diff --git a/src/examples.jl b/src/examples.jl
index 19b167ad..62600217 100644
--- a/src/examples.jl
+++ b/src/examples.jl
@@ -480,6 +480,23 @@ PlotExample("Histogram2D (complex values)",
     end)]
 ),
 
+PlotExample("Unconnected lines using `missing` or `NaN`",
+"""
+Missing values and non-finite values, including `NaN`, are not plotted.
+Instead, lines are separated into segments at these values.
+""",
+    [:(begin
+        x,y = [1,2,2,1,1], [1,2,1,2,1]
+        plot(
+              plot([rand(5); NaN; rand(5); NaN; rand(5)]),
+              plot([1,missing,2,3], marker=true),
+              plot([x; NaN; x.+2], [y; NaN; y.+1], arrow=2),
+              plot([1, 2+3im, Inf, 4im, 3, -Inf*im, 0, 3+3im], marker=true),
+              legend=false
+        )
+    end)]
+),
+
 ]
 
 # Some constants for PlotDocs and PlotReferenceImages
diff --git a/src/series.jl b/src/series.jl
index ded927fb..61da260f 100644
--- a/src/series.jl
+++ b/src/series.jl
@@ -10,17 +10,17 @@ const FuncOrFuncs{F} = Union{F, Vector{F}, Matrix{F}}
 const MaybeNumber = Union{Number, Missing}
 const MaybeString = Union{AbstractString, Missing}
 const DataPoint = Union{MaybeNumber, MaybeString}
-const SeriesData = Union{AVec{<:DataPoint}, Function, Surface, Volume}
 
 prepareSeriesData(x) = error("Cannot convert $(typeof(x)) to series data for plotting")
 prepareSeriesData(::Nothing) = nothing
-prepareSeriesData(s::SeriesData) = handlemissings(s)
-
-handlemissings(v) = v
-handlemissings(v::AbstractArray{<:MaybeNumber}) = replace(v, missing => NaN)
-handlemissings(v::AbstractArray{<:MaybeString}) = replace(v, missing => "")
-handlemissings(s::Surface) = Surface(handlemissings(s.surf))
-handlemissings(v::Volume) = Volume(handlemissings(v.v), v.x_extents, v.y_extents, v.z_extents)
+prepareSeriesData(f::Function) = f
+prepareSeriesData(a::AbstractArray{<:MaybeNumber}) = replace!(
+                                    x -> ismissing(x) || isinf(x) ? NaN : x,
+                                    map(float,a))
+prepareSeriesData(a::AbstractArray{<:MaybeString}) = replace(x -> ismissing(x) ? "" : x, a)
+prepareSeriesData(s::Surface{<:AMat{<:MaybeNumber}}) = Surface(prepareSeriesData(s.surf))
+prepareSeriesData(s::Surface) = s  # non-numeric Surface, such as an image
+prepareSeriesData(v::Volume) = Volume(prepareSeriesData(v.v), v.x_extents, v.y_extents, v.z_extents)
 
 # default: assume x represents a single series
 convertToAnyVector(x, plotattributes) = Any[prepareSeriesData(x)]