Complete Reference

BSplineCurve{P,S,N,M} <: Spline{P,S,N,M}

N is the spatial dimension of the curve. M is the curve order, i.e., the highest power of the parameterizing variable, u. All curve segments are assumed to be of the same order.

BSplineCurve{P,S,N,M}(knots::KnotVector{S}, controlpoints::AbstractArray{MVector{N,S},1})

ConvergingBeam, DivergingBeam or CollimatedBeam, defines the behavior of a beam in a HologramInterface.

BezierCurve{P,S,N,M} <: Spline{P,S,N,M}

N is the dimension of the curve, M is the curve order

BezierCurve{P,S,N,M}(controlpoints::AbstractArray{<:AbstractArray{S,1},1})

CircularStopShape <: StopShape

Either Rational or Euclidean, used for Splines and SplineSurfaces.

Either GridSagLinear or GridSagBicubic - determines the interpolation between sample points in the grid for a GridSagSurface.

Valid modes for deterministic raytracing

KnotVector{T<:Number}

Vector to define knots used for BSplineCurve and BSplineSurface.

Primitive{T<:Real}

T is the number type used to represent the primitive, e.g., Float64. Primitives are the basic elements which can be stored in bounding volume hierarchies and include surfaces and CSG objects

Must implement the following:

boundingbox(a::Primitive{T})::BoundingBox{T}
centroid(a::Primitive{T})::SVector{3,T}

RectangularStopShape <: StopShape

Spline{P<:CurveType,S<:Number,N,M}

M is the curve order, i.e., the highest power of the parameterizing variable, u. P determines the CurveType.

All Spline types must implement:

point(curve,u)

and have field controlpolygon

SplineSurface{P,S,N,M} <: ParametricSurface{S,N}

Curve order, M, is the same in the u and v direction and fixed over all spans. P determines the CurveType.

StopSurface{T} <: Surface{T}

Abstract type to encapsulate any surfaces acting as a stop.

Either ZernikeIndexingOSA or ZernikeIndexingNoll, see Zernike polynomials wikipedia entry for details.

Apply a Transform to an Intersection object

Apply a Transform to an Interval object

Apply a Transform to a Ray object

Apply a Transform to a TriangleMesh object

Apply a Transform to a Triangle object

Annulus(innerradius::T, outerradius::T, surfacenormal::SVector{3,T}, centrepoint::SVector{3,T})

Creates a circular aperture in a circle i.e. FiniteStop{T,CircularStopShape,CircularStopShape}.

ArizonaEye(::Type{T} = Float64; accommodation::T = 0.0)

The popular Arizona eye model taken from this definition. The accommodation of the eye can be varied in this model. Returns a DataFrame specifying the prescription of the eye model.

AsphericLens(insidematerial, frontvertex, frontradius, frontconic, frontaspherics, backradius, backconic, backaspherics, thickness, semidiameter;  lastmaterial = OpticSim.GlassCat.Air, nextmaterial = OpticSim.GlassCat.Air, frontsurfacereflectance = 0.0, backsurfacereflectance = 0.0, frontdecenter = (0, 0), backdecenter = (0, 0), interfacemode = ReflectOrTransmit)

Cosntructs a simple cylindrical lens with front and back surfaces with a radius, conic and apsheric terms. The side walls of the lens are absorbing.

BoundedCylinder(radius::T, height::T; interface::NullOrFresnel{T} = nullinterface(T)) -> CSGGenerator{T}

Create a cylinder with planar caps on both ends centred at (0, 0, 0) with axis (0, 0, 1).

Circle(radius, [surfacenormal, centrepoint]; interface = nullinterface(T))

Shortcut method to create a circle. The minimal case returns a circle centred at the origin with normal = [0, 0, 1].

CircularAperture(radius::T, surfacenormal::SVector{3,T}, centrepoint::SVector{3,T})

Creates a circular aperture in a plane i.e. InfiniteStop{T,CircularStopShape}.

CircularAperture(radius::T, outerhalfsizeu::T, outerhalfsizev::T, surfacenormal::SVector{3,T}, centrepoint::SVector{3,T}; rotationvec::SVector{3,T} = [0.0, 1.0, 0.0])

Creates a circular aperture in a rectangle i.e. FiniteStop{T,CircularStopShape,RectangularStopShape}. The rotation of the rectangle around its normal is defined by rotationvec. rotationvec×surfacenormal is taken as the vector along the u axis.

