optics

2026-09-20 01:59:59 +00:00 · 2016-06-02 22:58:54 +03:00
parent 07812f3bc7
commit bf9b44e057
9 changed files with 253 additions and 68 deletions
@@ -23,11 +23,11 @@ export AbstractPoint, Point, IntegrationPoint, IP, Node

 ### ELEMENTS ###
 include("elements.jl") # common element routines
-export Node, AbstractElement, Element, update!, get_connectivity
+export Node, AbstractElement, Element, update!, get_connectivity, get_basis, get_dbasis
 include("lagrange_macro.jl") # Continuous Galerkin (Lagrange) elements generated using macro
 export Seg2, Seg3, Tri3, Tri6, Quad4, Hex8, Tet4, Tet10
 include("nurbs.jl")
-export NSeg, NSurf, NSolid
+export NSeg, NSurf, NSolid, is_nurbs

 #include("hierarchical.jl") # P-elements
 #include("mortar_elements.jl") # Mortar elements
@@ -64,6 +64,9 @@ include("solver_utils.jl")
 include("solvers.jl")
 export Solver

+include("optics.jl")
+export find_intersection, calc_reflection
+
 ### MORTAR STUFF ###
 include("mortar.jl")  # mortar projection

@@ -46,6 +46,7 @@ function set_debug_off!()
    pop!(ENV, "DEBUG");
 end

+#=
 """ Simple linspace extension to arrays.

 Examples
@@ -60,6 +61,7 @@ Examples
 function linspace{T<:Array}(X1::T, X2::T, n)
    [1/2*(1-ti)*X1 + 1/2*(1+ti)*X2 for ti in linspace(-1, 1, n)]
 end
+=#

 function resize!(A::SparseMatrixCSC, m::Int64, n::Int64)
    (n == A.n) && (m == A.m) && return
@@ -116,7 +116,11 @@ function update!(element::Element, field_name::ASCIIString, data::Dict)
 end

 function update!(element::Element, field_name::ASCIIString, data::Union{Real, Vector, Pair})
-    element[field_name] = data
+    if haskey(element, field_name)
+        update!(element[field_name], data)
+    else
+        element[field_name] = data
+    end
 end

 function update!(elements::Vector, field_name::ASCIIString, data)
@@ -1,3 +1,6 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
 """ NURBS segment. """
 type NSeg <: AbstractElement
    order :: Int
@@ -62,7 +65,7 @@ function get_basis(element::Element{NSeg}, xi::Vector, time)
    w = element.properties.weights
    nu = length(tu)-pu-1
    u = xi[1]
-    N = [w[j]*NURBS(j,pu,u,tu) for j=1:nu]
+    N = vec([w[j]*NURBS(j,pu,u,tu) for j=1:nu])'
    return N/sum(N)
 end

@@ -75,7 +78,7 @@ function get_basis(element::Element{NSurf}, xi::Vector, time)
    nu = length(tu)-pu-1
    nv = length(tv)-pv-1
    u, v = xi
-    N = [w[i,j]*NURBS(i,pu,u,tu)*NURBS(j,pv,v,tv) for i=1:nu, j=1:nv]
+    N = vec([w[i,j]*NURBS(i,pu,u,tu)*NURBS(j,pv,v,tv) for i=1:nu, j=1:nv])'
    return N / sum(N)
 end

@@ -125,3 +128,11 @@ function size(element::Element{NSolid})
    return (3, length(element))
 end

