Total circles area: Difference between revisions

Line 3,773:

Note that the error on the Monte Carlo sampling is actually very high; the above run happened to deliver a figure closer to the real value than usual.

=={{header|Uiua}}==

Developed mainly to play with Uiua's image handling. Getting a very rough area figure is a bonus.

Cs ← [[1.6417233788 1.6121789534 0.0848270516]

[¯1.4944608174 1.2077959613 1.1039549836]

[0.6110294452 ¯0.6907087527 0.9089162485]

[0.3844862411 0.2923344616 0.2375743054]

[¯0.249589295 ¯0.3832854473 1.0845181219]

[1.7813504266 1.6178237031 0.8162655711]

[¯0.1985249206 ¯0.8343333301 0.0538864941]

[¯1.7011985145 ¯0.1263820964 0.4776976918]

[¯0.4319462812 1.4104420482 0.7886291537]

[0.2178372997 ¯0.9499557344 0.0357871187]

[¯0.6294854565 ¯1.3078893852 0.7653357688]

[1.7952608455 0.6281269104 0.2727652452]

[1.4168575317 1.0683357171 1.1016025378]

[1.4637371396 0.9463877418 1.1846214562]

[¯0.5263668798 1.7315156631 1.4428514068]

[¯1.2197352481 0.9144146579 1.0727263474]

[¯0.1389358881 0.109280578 0.7350208828]

[1.5293954595 0.0030278255 1.2472867347]

[¯0.5258728625 1.3782633069 1.3495508831]

[¯0.1403562064 0.2437382535 1.3804956588]

[0.8055826339 ¯0.0482092025 0.3327165165]

[¯0.6311979224 0.7184578971 0.2491045282]

[1.4685857879 ¯0.8347049536 1.3670667538]

[¯0.6855727502 1.6465021616 1.0593087096]

[0.0152957411 0.0638919221 0.9771215985]]

MinY ← /↧≡(¯/-↘1) Cs

MinX ← /↧≡(/-↘1↻1) Cs

# Normalise minimal X, Y values to 0

Ncs ← ≡⍜(⊡0|-MinX)≡⍜(⊡1|-MinY)Cs

# Scale total range to (0-Dim,0-Dim), save for later.

Dim ← 500

Scale ← /↥♭≡(+⊃(⊢|↘1)↻¯1) Ncs

Scs ← ⌊×Dim÷: Ncs Scale

# For each r generate a 2r.2r grid and set cells that are within circle.

InCircle ← <ⁿ2⟜(⊞(/+≡ⁿ2⊟).+⇡⊃(×2|¯))

# Offset that grid down/right, and fade it out, then add to accum.

Filler ← ⍜(↻|⬚0+)⊙: ⊃(+¯|×0.1InCircle) ⊃(⊢|↘1) ↻¯1

# Fold over all circles, accumulating into a blank grid.

&p ⍜now(∧Filler Scs ↯Dim_Dim 0) &pf "Runtime (s): "

&p ×ⁿ2 ÷Dim Scale (⧻⊚≠0) ♭. &pf "*Very* approximate area: "

# Uncomment to save image.

# &ime "png"

# &fwa "UiuaOverlappingCircles.png"

</syntaxhighlight>

<pre>

stdout:

Runtime (s): 3.7929999999978463

*Very* approximate area: 21.402218310691705

</pre>

[[File:UiuaOverlappingCircles.png|300px|thumbnail|center|Overlapping translucent circles]]

<p></p>

=={{header|VBA}}==

Analytical solution adapted from Haskell/Python.