ConicLens(insidematerial, frontvertex, frontradius, frontconic, backradius, backconic, thickness, semidiameter;  lastmaterial = OpticSim.GlassCat.Air, nextmaterial = OpticSim.GlassCat.Air, frontsurfacereflectance = 0.0, backsurfacereflectance = 0.0, frontdecenter = (0, 0), backdecenter = (0, 0), interfacemode = ReflectOrTransmit)

Constructs a simple cylindrical lens with front and back surfaces with a radius and conic term. The side walls of the lens are absorbing.

Cuboid(halfsizex::T, halfsizey::T, halfsizez::T; interface::NullOrFresnel{T} = nullinterface(T)) -> CSGGenerator{T}

Create a cuboid centred at (0, 0, 0).

FresnelLens(insidematerial, frontvertex, radius, thickness, semidiameter, groovedepth; conic = 0.0, aspherics = nothing, outsidematerial = OpticSim.GlassCat.Air)

Create a Fresnel lens as a CSG object, can be concave or convex. Groove positions are found iteratively based on groovedepth. For negative radii the vertex on the central surface is at frontvertex, so the total thickness of the lens is thickness + groovedepth. Aspherics currently not supported.

GridField(sys::AxisymmetricOpticalSystem; collimated = true, samples = 20, wavelength = 0.55, sourcepos = (0.0, 0.0, 3.0), sourceangle = 0.0, sourcenum = 0)

Distributes rays over the entrance pupil of the system in a rectangular grid pattern.

GridField(semidiameter, pupilpos; collimated = true, samples = 20, wavelength = 0.55, sourcepos = (0.0, 0.0, 3.0), sourceangle = 0.0, sourcenum = 0)

Distributes rays over a circular pupil with half-diameter defined by semidiameter, centred at pupilpos in a rectangular grid pattern. samples is the number of rays on each side of the grid, so there are samples×samples rays in total.

HexagonalPrism(side_length::T, visheight::T = 2.0; interface::NullOrFresnel{T} = nullinterface(T)) -> CSGGenerator{T}

Create an infinitely tall hexagonal prism with axis (0, 0, 1), the longer hexagon diameter is along the x axis. For visualization visheight is used, note that this does not fully represent the surface.

HexapolarField(sys::AxisymmetricOpticalSystem; collimated = true, samples = 8, wavelength = 0.55, sourcepos = (0.0, 0.0, 3.0), sourceangle = 0.0, sourcenum = 0)

Distributes rays over the entrance pupil of the system in a hexapolar pattern.

HexapolarField(semidiameter, pupilpos; collimated = true, samples = 8, wavelength = 0.55, sourcepos = (0.0, 0.0, 3.0), sourceangle = 0.0, sourcenum = 0)

Distributes rays over a circular pupil with half-diameter defined by semidiameter, centred at pupilpos in a hexapolar pattern. samples is the number of rings in the hexapolar pattern, so the number of rays in total is samples * (samples + 1) / 2) * 6 + 1.

ModelEye(assembly::LensAssembly{T}, nsamples::Int = 17; pupil_radius::T = 3.0, detpixels::Int = 1000, transform::Transform{T} = identitytransform(T))

Geometrically accurate model of the human eye focussed at infinity with variable pupil_radius. The eye is added to the provided assembly to create a CSGOpticalSystem with the retina of the eye as the detector.

The eye can be positioned in the scene using the transform argument and the resolution of the detector specified with detpixels. By default the eye is directed along the positive z-axis with the vertex of the cornea at the origin.

nsamples determines the resolution at which accelerated surfaces within the eye are triangulated.

RectangularAperture(aphalfsizeu::T, aphalfsizev::T, surfacenormal::SVector{3,T}, centrepoint::SVector{3,T}; rotationvec::SVector{3,T} = [0.0, 1.0, 0.0])

Creates a rectangular aperture in a plane i.e. InfiniteStop{T,RectangularStopShape}. The rotation of the rectangle around its normal is defined by rotationvec. rotationvec×surfacenormal is taken as the vector along the u axis.

