From ea4515d0516dc3f0bd20428f6d032714ca5ffdea Mon Sep 17 00:00:00 2001
From: Florian Jung <flo@windfisch.org>
Date: Thu, 27 Aug 2015 21:05:22 +0200
Subject: reverse engineered zoom level

---
 reversing_game_mechanics/zoomlevel/README          |  30 ++
 reversing_game_mechanics/zoomlevel/filter_data.py  |  10 +
 reversing_game_mechanics/zoomlevel/fit.log         |  46 +++
 reversing_game_mechanics/zoomlevel/stats.pickle.xz | Bin 0 -> 581852 bytes
 reversing_game_mechanics/zoomlevel/win.mass.1      | 116 ++++++
 reversing_game_mechanics/zoomlevel/win.mass.2      | 455 +++++++++++++++++++++
 reversing_game_mechanics/zoomlevel/win.mass.3      | 126 ++++++
 reversing_game_mechanics/zoomlevel/win.mass.4      | 130 ++++++
 reversing_game_mechanics/zoomlevel/win.mass.5      |   8 +
 reversing_game_mechanics/zoomlevel/win.mass.6      |   4 +
 .../zoomlevel/win.mass.gnuplot                     |   9 +
 reversing_game_mechanics/zoomlevel/win.size.1      | 116 ++++++
 reversing_game_mechanics/zoomlevel/win.size.2      | 150 +++++++
 reversing_game_mechanics/zoomlevel/win.size.3      |  69 ++++
 reversing_game_mechanics/zoomlevel/win.size.4      |  77 ++++
 reversing_game_mechanics/zoomlevel/win.size.5      |   8 +
 reversing_game_mechanics/zoomlevel/win.size.6      |   4 +
 reversing_game_mechanics/zoomlevel/win.size.all    | 424 +++++++++++++++++++
 .../zoomlevel/win.size.all.filtered                | 227 ++++++++++
 .../zoomlevel/win.size.gnuplot                     |  16 +
 stats.py                                           |   4 +-
 21 files changed, 2027 insertions(+), 2 deletions(-)
 create mode 100644 reversing_game_mechanics/zoomlevel/README
 create mode 100644 reversing_game_mechanics/zoomlevel/filter_data.py
 create mode 100644 reversing_game_mechanics/zoomlevel/fit.log
 create mode 100644 reversing_game_mechanics/zoomlevel/stats.pickle.xz
 create mode 100644 reversing_game_mechanics/zoomlevel/win.mass.1
 create mode 100644 reversing_game_mechanics/zoomlevel/win.mass.2
 create mode 100644 reversing_game_mechanics/zoomlevel/win.mass.3
 create mode 100644 reversing_game_mechanics/zoomlevel/win.mass.4
 create mode 100644 reversing_game_mechanics/zoomlevel/win.mass.5
 create mode 100644 reversing_game_mechanics/zoomlevel/win.mass.6
 create mode 100644 reversing_game_mechanics/zoomlevel/win.mass.gnuplot
 create mode 100644 reversing_game_mechanics/zoomlevel/win.size.1
 create mode 100644 reversing_game_mechanics/zoomlevel/win.size.2
 create mode 100644 reversing_game_mechanics/zoomlevel/win.size.3
 create mode 100644 reversing_game_mechanics/zoomlevel/win.size.4
 create mode 100644 reversing_game_mechanics/zoomlevel/win.size.5
 create mode 100644 reversing_game_mechanics/zoomlevel/win.size.6
 create mode 100644 reversing_game_mechanics/zoomlevel/win.size.all
 create mode 100644 reversing_game_mechanics/zoomlevel/win.size.all.filtered
 create mode 100644 reversing_game_mechanics/zoomlevel/win.size.gnuplot

