From 272c94348f1fa27629391d1807be0607083bad96 Mon Sep 17 00:00:00 2001
From: treeform <starplant@gmail.com>
Date: Fri, 29 Jan 2021 22:42:49 -0800
Subject: [PATCH] add trapezoid experiment.

---
 experiments/trapezoid.nim          | 261 +++++++++++++++++++++++++++++
 experiments/trapezoids/g.png       | Bin 0 -> 10980 bytes
 experiments/trapezoids/heart.png   | Bin 0 -> 4329 bytes
 experiments/trapezoids/l.png       | Bin 0 -> 7765 bytes
 experiments/trapezoids/rect.png    | Bin 0 -> 921 bytes
 experiments/trapezoids/rhombus.png | Bin 0 -> 1260 bytes
 6 files changed, 261 insertions(+)
 create mode 100644 experiments/trapezoid.nim
 create mode 100644 experiments/trapezoids/g.png
 create mode 100644 experiments/trapezoids/heart.png
 create mode 100644 experiments/trapezoids/l.png
 create mode 100644 experiments/trapezoids/rect.png
 create mode 100644 experiments/trapezoids/rhombus.png

diff --git a/experiments/trapezoid.nim b/experiments/trapezoid.nim
new file mode 100644
index 0000000..e9146de
--- /dev/null
+++ b/experiments/trapezoid.nim
@@ -0,0 +1,261 @@
+
+
+import pixie, pixie/paths, pixie/images, chroma, print, vmath, algorithm, sequtils, bumpy
+
+printColors = false
+
+
+proc intersectsInner*(a, b: Segment, at: var Vec2): bool {.inline.} =
+  ## Checks if the a segment intersects b segment.
+  ## If it returns true, at will have point of intersection
+  let
+    s1 = a.to - a.at
+    s2 = b.to - b.at
+    denominator = (-s2.x * s1.y + s1.x * s2.y)
+    s = (-s1.y * (a.at.x - b.at.x) + s1.x * (a.at.y - b.at.y)) / denominator
+    t = (s2.x * (a.at.y - b.at.y) - s2.y * (a.at.x - b.at.x)) / denominator
+
+  if s > 0 and s < 1 and t >= 0 and t <= 1:
+    at = a.at + (t * s1)
+    return true
+
+type Trapezoid = object
+  nw, ne, se, sw: Vec2
+
+proc roundBy*(v: Vec2, n: float32): Vec2 {.inline.} =
+  result.x = sign(v.x) * round(abs(v.x) / n) * n
+  result.y = sign(v.y) * round(abs(v.y) / n) * n
+
+proc pathToTrapezoids(p: Path): seq[Trapezoid] =
+
+  var polygons = p.commands.commandsToPolygons()
+
+  const q = 1/256.0
+
+  # Creates segment q, quantize and remove verticals.
+  var segments1: seq[Segment]
+  for shape in polygons:
+    for s in shape.segments:
+      var s = s
+      s.at = s.at.roundBy(q)
+      s.to = s.to.roundBy(q)
+      if s.at.y != s.to.y:
+        segments1.add(s)
+  #print segments1
+
+  # Handle segments overlapping each other:
+  # var segments1: seq[Segment]
+  # while segments0.len > 0:
+  #   var a = segments0.pop()
+  #   var collision = false
+  #   for b in segments0:
+  #     if a != b:
+  #       var at: Vec2
+  #       if a.intersectsInner(b, at):
+  #         print "seg2seg intersects!", a, b, at
+  #         quit()
+  #   if not collision:
+  #     segments1.add(a)
+
+  # There is probably a clever way to insert-sort them.