RectangularAperture(innerhalfsizeu::T, innerhalfsizev::T, outerhalfsizeu::T, outerhalfsizev::T, surfacenormal::SVector{3,T}, centrepoint::SVector{3,T}; rotationvec::SVector{3,T} = [0.0, 1.0, 0.0])

Creates a rectangular aperture in a rectangle i.e. FiniteStop{T,RectangularStopShape,RectangularStopShape}. The rotation of the rectangle around its normal is defined by rotationvec. rotationvec×surfacenormal is taken as the vector along the u axis.

RectangularPrism(halfsizex::T, halfsizey::T, visheight::T=2.0; interface::NullOrFresnel{T} = nullinterface(T)) -> CSGGenerator{T}

Create an infinitely tall rectangular prism with axis (0, 0, 1). For visualization visheight is used, note that this does not fully represent the surface.

SphericalLens(insidematerial, frontvertex, frontradius, backradius, thickness, semidiameter;  lastmaterial = OpticSim.GlassCat.Air, nextmaterial = OpticSim.GlassCat.Air, frontsurfacereflectance = 0.0, backsurfacereflectance = 0.0, frontdecenter = (0, 0), backdecenter = (0, 0), interfacemode = ReflectOrTransmit)

Constructs a simple cylindrical lens with spherical front and back surfaces. The side walls of the lens are absorbing.

Spider(narms::Int, armwidth::T, radius::T, origin::SVector{3,T} = SVector{3,T}(0.0, 0.0, 0.0), normal::SVector{3,T} = SVector{3,T}(0.0, 0.0, 1.0)) -> Vector{Rectangle{T}}

Creates a 'spider' obscuration with narms rectangular arms evenly spaced around a circle defined by origin and normal. Each arm is a rectangle armwidth×radius.

e.g. for 3 and 4 arms we get:

   |         _|_
  / \         |

TriangularPrism(side_length::T, visheight::T = 2.0; interface::NullOrFresnel{T} = nullinterface(T)) -> CSGGenerator{T}

Create an infinitely tall triangular prism with axis (0, 0, 1). For visualization visheight is used, note that this does not fully represent the surface.

assembly(system::AbstractOpticalSystem{T}) -> LensAssembly{T}

Get the LensAssembly of system.

closestintersection(a::Union{EmptyInterval{T},Interval{T},DisjointUnion{T}}, ignorenull::Bool = true) -> Union{Nothing,Intersection{T,3}}

Returns the closest Intersection from an Interval or DisjointUnion. Ignores intersection with null interfaces if ignorenull is true. Will return nothing if there is no valid intersection.

closestpointonray(r::Ray{T,N}, point::SVector{N,T}) -> SVector{T,N

Returns the point on the ray closest to point.

csgdifference(a::CSGGenerator{T}, b::CSGGenerator{T}, transform::Transform{T} = identitytransform(T)) -> CSGGenerator{T}

Create a binary node in the CSG tree representing the difference of a and b, essentially a - b. A shortcut method for a and b as ParametricSurfaces is also available.

csgintersection(a::CSGGenerator{T} b::CSGGenerator{T}, transform::Transform{T} = identitytransform(T)) -> CSGGenerator{T}

Create a binary node in the CSG tree representing an intersection between a and b. A shortcut method for a and b as ParametricSurfaces is also available.

csgunion(a::CSGGenerator{T}, b::CSGGenerator{T}, transform::Transform{T} = identitytransform(T)) -> CSGGenerator{T}

Create a binary node in the CSG tree representing a union between a and b. A shortcut method for a and b as ParametricSurfaces is also available.

spatial dimension of curve represented as an array of coefficients x[i] = ∑Bj(θ)*x[i,j] where Bj(θ) is the curve basis

highest polynomial power of the curve represented as an array of coefficients x[i] = ∑Bj(θ)*x[i,j] where Bj(θ) is the curve basis

detectorimage(system::AbstractOpticalSystem{T}) -> HierarchicalImage{D}

Get the detector image of system. D is the datatype of the detector image and is not necessarily the same as the datatype of the system T.

distance(r::Ray{T,N}, point::SVector{N,T}) -> Union{T,Nothing}

Returns distance to the position on the ray closest to point. If t < 0 returns nothing.

doesintersect(bbox::BoundingBox{T}, r::AbstractRay{T,3}) -> Bool

Tests whether r intersects an axis-aligned BoundingBox, bbox.

