallow; fi
-script:
-    - julia -e 'versioninfo(); Pkg.init(); Pkg.clone(pwd())'
-    - julia ./test/runtests.jl
+  email: false
+# uncomment the following lines to override the default test script

src/Quaternion.jl

@@ -241,3 +241,39 @@ function normalize{T}(v::Vector{T})
     end
     zeros(promote_type(T,typeof(nv)), length(v))
 end
+
+
+function slerp{T}(qa::Quaternion{T}, qb::Quaternion{T}, t::T)
+    # http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/
+    coshalftheta = qa.s * qb.s + qa.v1 * qb.v1 + qa.v2 * qb.v2 + qa.v3 * qb.v3;
+
+    if coshalftheta < 0
+        qm = -qb
+        coshalftheta = -coshalftheta
+    else
+        qm = qb
+    end
+    abs(coshalftheta) >= 1.0 && return qa
+
+    halftheta    = acos(coshalftheta)
+    sinhalftheta = sqrt(one(T) - coshalftheta * coshalftheta)
+
+    if abs(sinhalftheta) < 0.001
+        return Quaternion(
+            T(0.5) * (qa.s  + qb.s),
+            T(0.5) * (qa.v1 + qb.v1),
+            T(0.5) * (qa.v2 + qb.v2),
+            T(0.5) * (qa.v3 + qb.v3),
+        )
+    end
+
+    ratio_a = sin((one(T) - t) * halftheta) / sinhalftheta
+    ratio_b = sin(t * halftheta) / sinhalftheta
+
+    Quaternion(
+        qa.s  * ratio_a + qm.s  * ratio_b,
+        qa.v1 * ratio_a + qm.v1 * ratio_b,
+        qa.v2 * ratio_a + qm.v2 * ratio_b,
+        qa.v3 * ratio_a + qm.v3 * ratio_b,
+    )
+end

src/Quaternions.jl

@@ -1,6 +1,6 @@
 module Quaternions
   importall Base
-  
+
   include("Quaternion.jl")
   include("Octonion.jl")
   include("DualQuaternion.jl")
@@ -25,4 +25,5 @@ module Quaternions
   export ndualquatrand
   export qrotation
   export rotationmatrix
+  export slerp
 end

test/runtests.jl

@@ -23,3 +23,8 @@ Rz = [c -s 0; s c 0; 0 0 1]
 @test_approx_eq rotationmatrix(qx*qy*qz) Rx*Ry*Rz
 @test_approx_eq rotationmatrix(qy*qx*qz) Ry*Rx*Rz
 @test_approx_eq rotationmatrix(qz*qx*qy) Rz*Rx*Ry
+
+a, b = qrotation([0,0,1], deg2rad(0)), qrotation([0,0,1], deg2rad(180))
+@test_approx_eq slerp(a,b,0.0) a
+@test_approx_eq slerp(a,b,1.0) b
+@test_approx_eq slerp(a,b,0.5) qrotation([0,0,1], deg2rad(90))