+  var yScanLines: seq[float32]
+  for s in segments1:
+    if s.at.y notin yScanLines:
+      yScanLines.add s.at.y
+    if s.to.y notin yScanLines:
+      yScanLines.add s.to.y
+  yScanLines.sort()
+
+  var segments: seq[Segment]
+  while segments1.len > 0:
+    #print segments1.len, segments.len
+    var s = segments1.pop()
+    var collision = false
+    for y in yScanLines:
+      var at: Vec2
+      if intersects(line(vec2(0,y), vec2(1,y)), s, at):
+        at = at.roundBy(q)
+        at.y = y
+        if s.at.y != at.y and s.to.y != at.y:
+          #print "seg2yline intersects!", a, y, at
+          collision = true
+          var s1 = segment(s.at, at)
+          var s2 = segment(at, s.to)
+          #print s.length, "->", s1.length, s2.length
+          segments1.add(s1)
+          segments1.add(s2)
+          break
+
+    if not collision:
+      segments.add(s)
+
+  #print segments
+
+  # sort at/to in segments
+  for s in segments.mitems:
+    if s.at.y > s.to.y:
+      swap(s.at, s.to)
+
+  #print segments
+  #print yScanLines
+
+  for yScanLine in yScanLines[0..^2]:
+
+    var scanSegments: seq[Segment]
+    for s in segments:
+      if s.at.y == yScanLine:
+        scanSegments.add(s)
+    scanSegments.sort(proc(a, b: Segment): int =
+      cmp(a.at.x, b.at.x))
+
+    if scanSegments.len mod 2 != 0:
+      print "error???"
+      print yScanLine
+      print scanSegments
+      quit()
+
+    # if scanSegments.len == 0:
+    #   print "error???"
+    #   print yScanLine
+    #   print scanSegments
+    #   quit()
+
+    # TODO: winding rules will go here
+
+    for i in 0 ..< scanSegments.len div 2:
+      let
+        a = scanSegments[i*2+0]
+        b = scanSegments[i*2+1]
+
+      assert a.at.y == b.at.y
+      assert a.to.y == b.to.y
+      #assert a.at.x < b.at.x
+      #assert a.to.x < b.to.x
+
+      result.add(
+        Trapezoid(
+          nw: a.at,
+          ne: b.at,
+          se: b.to,# + vec2(0,0.7),
+          sw: a.to# + vec2(0,0.7)
+        )
+      )
+
+proc trapFill(image: Image, t: Trapezoid, color: ColorRGBA) =
+  # assert t.nw.y == t.ne.y