Evaluates a curve defined in the power basis. Curves and moving lines accessed like this: [xi,ci] where xi is the dimension index, and ci is the coefficient index.

returns 3D array indexed like this: x[line curve order,spatial dimension, line number]`

fresnel(nᵢ::T, nₜ::T, sinθᵢ::T, sinθₜ::T) -> Tuple{T,T}

Returns reflectance and tranmission power coefficients according to the Fresnel equations. For geometric ray tracing this coefficient can be used directly to compute intensity on the detector plane. For Huygens phase optics need to take the square root to compute the amplitude. The power of the transmitted and refracted rays may not sum to one because of the area correction applied to the transmitted component. The intensity per area can increase or decrease depending on the indices of refraction.

nᵢ is the RI of the material which the incident ray travels in, nₜ is the RI of the material the transmitted ray travels in. sinθᵢ and sinθₜ are the sin of the angles of incidence and transmission respectively.

gendirection(o::GeometricRayGenerator{T}, n::Int) -> SVector{3,T}

Generate directions for rays based on the type of the generator, e.g., randomly within a cone or collimated. n is the index of the point being generated, starting from 0. This has little meaning for random generators, but is important for GridSource.

generateray(a::PixelSource{T}, n::Int) -> OpticalRay{T,3}

Generates optical rays from all subpixels in the pixel. One ray is generated from each subpixel sequentially before looping back to the start.

generateray(o::GeometricRayGenerator{T}, n::Int) -> Ray{T,3}

Generate geometric rays distributed according to the type of the generator. n is the index of the point being generated, starting from 0. This has little meaning for random generators, but is important for GridSource, for example.

generateray(a::BasicDisplayPanel{T}, n::Int) -> OpticalRay{T,3}

Generates optical rays from all pixels in the display. One ray is generated from each pixel sequentially before looping back to the start of the display.

generateray(o::OpticalRayGenerator{T}, n::Int) -> OpticalRay{T,3}

Generate optical rays distributed according to the type of the generator. n is the index of the point being generated, starting from 0. This has little meaning for random generators, but is important for generators using GridSource or GridRectOriginPoints, for example.

generateray(a::OpticalSourceArray{T}, n::Int) -> OpticalRay{T,3}

Generates optical rays from all generators in the array. One ray is generated from each element sequentially before looping back to the start of the array.

generateray(a::OpticalSourceGroup{T}, n::Int) -> OpticalRay{T,3}

Generate optical rays for each source in the group. All rays are generated for the first source, then all for the second source and so on as n increases.

genorigin(o::RayOriginGenerator{T}, n::Int) -> SVector{3,T}

Generate origin positions for rays based on the type of the generator, e.g., randomly within a rectangle or ellipse. n is the index of the point being generated, starting from 0. This has little meaning for random generators, but is important for HexapolarOriginPoints and GridRectOriginPoints.

halfspaceintersection(a::Interval{T}) -> Intersection{T,3}

Returns the Intersection from a half space Interval, throws an error if not a half space.

interface(surf::Surface{T}) -> OpticalInterface{T}

Return the OpticalInterface associated with surf.

returns an array of intersection points. Each element in the array is ([x,y,...],alpha,theta) where [x,y,...] is the n-dimensional intersection point, alpha is the line parameter value at the intersection point, and theta is the curve parameter value at the intersection point

isemptyinterval(a) -> Bool

Returns true if a is an EmptyInterval. In performance critical contexts use a isa EmptyInterval{T}.

isinfinity(a) -> Bool

Returns true if a is Infinity. In performance critical contexts use a isa Infinity{T}.

ispositivehalfspace(a) -> Bool

Returns true if upper(a) is Infinity. In performance critical contexts check directly i.e. upper(a) isa Infinity{T}.

israyorigin(a) -> Bool

Returns true if a is RayOrigin. In performance critical contexts use a isa RayOrigin{T}.

israyorigininterval(a) -> Bool

Returns true if lower(a) is RayOrigin. In performance critical contexts check directly i.e. lower(a) isa RayOrigin{T}.

jacobian(surf::ParametricSurface{T,N}, u::T, v::T, P1::SVector{M,T}, P2::SVector{M,T})

Computes Jacobian of f(t,u,v) = ( dot(P1,[surf(u,v),1],P2,[surf(u,v),1]) ). P1, P2 are orthogonal planes that pass through the ray. J = [ ∂f1/∂u ∂f1/∂v ; ∂f2/∂u ∂f2/∂v]

leaf(surf::CSGGenerator{T}, transform::Transform{T} = identitytransform(T)) -> CSGGenerator{T}