+function is_nurbs(element::Element)
+    return false
+end
+
+function is_nurbs{E<:Union{NSeg, NSurf, NSolid}}(element::Element{E})
+    return true
+end
+
@@ -0,0 +1,124 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+function gen_rtic_grid!{S<:Union{Seg2,Seg3}}(thetas, element::Element{S}; npts=2)
+    xi1 = midpoints(linspace(-1, 1, npts+1))
+    for xi in xi1
+        push!(thetas, [0.0, xi])
+    end
+end
+
+function gen_rtic_grid!(thetas, element::Element{NSeg}; npts=2)
+    knots_u = element.properties.knots
+    u = midpoints(linspace(minimum(knots_u), maximum(knots_u), npts+1))
+    for ui in u
+        push!(thetas, [0.0, ui])
+    end
+end
+
+function gen_rtic_grid!(thetas, element::Element{NSurf}; npts=2)
+    knots_u = element.properties.knots_u
+    knots_v = element.properties.knots_v
+    u = midpoints(linspace(minimum(knots_u), maximum(knots_u), npts+1))
+    v = midpoints(linspace(minimum(knots_v), maximum(knots_v), npts+1))
+    for ui in u
+        for vi in v
+            push!(thetas, [0.0, ui, vi])
+        end
+    end
+end
+
+"""
+Find intersection between element surface X(ξ) and ray x(t) = s + t*n by
+solving equation F(t, ξ) = x(t) - X(ξ) = 0
+
+Returns
+-------
+t, ξ
+
+References
+----------
+[1] https://en.wikipedia.org/wiki/Ray_tracing_%28graphics%29
+
+"""
+function find_intersection{S<:Union{Seg2, Seg3, NSeg, NSurf}}(element::Element{S}, s, n, time;
+    max_iterations=10, tolerance=1.0e-12, info_output=false, deformed=true, secondary=false, npts=2)
+
+    x = element["geometry"](time)
+    if deformed && haskey(element, "displacement")
+        x += element["displacement"](time)
+    end
+
+    function calc_intersection!(theta)
+        i = 0
+        dtheta = zeros(theta)
+        for i=1:max_iterations
+            t = theta[1]
+            xi = theta[2:end]
+            N = get_basis(element, xi, time)
+            dN = get_dbasis(element, xi, time)
+            A = [n -dN*x]
+            r = s + t*n - N*x
+            try
+                dtheta = A \ -r
+            catch err
+                info("failed to solve equation.")
+                dump(theta)
+                dump(A)
+                dump(r)
+                throw(err)
+            end
+            theta[:] += dtheta
+            info_output && info("iter $i, theta = $theta, norm(dtheta) = $(norm(dtheta))")
+            norm(dtheta) < tolerance && return theta
+            isnan(theta[1]) && break
+        end
+        theta[1] = NaN
+        return theta
+        # error("didn't converge in $i iterations")
+    end
+
+    thetas = Vector{Float64}[]
+    gen_rtic_grid!(thetas, element; npts=npts)
+    map(calc_intersection!, thetas)
+    filter!(t -> !isnan(t[1]), thetas)
+    info_output && info("thetas: $thetas")
+    secondary && filter!(t -> t[1] > 1.0e-12, thetas)
+    # error("failure finding ray trace, thetas vec is empty")
+    length(thetas) == 0 && return NaN, [NaN, NaN]
+    sort!(thetas, alg=MergeSort, lt=(a,b)->a[1]<b[1])
+    theta = thetas[1]
+    return theta[1], theta[2:end]
+end
+
+"""
+References
+----------
+[1] http://fp.optics.arizona.edu/optomech/Fall13/Notes/6%20Mirror%20matrices.pdf
+"""
+function calc_reflection{S<:Union{Seg2, Seg3, NSeg}}(element::Element{S}, xi, k, time; deformed=true)
+    x = element["geometry"](time)
+    if deformed && haskey(element, "displacement")
+        x += element["displacement"](time)
+    end
+    Q = [0.0 1.0; -1.0 0.0]
+    dN = get_dbasis(element, xi, time)
+    n = Q*(dN*x)
+    n /= norm(n)
+    k2 = k - 2*vecdot(k, n)*n
+    return k2
+end
+
+function calc_reflection{S<:Union{Quad4, NSurf}}(element::Element{S}, xi, k, time; deformed=true)
+    x = element["geometry"](time)
+    if deformed && haskey(element, "displacement")
+        x += element["displacement"](time)
+    end
+    dN = get_dbasis(element, xi, time)
+    J = transpose(sum([kron(dN[:,i], x[i]') for i=1:length(x)]))
+    n = cross(J[:,1], J[:,2])
+    n /= norm(n)
+    k2 = k - 2*vecdot(k, n)*n
+    return k2
+end
+