+  # assert t.sw.y == t.se.y
+
+  let
+    height = t.sw.y - t.nw.y
+    minY = clamp(t.nw.y, 0, image.height.float)
+    maxY = clamp(t.sw.y, 0, image.height.float)
+  for y in minY.int ..< maxY.int:
+    var yRate, minX, maxX: float32
+
+    yRate = clamp((y.float - t.nw.y) / height, 0, 1)
+    minX = clamp(lerp(t.nw.x, t.sw.x, yRate).round, 0, image.width.float)
+    maxX = clamp(lerp(t.ne.x, t.se.x, yRate).round, 0, image.width.float)
+
+    for x in minX.int ..< maxX.int:
+      image.setRgbaUnsafe(x, y, color)
+
+proc drawTrapezoids(image: Image, trapezoids: seq[Trapezoid]) =
+
+  for trapezoid in trapezoids:
+    image.trapFill(trapezoid, rgba(0, 0, 0, 255))
+
+  # for trapezoid in trapezoids:
+  #   var p = newPath()
+  #   p.moveTo(trapezoid.nw)
+  #   p.lineTo(trapezoid.ne)
+  #   p.lineTo(trapezoid.se)
+  #   p.lineTo(trapezoid.sw)
+  #   p.closePath()
+  #   image.fillPath(p, rgba(0, 0, 0, 255))
+  #   image.strokePath(p, rgba(255, 0, 0, 255))
+
+block:
+  # Rect
+  print "rect"
+  var image = newImage(200, 200)
+  image.fill(rgba(255, 255, 255, 255))
+
+  var p = newPath()
+  p.moveTo(50, 50)
+  p.lineTo(50, 150)
+  p.lineTo(150, 150)
+  p.lineTo(150, 50)
+  p.closePath()
+
+  var trapezoids = p.pathToTrapezoids()
+  image.drawTrapezoids(trapezoids)
+
+  image.writeFile("trapezoids/rect.png")
+
+block:
+  # Rhombus
+  print "rhombus"
+  var image = newImage(200, 200)
+  image.fill(rgba(255, 255, 255, 255))
+
+  var p = newPath()
+  p.moveTo(100, 50)
+  p.lineTo(150, 100)
+  p.lineTo(100, 150)
+  p.lineTo(50, 100)
+  p.closePath()
+
+  var trapezoids = p.pathToTrapezoids()
+  image.drawTrapezoids(trapezoids)
+
+  image.writeFile("trapezoids/rhombus.png")
+
+block:
+  # heart
+  print "heart"
+  var image = newImage(400, 400)
+  image.fill(rgba(255, 255, 255, 255))
+
+  var p = parsePath("""
+    M 40 120 A 80 80 90 0 1 200 120 A 80 80 90 0 1 360 120
+    Q 360 240 200 360 Q 40 240 40 120 z
+  """)
+
+  var trapezoids = p.pathToTrapezoids()
+  image.drawTrapezoids(trapezoids)
+
+  image.writeFile("trapezoids/heart.png")
+
+block:
+  # l
+  print "l"