Create a (pseudo) leaf node from another CSGGenerator, this is useful if you want multiple copies of a premade CSG structure with different transforms, for example in an MLA.

leaf(surf::ParametricSurface{T}, transform::Transform{T} = identitytransform(T)) -> CSGGenerator{T}

Create a leaf node from a parametric surface with a given transform.

spatial dimension of the moving line represented as an array of coefficients g[i] = ∑Bl(θ)*gl[i,j] where Bl(θ) is the polynomial basis

makemesh(object, subdivisions::Int = 30) -> TriangleMesh

Creates a TriangleMesh from an object, either a ParametricSurface, CSGTree or certain surfaces (e.g. Circle, Rectangle). This is used for visualization purposes only.

movinglines[:,i] is the ith moving line. For li = movinglines[:,i] (dimension+1,lineorder) = size(li). rline[:,1] = pt1 and rline[:,2] = pt2. The line equation is pt1 + alpha*pt2.

newton(surf::ParametricSurface{T,N}, r::AbstractRay{T,N}, startingpoint::SVector{2,T})

Newton iteration to find the precise intersection of a parametric surface with a ray given a starting point (in uv space) on the surface.

normal(surf::ParametricSurface{T}, u::T, v::T) -> SVector{3,T}
normal(surf::ParametricSurface{T}, uv::SVector{2,T}) -> SVector{3,T}

Returns the normal to surf at the given uv coordinate.

number of lines in moving line array

returns a matrix expressing the relationship [x(θ) 1]⋅g(θ) = 0. The vectors in the right nullspace of this matrix contain the coefficients of the moving lines gᵢ(θ).

point(ray::AbstractRay{T,N}, alpha::T) -> SVector{T, N}

Returns a point on the ray at origin + alpha * direction. Alpha must be >= 0.

pressure(system::AbstractOpticalSystem{T}) -> T

Get the pressure of system in Atm.

processintersection(opticalinterface::OpticalInterface{T}, point::SVector{N,T}, normal::SVector{N,T}, incidentray::OpticalRay{T,N}, temperature::T, pressure::T, ::Bool, firstray::Bool = false) -> Tuple{SVector{N,T}, T, T}

Processes an intersection of an OpticalRay with an OpticalInterface, distinct behaviors must be implemented for each subclass of OpticalInterface.

point is the 3D intersection point in global space, normal is the surface normal at the intersection point.

If test is true then the behavior of the ray should be deterministic. firstray indicates that this ray is the first segment of the trace and therefore the origin is not offset.

The values returned are the normalized direction of the ray after the intersection, the instantaneous power of the ray after the intersection and the optical path length of the ray up to the intersection.

nothing is returned if the ray should stop here, in order to obtain the correct intensity on the detector through monte carlo integration nothing should be returned proportionally to create the correct power distribution. i.e. If the interface should modulate power to 76% then 24% of calls to this function should return nothing.

randinsolidangle(direction::SVector{3,T}, uvec::SVector{3,T}, vvec::SVector{3,T}, θmax::T)

Generates a unit vector pointing somewhere within the cone with half angle θmax around direction. uvec and vvec should be orthogonal to each other and direction.

reset!(a::HierarchicalImage{T})

Resets the pixels in the image to zero(T). Do this rather than image .= zero(T) because that will cause every pixel to be accessed, and therefore allocated. For large images this can cause huge memory traffic.

resetdetector!(system::AbstractOpticalSystem{T})

Reset the deterctor image of system to zero.

reversenormal(a::Intersection{T,N})

Used by the CSG complement operator (i.e. csgdifference) to reverse the inside outside sense of the object.

samplesurface(surf::ParametricSurface{T,N}, samplefunction::Function, numsamples::Int = 30)

Sample a parametric surface on an even numsamples×numsamples grid in UV space with provided function

semidiameter(system::AxisymmetricOpticalSystem{T}) -> T

Get the semidiameter of system, that is the semidiameter of the entrance pupil (i.e. first surface) of the system.

snell(surfacenormal::AbstractVector{T}, raydirection::AbstractVector{T}, nᵢ::T, nₜ::T) -> Tuple{T,T}

nᵢ is the index of refraction on the incidence side of the interface. nₜ is the index of refraction on the transmission side.