diff --git a/reversing_game_mechanics/zoomlevel/README b/reversing_game_mechanics/zoomlevel/README
new file mode 100644
index 0000000..72cd14d
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/README
@@ -0,0 +1,30 @@
+The goal is to find out the formula to calculate the appropriate zoom level,
+or equivalent: to calculate the size of the world viewport depending on, well,
+dunno.
+
+Data collected using bea9a124317, on 2015-08-25 *iirc*. (-> stats.pickle.xz)
+
+Data analyzed using a973a898619, with:
+
+	python analyze.py stats.pickle > temp
+
+then manually, create win.{size,mass}.{1,2,3,4,5,6} by cutting the
+analyze.py output into pieces (depending on number of cells).
+
+view with
+
+	gnuplot win.{size,mass}.gnuplot
+
+the gray lines in win.size.gnuplot denote the filtering conditions of
+filter_data.py
+
+Then merge and filter the data using
+
+	cat win.size.[123456] | python filter_data.py > win.size.all.filtered
+
+win.size.gnuplot will automatically fit a "a * size**b" - like function.
+
+Result: visible diagonal = 369.399 * sum(sizes)**0.431776
+
+Also, analyze.py tells us that the viewport ratio is 1.7 : 1
+
diff --git a/reversing_game_mechanics/zoomlevel/filter_data.py b/reversing_game_mechanics/zoomlevel/filter_data.py
new file mode 100644
index 0000000..e801d78
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/filter_data.py
@@ -0,0 +1,10 @@
+import sys
+
+for line in sys.stdin:
+    line = line.split()
+    size, diag = int(line[0]), float(line[1])
+    upper = size**0.4 * 460   +   50
+    lower = size**0.407 * 460   -   400
+    if lower < diag and diag < upper:
+        print(str(size) + "\t" + str(diag) + "\t\t" + line[2])
+
diff --git a/reversing_game_mechanics/zoomlevel/fit.log b/reversing_game_mechanics/zoomlevel/fit.log
new file mode 100644
index 0000000..10e4639
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/fit.log
@@ -0,0 +1,46 @@
+
+
+*******************************************************************************
+Thu Aug 27 21:04:27 2015
+
+
+FIT:    data read from "win.size.all.filtered" using 1:2
+        format = x:z
+        #datapoints = 227
+        residuals are weighted equally (unit weight)
+
+function used for fitting: f(x)
+fitted parameters initialized with current variable values
+
+
+
+ Iteration 0
+ WSSR        : 1.99006e+09       delta(WSSR)/WSSR   : 0
+ delta(WSSR) : 0                 limit for stopping : 1e-05
+ lambda	  : 543.709
+
+initial set of free parameter values
+
+a               = 1
+b               = 1
+
+After 187 iterations the fit converged.
+final sum of squares of residuals : 316175
+rel. change during last iteration : -9.20903e-11
+
+degrees of freedom    (FIT_NDF)                        : 225
+rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 37.4863
+variance of residuals (reduced chisquare) = WSSR/ndf   : 1405.22
+
+Final set of parameters            Asymptotic Standard Error
+=======================            ==========================
+
+a               = 369.399          +/- 4.401        (1.191%)
+b               = 0.431776         +/- 0.002383     (0.5519%)
+
+
+correlation matrix of the fit parameters:
+
+               a      b      
+a               1.000 
+b              -0.998  1.000 
diff --git a/reversing_game_mechanics/zoomlevel/stats.pickle.xz b/reversing_game_mechanics/zoomlevel/stats.pickle.xz
new file mode 100644
index 0000000..c915674
Binary files /dev/null and b/reversing_game_mechanics/zoomlevel/stats.pickle.xz differ
diff --git a/reversing_game_mechanics/zoomlevel/win.mass.1 b/reversing_game_mechanics/zoomlevel/win.mass.1
new file mode 100644
index 0000000..1bac0fb
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.mass.1
@@ -0,0 +1,116 @@
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diff --git a/reversing_game_mechanics/zoomlevel/win.mass.2 b/reversing_game_mechanics/zoomlevel/win.mass.2
new file mode 100644
index 0000000..8c08b58
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.mass.2
@@ -0,0 +1,455 @@
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diff --git a/reversing_game_mechanics/zoomlevel/win.mass.3 b/reversing_game_mechanics/zoomlevel/win.mass.3
new file mode 100644
index 0000000..ba343eb
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.mass.3
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diff --git a/reversing_game_mechanics/zoomlevel/win.mass.4 b/reversing_game_mechanics/zoomlevel/win.mass.4
new file mode 100644
index 0000000..aa0de62
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.mass.4