+  var image = newImage(500, 800)
+  image.fill(rgba(255, 255, 255, 255))
+
+  var p = parsePath("""
+    M 236 20 Q 150 22 114 57 T 78 166 V 790 L 171 806 V 181 Q 171 158 175 143 T 188 119 T 212 105.5 T 249 98 Z
+  """)
+
+  #image.strokePath(p, rgba(0, 0, 0, 255))
+
+  var trapezoids = p.pathToTrapezoids()
+  image.drawTrapezoids(trapezoids)
+
+  image.writeFile("trapezoids/l.png")
+
+block:
+  # g
+  print "g"
+  var image = newImage(500, 800)
+  image.fill(rgba(255, 255, 255, 255))
+
+  var p = parsePath("""
+    M 406 538 Q 394 546 359.5 558.5 T 279 571 Q 232 571 190.5 556 T 118 509.5 T 69 431 T 51 319 Q 51 262 68 214.5 T 117.5 132.5 T 197 78.5 T 303 59 Q 368 59 416.5 68.5 T 498 86 V 550 Q 498 670 436 724 T 248 778 Q 199 778 155.5 770 T 80 751 L 97 670 Q 125 681 165.5 689.5 T 250 698 Q 333 698 369.5 665 T 406 560 V 538 Z M 405 152 Q 391 148 367.5 144.5 T 304 141 Q 229 141 188.5 190 T 148 320 Q 148 365 159.5 397 T 190.5 450 T 235.5 481 T 288 491 Q 325 491 356 480.5 T 405 456 V 152 Z
+  """)
+
+  #image.strokePath(p, rgba(0, 0, 0, 255))
+
+  var trapezoids = p.pathToTrapezoids()
+  image.drawTrapezoids(trapezoids)
+
+  image.writeFile("trapezoids/g.png")
diff --git a/experiments/trapezoids/g.png b/experiments/trapezoids/g.png
new file mode 100644
index 0000000000000000000000000000000000000000..c63be150ddbe446da082cb13322f8ec66d45fc9b
GIT binary patch
literal 10980
zcmd6NXIzt8ws#sNfRsp8Ix3)m5b+2E2%(7u0S`*A0jv~h(jlQpQ{jjLN(-pq8EFRT
z0ugBnLO6m{0R<sS6A8WD{cvXHo%i0k_jli!FYl-QJZrDD_FikR_1`t#%*2SBb3Z2x
z2ID?`%HUTR49<eVkWv_SK<S-KeguOZd4AeJ_d+0ib~yIeH^e<`bk|kyjrKPfzG#U^
zCC7oRg(rO<zJ2{e;%HjC8yr@%%(t?Qg87}JBIz&`9=3=0FMg<|@YA13q`Fz347&kS
z;iB-skbF#-3hZC~P|4@_4YEpgdpIqPqzC>xJ^QO+PCtn{a5^8<#an>~VJf))UC-`o
z=5!VK+h>e!&I@T{ne?13wd9Z&D~UYHBK`M>==vr58)bJI>YaWd$T=9l^qv6cF!5tA
zzXrQ|4$QOB?NE5*FD_)&`guJ^M$&2O8!AeD6w7ki%VhkXMA>?AI^t%eWYP3`froXf
zWJ!_@Zz7gboY^&1kk4h*E({|*;YNt>PlIQ_=eJ2IU-PzP^zCKdD1{^s>y;2b{xpq^
z+1cUnQ@1*<k)B1|(V_4(6N=j?A3ksm1$u|najZ39nWc}DK8wHStUA|`mUDu#lTD1x
zGDt^mye$=;=|bV%4<fWgjb{+Qkm|!K-wP}w#ODsubHh~G>WHzLfN$#^Rq`sEGUGF^
zOxt5D%q4Cuv~Ef42SU95x6fhP1C$r`T`MKam13(1aYCCEdX?$YRw)3gi-GL$5oCRg