Returns sinθᵢ and sinθₜ according to Snell's law.

sum!(a::HierarchicalImage{T}, b::HierarchicalImage{T})

Add the contents of b to a in an efficient way.

surfaceintersection(surf::Surface{T}, r::AbstractRay{T}) where {T}

Calculates the intersection of r with a surface of any type, surf. Note that some surfaces cannot be intersected analytically so must be wrapped in an AcceleratedParametricSurface in order to be intersected.

Returns an EmptyInterval if there is no Intersection, an Interval if there is one or two intersections and a DisjointUnion if there are more than two intersections.

temperature(system::AbstractOpticalSystem{T}) -> T

Get the temperature of system in °C.

trace(system::AbstractOpticalSystem{T}, ray::OpticalRay{T}; trackrays = nothing, test = false)

Traces system with ray, if test is enabled then fresnel reflections are disabled and the power distribution will not be correct. Returns either a LensTrace if the ray hits the detector or nothing otherwise.

trackrays can be passed an empty vector to accumulate the LensTrace objects at each intersection of ray with a surface in the system.

trace(assembly::LensAssembly{T}, r::OpticalRay{T}, temperature::T = 20.0, pressure::T = 1.0; trackrays = nothing, test = false)

Returns the ray as it exits the assembly in the form of a LensTrace object if it hits any element in the assembly, otherwise nothing. Recursive rays are offset by a small amount (RAY_OFFSET) to prevent it from immediately reintersecting the same lens element.

trackrays can be passed an empty vector to accumulate the LensTrace objects at each intersection of ray with a surface in the assembly.

trace(system::AbstractOpticalSystem{T}, raygenerator::OpticalRayGenerator{T}; printprog = true, test = false)

Traces system with rays generated by raygenerator on a single thread. Optionally the progress can be printed to the REPL. If test is enabled then fresnel reflections are disabled and the power distribution will not be correct. If outpath is specified then the result will be saved to this path.

Returns the detector image of the system.

traceMT(system::AbstractOpticalSystem{T}, raygenerator::OpticalRayGenerator{T}; printprog = true, test = false)

Traces system with rays generated by raygenerator using as many threads as possible. Optionally the progress can be printed to the REPL. If test is enabled then fresnel reflections are disabled and the power distribution will not be correct. If outpath is specified then the result will be saved to this path.

Returns the accumulated detector image from all threads.

tracehits(system::AbstractOpticalSystem{T}, raygenerator::OpticalRayGenerator{T}; printprog = true, test = false)

Traces system with rays generated by raygenerator on a single thread. Optionally the progress can be printed to the REPL. If test is enabled then fresnel reflections are disabled and the power distribution will not be correct.

Returns a list of LensTraces which hit the detector.

tracehitsMT(system::AbstractOpticalSystem{T}, raygenerator::OpticalRayGenerator{T}; printprog = true, test = false)

Traces system with rays generated by raygenerator using as many threads as possible. Optionally the progress can be printed to the REPL. If test is enabled then fresnel reflections are disabled and the power distribution will not be correct.

Returns a list of LensTraces which hit the detector, accumulated from all threads.

triangulate(surf::ParametricSurface{S,N}, quads_per_row::Int, extensionu::Bool = false, extensionv::Bool = false, radialu::Bool = false, radialv::Bool = false)

Create an array of triangles representing the parametric surface where vertices are sampled on an even grid in UV space. The surface can be extended by 1% in u and v separately, and specifying either u or v as being radial - i.e. detemining the radius on the surface e.g. rho for zernike - will result in that dimension being sampled using sqwrt so that area of triangles is uniform. The extension will also only apply to the maximum in this case.

triangulatedintersection(surf::AcceleratedParametricSurface{T,N,S}, r::AbstractRay{T,N})

Intersection of a ray, r, with a triangulated surface, surf, no concept of inside so never returns a RayOrigin Interval.

uv(surf::ParametricSurface{T}, p::SVector{3,T}) -> SVector{2,T}
uv(surf::ParametricSurface{T}, x::T, y::T, z::T) -> SVector{2,T}

Returns the uv coordinate on surf of a point, p, in 3D space. If onsurface(surf, p) is false then the behavior is undefined, it may return an inorrect uv, an invalid uv, NaN or crash.

uvrange(s::ParametricSurface)
uvrange(::Type{S}) where {S<:ParametricSurface}

Returns a tuple of the form: ((umin, umax), (vmin, vmax)) specifying the limits of the parameterisation for this surface type. Also implemented for some Surfaces which are not ParametricSurfaces (e.g. Rectangle).

uvtopix(surf::Surface{T}, uv::SVector{2,T}, imsize::Tuple{Int,Int}) -> Tuple{Int,Int}

Converts a uvcoordinate on surf to an integer index to a pixel in an image of size imsize. Not implemented on all Surface objects. Used to determine where in the detector image a ray has hit when in intersects the detector surface of an AbstractOpticalSystem.

