daviddoji/CalculusWithJuliaNotes.jl
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

WIP: Plots

Browse Source
This commit is contained in:
jverzani
2025-06-27 19:21:20 -04:00
parent 4f60e9a414
commit c4bd214ecd
5 changed files with 28 additions and 61 deletions
Download Patch File Download Diff File Expand all files Collapse all files

7
quarto/alternatives/Project.toml
View File

@@ -5,11 +5,13 @@ ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a"
GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
Implicit3DPlotting = "d997a800-832a-4a4c-b340-7dddf3c1ad50"
Integrals = "de52edbc-65ea-441a-8357-d3a637375a31"
LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
Meshing = "e6723b4c-ebff-59f1-b4b7-d97aa5274f73"
ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
Mustache = "ffc61752-8dc7-55ee-8c37-f3e9cdd09e70"
NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
Optimization = "7f7a1694-90dd-40f0-9382-eb1efda571ba"
OptimizationOptimJL = "36348300-93cb-4f02-beb5-3c3902f8871e"
@@ -19,6 +21,7 @@ PlotlyKaleido = "f2990250-8cf9-495f-b13a-cce12b45703c"
PlotlyLight = "ca7969ec-10b3-423e-8d99-40f33abb42bf"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
QuizQuestions = "612c44de-1021-4a21-84fb-7261cf5eb2d4"
Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
SplitApplyCombine = "03a91e81-4c3e-53e1-a0a4-9c0c8f19dd66"
StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
@@ -26,3 +29,5 @@ SymPy = "24249f21-da20-56a4-8eb1-6a02cf4ae2e6"
SymbolicLimits = "19f23fe9-fdab-4a78-91af-e7b7767979c3"
SymbolicNumericIntegration = "78aadeae-fbc0-11eb-17b6-c7ec0477ba9e"
Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
TextWrap = "b718987f-49a8-5099-9789-dcd902bef87d"

2
quarto/alternatives/SciML.qmd
View File

@@ -250,7 +250,7 @@ With the system defined, we can pass this to `NonlinearProblem`, as was done wit
```{julia}
prob = NonlinearProblem(ns, [1.0], [α => 1.0])
prob = NonlinearProblem(mtkcompile(ns), [1.0], Dict(α => 1.0))
```
The problem is solved as before:

36
quarto/alternatives/makie_plotting.qmd
View File

@@ -865,20 +865,19 @@ end
#### Implicitly defined surfaces, $F(x,y,z)=0$
To plot the equation $F(x,y,z)=0$, for $F$ a scalar-valued function, again the implicit function theorem says that, under conditions, near any solution $(x,y,z)$, $z$ can be represented as a function of $x$ and $y$, so the graph will look likes surfaces stitched together. The `Implicit3DPlotting` package takes an approach like `ImplicitPlots` to represent these surfaces. It replaces the `Contour` package computation with a $3$-dimensional alternative provided through the `Meshing` and `GeometryBasics` packages.
To plot the equation $F(x,y,z)=0$, for $F$ a scalar-valued function, again the implicit function theorem says that, under conditions, near any solution $(x,y,z)$, $z$ can be represented as a function of $x$ and $y$, so the graph will look like surfaces stitched together.
```{julia}
using Implicit3DPlotting
```
With `Makie`, many implicitly defined surfaces can be adequately represented using `countour` with the attribute `levels=[0]`. We will illustrate this technique.
The `Implicit3DPlotting` package takes an approach like `ImplicitPlots` to represent these surfaces. It replaces the `Contour` package computation with a $3$-dimensional alternative provided through the `Meshing` and `GeometryBasics` packages. This package has a `plot_implicit_surface` function that does something similar to below. We don't illustrate it, as it *currently* doesn't work with the latest version of `Makie`.
This example, plotting an implicitly defined sphere, comes from the documentation of `Implicit3DPlotting`. The `f` to be plotted is a scalar-valued function of a vector:
To begin, we plot a sphere implicitly as a solution to $F(x,y,z) = x^2 + y^2 + z^2 - 1 = 0$>
```{julia}
f(x) = sum(x.^2) - 1
xlims = ylims = zlims = (-5, 5)
plot_implicit_surface(f; xlims, ylims, zlims)
f(x,y,z) = x^2 + y^2 + z^2 - 1
xs = ys = zs = range(-3/2, 3/2, 100)
contour(xs, ys, zs, f; levels=[0])
```
@@ -887,11 +886,13 @@ Here we visualize an intersection of a sphere with another figure:
```{julia}
r₂(x) = sum(x.^2) - 5/4 # a sphere
r₂(x) = sum(x.^2) - 2 # a sphere
r₄(x) = sum(x.^4) - 1
xlims = ylims = zlims = (-2, 2)
p = plot_implicit_surface(r₂; xlims, ylims, zlims, color=:yellow)
plot_implicit_surface!(p, r₄; xlims, ylims, zlims, color=:red)
ϕ(x,y,z) = (x,y,z)
xs = ys = zs = range(-2, 2, 100)
contour(xs, ys, zs, r₂∘ϕ; levels = [0], colormap=:RdBu)
contour!(xs, ys, zs, r₄∘ϕ; levels = [0], colormap=:viridis)
current_figure()
```
@@ -900,11 +901,12 @@ This example comes from [Wikipedia](https://en.wikipedia.org/wiki/Implicit_surfa
```{julia}
f(x,y,z) = 2y*(y^2 -3x^2)*(1-z^2) + (x^2 +y^2)^2 - (9z^2-1)*(1-z^2)
xlims = ylims = zlims = (-5/2, 5/2)
plot_implicit_surface(x -> f(x...); xlims, ylims, zlims)
xs = ys = zs = range(-5/2, 5/2, 100)
contour(xs, ys, zs, f; levels=[0], colormap=:RdBu)
```
(This figure does not render well through `contour(xs, ys, zs, f, levels=[0])`, as the hole is not shown.)
(This figure does not render well though, as the hole is not shown.)
For one last example from Wikipedia, we have the Cassini oval which "can be defined as the point set for which the *product* of the distances to $n$ given points is constant." That is:
@@ -915,8 +917,8 @@ function cassini(λ, ps = ((1,0,0), (-1, 0, 0)))
n = length(ps)
x -> prod(norm(x .- p) for p ∈ ps) - λ^n
end
xlims = ylims = zlims = (-2, 2)
plot_implicit_surface(cassini(1.05); xlims, ylims, zlims)
xs = ys = zs = range(-2, 2, 100)
contour(xs, ys, zs, cassini(0.80) ∘ ϕ; levels=[0], colormap=:RdBu)
```
## Vector fields. Visualizations of $f:R^2 \rightarrow R^2$

35
quarto/alternatives/plotly_plotting.qmd
View File

@@ -251,40 +251,7 @@ The `text` mode specification is necessary to have text be displayed on the char
#### RGB Colors
The `ColorTypes` package is the standard `Julia` package providing an `RGB` type (among others) for specifying red-green-blue colors. To make this work with `Config` and `JSON3` requires some type-piracy (modifying `Base.string` for the `RGB` type) to get, say, `RGB(0.5, 0.5, 0.5)` to output as `"rgb(0.5, 0.5, 0.5)"`. (RGB values in JavaScript are integers between $0$ and $255$ or floating point values between $0$ and $1$.) A string with this content can be specified. Otherwise, something like the following can be used to avoid the type piracy:
```{julia}
struct rgb
r
g
b
end
PlotlyLight.JSON3.StructTypes.StructType(::Type{rgb}) = PlotlyLight.JSON3.StructTypes.StringType()
Base.string(x::rgb) = "rgb($(x.r), $(x.g), $(x.b))"
```
With these defined, red-green-blue values can be used for colors. For example to give a range of colors, we might have:
```{julia}
#| hold: true
cols = [rgb(i,i,i) for i in range(10, 245, length=5)]
sizes = [12, 16, 20, 24, 28]
data = Config(x = 1:5,
y = rand(5),
mode="markers+text",
type="scatter",
name="scatter plot",
text = ["marker $i" for i in 1:5],
textposition = "top center",
marker = Config(size=sizes, color=cols)
)
Plot(data)
```
The `opacity` key can be used to control the transparency, with a value between $0$ and $1$.
The `ColorTypes` package is the standard `Julia` package providing an `RGB` type (among others) for specifying red-green-blue colors. To make this work with `Config` and `JSON3` requires some type-piracy (modifying `Base.string` for the `RGB` type) to get, say, `RGB(0.5, 0.5, 0.5)` to output as `"rgb(0.5, 0.5, 0.5)"`. (RGB values in JavaScript are integers between $0$ and $255$ or floating point values between $0$ and $1$.) A string with this content can be specified.
#### Marker symbols

9
quarto/alternatives/symbolics.qmd
View File

@@ -601,14 +601,7 @@ det(N)
det(collect(N))
```
Similarly, with `norm`:
```{julia}
norm(v)
```
and
Similarly, with `norm`, which returns a generator unless collected:
```{julia}