zlQ7d*Sx-yu5M7%V8(MBFxQxiU>XwW=fd9qCz7I0oe*VK7+KLj<rE_ZW!vx~l{nz1j
zwQeXbzx-rr34RW$V0TLW;2cLVrIT^24IcaxH{rz*Na-w<>42ZSA^u}Drj~eF9XoM;
z6LuhB`(~XRoy+f*bQ@(K$8PbE!>>lJ4Q_(S+IA&RT{ePY{O|(0JoJzep90b9W9Tte
ziit2#wVF*VxQd+^A)!~Zhy|x3#m2l)`1kQDXsC=$ge6t>`Xa~XQTT!n->jx<Btp<I
z_EN?6503+_d?W?%IbAW8>?*~#y(uQYV|)~R$+H;0cZTW6QYDJXLyXUJA95JR?+kEC
zsU)SdSf;J$9ei1iF%Tn#es%~H7d41Vl+OIZ4)|SZ#(;6O2CS8j>8_WK6gx{@RK`va
zl+o(h#3@hgB<!Uw)mPY=hap7i%;E4QFJt^Xg>>f@eQE+CaZ2q!S#*iiVYH)qPM4z?
z7g6C@3mblP?<8!NpSgJ|9m&$AE-C?GUP@<Lv<A@;g`YP_E}34RQ-=-8F@gl0d5AeE
zys56|MIMG4<*o`^giOrItQ>&1NHOGOJK!zS47o#~kYUIj1jPY{+yPJ=WXJ&zwj5%}
zNrPh9jhZ9!ZY@;e`vUC808P=<h@e=Vl#B5tYq;L#V!=VDgD@;zP*h`f|JE?9*HA47
z>viEYzW)GXOb8JsWibU?+{=vOn}qrDGm)Ucu<jZrZ**j4+aFCUkQKOd<;nY36Bt}<
zq)zI$<b2)faITs2hAwsfs!0Q9dhGa^S@FFZFDIV=m<;HSju=D{DiiRWh`IxfnU6yS
z2fGbOE|Lqw+Z7yPdOfEBGvDNe)uUBc&5!>aJ&~(Z|BNEV&~*OwS7}k?I771~ZP9`n
zK>r>pSr89e|3FjBInlD%tL`XSSv(!c8+;6x{n`0#*zs?n1ht?BW_v3vRsj3slkCg}
z-?%U;c-&ZiTcJ^G4y&7sE>~_jjA7lf&hkyd{74_GejVW|9yTn<nvHwGfv7v*nAz}7
zDwY!~Q_ZpB(yWf6j7T|mI%0h83Q_K5+$a(53gcsPACs<%kt#4;x74PL$UpZDzbBo|
zFJg0mG3};Ps^=A_GWB>G)^(aoiJ!SdQ^T-MVtk9;lJ&h%!GK>Rg?wE@H&-p#x^70;
zg2`Qqm$QEOL6hQON>$TK=SOKg=3_3Qf|1c{!^fI@k2PXY!F4mzBR)FGjX9Rl8n;h5
zK9^(gUh*d>J9oB08pBl#b#gF2GXu?LFSy$G<=M)BD15mB+;Lwcr^~I<Q1ocpS<wL0
zO<B-CF#e>*(4*K1jR7ZiM4iL32*u%4dY81mmfXG$18QHp!vO}@VV1_kMC872zDu+z
z3`@ph$~Uf8qr;fm$IomQSnHQ*^ZoU82dgG{Af%ANWtEkr)F>7Rlyk6T8bjS1#YTYH
zs9<cf_EBe^oNqzk8~%K8!62@6BA$B{XlW0hP-Tf9o>`b^g4gHI_qNv`WCW1>3E5Uz
zNF7Lay;ESxDq3Us<UBAnz}251<jhmKTX9!_r5>%Zd1u?wlsez^JyfhwY}*9tS5DUU
zbSPnG<;az$uRd2NvWbo#{b#3nc%7_M3yc;@CkWf;q*s(9hwqa&zC|t3E_1N%fR0Pc
zvEPuSI4EzV5=Y}?<{S$<DLdU<zz}ZhtQFJrHzy$f)=RSut2y%wb@PG>AhmKX{Y}Mg
z1-5xe8B~1Wha^D7+4MJr-3oZjkeoBmMz=7ih@j!;EroPSwLv=}k4AGxPj@fB{Vulr
zRP7@_bH~Yl1mfH^PDj3f8{_*dR|ixC0I4LESUjRGo7j*-nl%;DEY;DbIV`I?CTtvN
z9u$7Q=#}NfJ6$v9UA_q!X)c*M+*$$<yksg@Jgxm{mL@U<1QLLsbxHZ2aE!0|ErPWv
zb?3L<AV(UVVgrr6rUFa!@E_q;S#P{q?}8CqyoH?`(jA|zphkC)Y=cRP?qeeBZgn#N
zs~aeY*{EI(G1G=ZIfmE7>@or4dnJlk0)C#TZzQvEi=FK%Oxx<Rozp4B&jZev`p~$j
znWfM2PcnqU%77h|Mt4V{V+{7NGKXbduj+_5L$kAG_}FC(3p9>yd==IxHh2(<BT4zT