α(ray::AbstractRay{T,N}, point::SVector{N,T}) -> T

Computes the alpha corresponding to the closest position on the ray to point

Transform(origin, forward) -> Transform{S}

Returns the Transform of type S (default Float64) representing the local frame with origin and forward direction. the other 2 axes are computed automaticlly.

Transform(colx::Vec3{T}, coly::Vec3{T},colz::Vec3{T}, colw::Vec3{T}, ::Type{T} = Float64) where {T<:Real}

Costruct a transform from the input columns.

Transform(rotation::AbstractArray{T,2}, translation::AbstractArray{T,1}) where {T<:Real} -> Transform{S}

Returns the Transform of type S (default Float64) created by a rotation matrix (3x3) and translation vector of length 3.

Transform(colx::Vec3{T}, coly::Vec3{T},colz::Vec3{T}, colw::Vec3{T}, ::Type{T} = Float64) where {T<:Real}

Costruct a transform from the input columns.

Transform(rotation::SMatrix{3,3,T}, translation::SVector{3,T}) where {T<:Real} -> Transform{S}

Returns the Transform of type S (default Float64) created by a rotation matrix and translation vector.

Transform([S::Type]) -> Transform{S}

Returns the Transform of type S (default Float64) representing the identity transform.

Vec4(v::Vec3{T}) -> Vec4

Accept Vec3 and create a Vec4 type [v[1], v[2], v[3], 1]

Vec4(v::SVector{3, T}) where {T<:Real} -> Vec4{T}

Accept SVector and create a Vec4 type [v[1], v[2], v[3], 1]

decomposeRTS(tr::Transform{T}) where {T<:Real}

return a touple containing the rotation matrix, the translation vector and the scale vecto represnting the transform.

identitytransform([S::Type]) -> Transform{S}

Returns the Transform of type S (default Float64) representing the identity transform.

local2world(t::Transform{T}) where {T<:Real}

return the transform matrix that takes a point in the local coordinate system to the global one

returns the unit vector [1, 1, 1]

returns the unit vector [1, 1, 1, 1]

rotate(a::Transform{T}, vector::Union{Vec3{T}, SVector{3,T}}) where {T<:Real} -> Vec3{T}

apply the rotation part of the transform a to the vector vector - this operation is usually used to rotate direction vectors.

rotation(t::Transform{T}) where {T<:Real} -> SMatrix{3,3,T}

returns the rotation part of the transform t - a 3x3 matrix.

rotation([S::Type], θ::T, ϕ::T, ψ::T) -> Transform{S}

Returns the Transform of type S (default Float64) representing the rotation by θ, ϕ and ψ around the x, y and z axes respectively in radians.

rotationX(angle::T) where {T<:Real} -> Transform

Builds a rotation matrix for a rotation around the x-axis. Parameters: The counter-clockwise angle in radians.

rotationY(angle::T) where {T<:Real} -> Transform

Builds a rotation matrix for a rotation around the y-axis. Parameters: The counter-clockwise angle in radians.

rotationZ(angle::T) where {T<:Real} -> Transform

Builds a rotation matrix for a rotation around the z-axis. Parameters: The counter-clockwise angle in radians.

rotationd([S::Type], θ::T, ϕ::T, ψ::T) -> Transform{S}

Returns the Transform of type S (default Float64) representing the rotation by θ, ϕ and ψ around the x, y and z axes respectively in degrees.

rotmat([S::Type], θ::T, ϕ::T, ψ::T) -> SMatrix{3,3,S}

Returns the rotation matrix of type S (default Float64) representing the rotation by θ, ϕ and ψ around the x, y and z axes respectively in radians.

rotmatbetween([S::Type], a::SVector{3,T}, b::SVector{3,T}) -> SMatrix{3,3,S}

Returns the rotation matrix of type S (default Float64) representing the rotation between vetors a and b, i.e. rotation(a,b) * a = b.