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diff --git a/reversing_game_mechanics/zoomlevel/win.mass.5 b/reversing_game_mechanics/zoomlevel/win.mass.5
new file mode 100644
index 0000000..f4b686e
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.mass.5
@@ -0,0 +1,8 @@
+126.83	9346.260482139367		1
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diff --git a/reversing_game_mechanics/zoomlevel/win.mass.6 b/reversing_game_mechanics/zoomlevel/win.mass.6
new file mode 100644
index 0000000..7994d85
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.mass.6
@@ -0,0 +1,4 @@
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diff --git a/reversing_game_mechanics/zoomlevel/win.mass.gnuplot b/reversing_game_mechanics/zoomlevel/win.mass.gnuplot
new file mode 100644
index 0000000..a948115
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.mass.gnuplot
@@ -0,0 +1,9 @@
+min(a,b)=(a<b)?a:b
+max(a,b)=(a>b)?a:b
+plot "win.mass.1" using 1:2:(min(1,$3/100)) lt rgb "red" pt 2 ps variable, \
+     "win.mass.2" using 1:2:(min(1,$3/100)) lt rgb "blue" pt 2 ps variable, \
+     "win.mass.3" using 1:2:(min(1,$3/100)) lt rgb "green" pt 2 ps variable, \
+     "win.mass.4" using 1:2:(1) lt rgb "purple" pt 2 ps variable, \
+     "win.mass.5" using 1:2:(1) lt rgb "cyan" pt 2 ps variable, \
+     "win.mass.6" using 1:2:(1) lt rgb "orange" pt 2 ps variable
+pause -1
diff --git a/reversing_game_mechanics/zoomlevel/win.size.1 b/reversing_game_mechanics/zoomlevel/win.size.1
new file mode 100644
index 0000000..8357f6a
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.size.1
@@ -0,0 +1,116 @@
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diff --git a/reversing_game_mechanics/zoomlevel/win.size.2 b/reversing_game_mechanics/zoomlevel/win.size.2
new file mode 100644
index 0000000..6168704
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.size.2
@@ -0,0 +1,150 @@
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diff --git a/reversing_game_mechanics/zoomlevel/win.size.3 b/reversing_game_mechanics/zoomlevel/win.size.3
new file mode 100644
index 0000000..564d37c
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.size.3
@@ -0,0 +1,69 @@
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diff --git a/reversing_game_mechanics/zoomlevel/win.size.5 b/reversing_game_mechanics/zoomlevel/win.size.5
new file mode 100644
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diff --git a/reversing_game_mechanics/zoomlevel/win.size.all.filtered b/reversing_game_mechanics/zoomlevel/win.size.all.filtered
new file mode 100644
index 0000000..b1abb5b
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.size.all.filtered
@@ -0,0 +1,227 @@
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diff --git a/reversing_game_mechanics/zoomlevel/win.size.gnuplot b/reversing_game_mechanics/zoomlevel/win.size.gnuplot
new file mode 100644
index 0000000..90886c3
--- /dev/null
+++ b/reversing_game_mechanics/zoomlevel/win.size.gnuplot
@@ -0,0 +1,16 @@
+min(a,b)=(a<b)?a:b
+max(a,b)=(a>b)?a:b
+
+f(x) = a* x**b
+fit f(x) "win.size.all.filtered" using 1:2 via a,b
+
+plot "win.size.1" using 1:2:(min(1,$3/100)) lt rgb "red" pt 2 ps variable, \
+     "win.size.2" using 1:2:(min(1,$3/100)) lt rgb "blue" pt 2 ps variable, \
+     "win.size.3" using 1:2:(min(1,$3/100)) lt rgb "green" pt 2 ps variable, \
+     "win.size.4" using 1:2:(1) lt rgb "purple" pt 2 ps variable, \
+     "win.size.5" using 1:2:(1) lt rgb "cyan" pt 2 ps variable, \
+     "win.size.6" using 1:2:(1) lt rgb "orange" pt 2 ps variable, \
+     x**0.4*460+50 lt rgb "gray", \
+     x**0.407*460-400 lt rgb "gray", \
+     f(x) lt rgb "black"
+pause -1
diff --git a/stats.py b/stats.py
index 6744d0b..0b460c5 100644
--- a/stats.py
+++ b/stats.py
@@ -190,12 +190,12 @@ class Stats:
             maxwidth = quantile(sorted(map(lambda x:x[0], rects)), 0.75)
             maxheight = quantile(sorted(map(lambda x:x[1], rects)), 0.75)
             
-            if (math.sqrt(maxwidth**2+maxheight**2) < 4000):
+            if math.sqrt(maxwidth**2+maxheight**2) < 4000:
                 # TODO FIXME 
                 svw[size] = (maxwidth,maxheight)
             ratios += [maxwidth/maxheight]
         
-            if verbose: print(str(size)+"\t"+str(math.sqrt(maxwidth**2+maxheight**2)))
+            if verbose: print(str(size)+"\t"+str(math.sqrt(maxwidth**2+maxheight**2))+"\t\t"+str(len(rects)))
         
         print ("median ratio = "+str(quantile(sorted(ratios),0.5)))
 
-- 
cgit v1.2.3