Plotting data on the Circle

For the circle there are two different representations: as angles in the interval $[-π,π)$ or as complex numbers of absolute value 1.

The real-valued Circle

For signals on the circle, we can plot them in a usual scatter

using Manifolds, ManifoldMakie, GLMakie

x = 0:0.25:5
y = (mod.((x./2).^2 .- 0.4 .+ π, 2π)) .- π
y2 = (mod.((x).^2 .- 0.4 .+ π, 2π)) .- π

M = Manifolds.Circle(ℝ)
fig, ax, pl = circleplot(M)
lines!(ax, M, y; color = :green)
scatter!(ax, M, x, y2; color = :green)
fig

For images, we can also color them (automatically) in hue

using Manifolds, ManifoldMakie, ManoptExamples, GLMakie

img = sym_rem.(ManoptExamples.artificialIn_SAR_image(128))
M = Manifolds.Circle(ℝ)
fig, ax, pl = circleimage(M)
image!(ax, M, img)
fig

where the default colormap for these plots is changed to :hsv.

The complex circle

The complex numbers representing points on the circle in the complex plane can be used as follows

using Manifolds, ManifoldMakie, GLMakie

M = Manifolds.Circle(ℂ)
fig, ax, pl = circleplot(M)

p = 1.0 + 0.0im
q = 1/sqrt(2) -1/sqrt(2) * 1im
r = 0.9 + sqrt(0.19)im
pts = shortest_geodesic(M, p, q, 0:0.05:1.0)
vecs = [log(M, s, r) for s in pts]

arrows2d!(ax, M, pts, vecs; color = :blue)
scatter!(ax, M, pts; color = :green, markersize = 16)
scatter!(ax, M, [r,]; color = :orange, markersize = 16)
fig

Function reference

ManifoldMakie.circleimage — Function

circleimage(::Manifolds.Circle{ℝ}; kwargs...)

Start a plot for 2D data with values on the Circle represented in angles an interval [-π,π).

This can be combined with

image(M, img) to show the image of the data.

Examples

fig, ax, p = circleimage(Manifolds.Circle(ℂ))

Plot type

The plot type alias for the circleimage function is CircleImage.

Attributes

clip_planes = @inherit clip_planes automatic — Clip planes offer a way to do clipping in 3D space. You can set a Vector of up to 8 Plane3f planes here, behind which plots will be clipped (i.e. become invisible). By default clip planes are inherited from the parent plot or scene. You can remove parent clip_planes by passing Plane3f[].

depth_shift = 0.0 — Adjusts the depth value of a plot after all other transformations, i.e. in clip space, where -1 <= depth <= 1. This only applies to GLMakie and WGLMakie and can be used to adjust render order (like a tunable overdraw).

fxaa = true — Adjusts whether the plot is rendered with fxaa (fast approximate anti-aliasing, GLMakie only). Note that some plots implement a better native anti-aliasing solution (scatter, text, lines). For them fxaa = true generally lowers quality. Plots that show smoothly interpolated data (e.g. image, surface) may also degrade in quality as fxaa = true can cause blurring.

inspectable = @inherit inspectable — Sets whether this plot should be seen by DataInspector. The default depends on the theme of the parent scene.

inspector_clear = automatic — Sets a callback function (inspector, plot) -> ... for cleaning up custom indicators in DataInspector.

inspector_hover = automatic — Sets a callback function (inspector, plot, index) -> ... which replaces the default show_data methods.

inspector_label = automatic — Sets a callback function (plot, index, position) -> string which replaces the default label generated by DataInspector.

model = automatic — Sets a model matrix for the plot. This overrides adjustments made with translate!, rotate! and scale!.

overdraw = false — Controls if the plot will draw over other plots. This specifically means ignoring depth checks in GL backends

space = :data — Sets the transformation space for box encompassing the plot. See Makie.spaces() for possible inputs.

ssao = false — Adjusts whether the plot is rendered with ssao (screen space ambient occlusion). Note that this only makes sense in 3D plots and is only applicable with fxaa = true.

transformation = :automatic — Controls the inheritance or directly sets the transformations of a plot. Transformations include the transform function and model matrix as generated by translate!(...), scale!(...) and rotate!(...). They can be set directly by passing a Transformation() object or inherited from the parent plot or scene. Inheritance options include:

:automatic: Inherit transformations if the parent and child space is compatible
:inherit: Inherit transformations
:inherit_model: Inherit only model transformations
:inherit_transform_func: Inherit only the transform function
:nothing: Inherit neither, fully disconnecting the child's transformations from the parent

Another option is to pass arguments to the transform!() function which then get applied to the plot. For example transformation = (:xz, 1.0) which rotates the xy plane to the xz plane and translates by 1.0. For this inheritance defaults to :automatic but can also be set through e.g. (:nothing, (:xz, 1.0)).

transparency = false — Adjusts how the plot deals with transparency. In GLMakie transparency = true results in using Order Independent Transparency.

visible = true — Controls whether the plot gets rendered or not.

source

ManifoldMakie.circleplot — Function

circleplot(::Manifolds.Circle{ℝ}; kwargs...)
circleplot(::Manifolds.Circle{ℂ}; kwargs...)

Draw a plot for data on the Circle. For the real-valued case this is a plot on an interval [-π,π), for the complex case a circle in the complex plane.