rotmatd([S::Type], θ::T, ϕ::T, ψ::T) -> SMatrix{3,3,S}

Returns the rotation matrix of type S (default Float64) representing the rotation by θ, ϕ and ψ around the x, y and z axes respectively in degrees.

scale(s::T) where {T<:Real}

Creates a uniform scaling transform

scale(t::Vec3{T}) where {T<:Real}

Creates a scaling transform

scale(x::T, y::T, z::T) where {T<:Real}

Creates a scaling transform

translation(x::T, y::T, z::T) where {T<:Real}

Creates a translation transform

translation(x::T, y::T, z::T) where {T<:Real}

Creates a translation transform

returns the unit vector [0, 0, 0, 1]

returns the unit vector [1, 0, 0]

returns the unit vector [1, 0, 0, 0]

returns the unit vector [0, 1, 0]

returns the unit vector [0, 1, 0, 0]

returns the unit vector [0, 0, 1]

returns the unit vector [0, 0, 1, 0]

world2local(t::Transform{T}) where {T<:Real}

return the transform matrix that takes a point in the global coordinate system to the local one

returns the unit vector [0, 0, 0]

returns the unit vector [0, 0, 0, 0]

Module to enclose Zernike polynomial specific functionality.

NolltoNM(j::Int) -> Tuple{Int, Int}

Convert Noll zernike index j to (N,M) form.

OSAtoNM(j::Int) -> Tuple{Int, Int}

Convert OSA zernike index j to (N,M) form according to formula J = N * (N + 2) + M.

R(N::Int, M::Int, ρ::T) -> T

Evaluate radial polynomial $R_{n}^{m}(\rho)$.

normalisation(::Type{T}, N::Int, M::Int) -> T

Normalisation coefficient for Zernike polynomial term $Z_{n}^{m}$.

δζ(N::Int, M::Int, ρ::T, ϕ::T) -> Tuple{T,T}

Evaluate partial derivatives of Zernike polynomial term $Z_{n}^{m}(\rho, \phi)$.

ζ(N::Int, M::Int, ρ::T, ϕ::T) -> Tuple{T,T}

Evaluate Zernike polynomial term $Z_{n}^{m}(\rho, \phi)$.

Module to enclose QType polynomial specific functionality. For reference see:

1. Robust, efficient computational methods for axially symmetric optical aspheres - G. W. Forbes, 2010
2. Characterizing the shape of freeform optics - G. W. Forbes, 2012

S(coeffs::SVector{NP1,T}, m::Int x::T) -> T

Evaluates $\sum_{n=0}^{N}c_n^mQ_n^m(x)$ where $c_n^m$ is either an $\alpha$ or $\beta$ QType coefficient and $m \gt 0$.

S0(coeffs::SVector{NP1,T}, x::T) -> T

Evaluates $\sum_{n=0}^{N}\alpha_n^0Q_n^0(x)$.

dS0dx(coeffs::SVector{NP1,T}, x::T) -> T

Evaluates $\frac{\partial}{\partial x}\sum_{n=0}^{N}\alpha_n^0Q_n^0(x)$.

dSdx(coeffs::SVector{NP1,T}, x::T) -> T

Evaluates $\frac{\partial}{\partial x}\sum_{n=0}^{N}c_n^mQ_n^m(x)$ where $c_n^m$ is either an $\alpha$ or $\beta$ QType coefficient and $m \gt 0$.

Module to enclose Chebyshev polynomial specific functionality.

T(n::Int, q::R, fast::Bool = true) -> R

Evaluate Chebyshev polynomial of the first kind $T_n(q)$.

fast will use trigonometric definition, rather than the recursive definition which is much faster but slightly less precise.

U(n::Int, q::R, fast::Bool = true) -> R

Evaluate Chebyshev polynomial of the second kind $U_n(q)$.

fast will use trigonometric definition, rather than the recursive definition which is much faster but slightly less precise.

dTdq(n::Int, q::R, fast::Bool = true) -> R

Evaluate derivative of Chebyshev polynomial of the first kind $\frac{dT_n}{dq}(q)$.

fast will use trigonometric definition, rather than the recursive definition which is much faster but slightly less precise.

Contains example usage of the features in the OpticSim.jl package.