zWj8p|qgw}L6f1Q@Sip6turt^G&T`j>wp6#E;6UE9bK|`=#U&e8lkUab{FbvsljCIZ
z0`p^CuDk^i@NEtzxvN$*;f05F6)}Uw2p$kFV(6INo~3~%zvY536Mpq+q(ae#Y7aT%
zqykHU^M$>|6ayXh64)Q9=WZ#a$T$)9(qY+1fh9cR>6O;2!P>P-Qoiw~+Y7|(hqKde
zNiX$uvI;vzFZuI?VWHp^Wa}?hyg=n$zgjnwV!<p(LAc)sf<}-#ECrl0Xs0OQ%z`DF
zrAdR{%Ixw9>n!~oC~CI#7RnEE2{040ZIm~@vK0K9`y`(GGSjkcOsN~ygWvq{Stela
z+bzshQ{Apk*25yoil;}9(i_~mLals8qXis7K(2=ba8^C6w^4Snqkg!rXiPPQ%zJ+o
zxfM$2)0y5p!o|-_A(o_t`3@2-{bm<#YO+kdisTq!-j6k`?-LtXAA<)pix^iUdo^zB
zQu{LSjIi*LY{gSlFGx?<VM``wv9@(Gag@~;JfOpdk6pZ}d3)C_#}6c8nK?kUwqK24
zO;^`YN;8IK3KCudZ%<XIs0geTZ^>%~(S2N+3o8PGCoQapGfUr18sP#$m6l{8$Ry}^
zB~}hOYa!}J?o)~xgZB(EOC~b_*0PEp&MUV6^!ww@y$x9^W6-<WZm?RFeu*^@yl)(l
zrSA$yxB&Ola!mM{Q;XHx)|0l@WV#guo&_IJH8R)F3Q4I5)m1nwn^R0Qa&q2OK|b$v
zrmd0}K%fkm7cmZ}HKT8XVQSCD8&Ws)>@;6};&B0)na}CR_VKQwmXq<iN8QYG^FoH8
zl_u>68TYMniB`htcgF2A9IPmJzu&EHinYiwrqA&+>-qZbD&n2&Ag_J=Y{^V`E^h5d
zuVM`c57@Hd4*})A5YpqH(#FUyI6xO18ys_UT1tzjMR=e1w$uE!F=Sh2^%AWCOy6E+
z3D3Es()Rt(>ncjy@@Eota=Mnf6dm71B3mF_j}XT*1T8cnRo`lX2&do8fNHy&4ct_2
zD4Pq6g+x^d5CRnn;%nPUNT`o)NrKFoqlw%iyF+F{Evr>L;S>sWx8E80$@Jsk7?-z-
zFvY=Zm1udvqfHMvNnQEaPSBj;v_D@i&BdJ_HDas0QAoUOX?=w*26?&+k!A0e3y18Y
zb%8F70|fwIO(E6CoFpLCgVL7FaN5UPinODdWTnFCn&#dg=ysY`)&`ickmt=jL`q+h
z9hnVFv_7C9#gM%NgjTzQ0%PEu&^{Gj$b=%|Wi@M8x)#)8IcU-DXqtVo@RbY*j0P?W
zi9mf;-Y5cwwjq#{GQiLVV5kh&p7cZza$CUAL`4;+qfl>#J|lLsA|v!38+(T#G&gD5
zQ5Et}xKiN0-BJHlQlmjPHV6zBBI}c@H+&I_xG9_5vTDVnP6SAy9i?-URz*IUwG1*d
z+_EzbpcQ@_m=<Mb+$vi5gsj5=TDt_9?ne{3(vzTEv84VNaj+l@9`I$uXS9DoOhU_w
zF7YFbt|{Lw)wgoicJxrl@@jpy8og`!Lc%JNVO4)``0tW6c1JTDBpJXJ!25}cicTg_
z_v{t?PCSTV>o^T8tp`56AS9$B2YIWQc-h?Aik=B+u0>>>b909KLLoiR`QHlcw8Ymc
zw)^ybCF8)Vu?6|<)bgj;Lo3`wX>l*A4`PnW`|r2$|J<p6TcA6Q-yOiso#J>~u#EEi
z`2T@LxQAs`<TV3cs>R>J>(5b+<zxk#C439S@z66_V<2Dvftr3dt(mREh`0Ek2NsKu
zS@0U*C@T)^Qq<!7?a@I8xAy<*arr+5GD+_;$fEc))1sM5kfu;dLHRNY^7^;GWgCb=
z!@p(h><x+pud%MUatk~?X&XQbL=fm%pwY?I5Fq@wf&dVNale<fk%O9s3oMpxD4muj
zw&3g{@i`n%E52^Da&ynXb+A5C<74Z+1wYHR8UwWdXBhe9`Wt)^0<QlHcQjq8tx@I|
zS`)otlX(FB8~_1r=>JM2O7XZ84{rYV2VnqDo<l!Sep!RPC5=JWfb#b;8@~1(08J^7
zzc~PajzEYB&3TYO`mnV-eU;Q{t`GtMGywX6Qt!nZ_FyeyOz$lbE+?LK&p!!fRvv8t
zu?yxuwo3qi+5a8NfgtX6*%(z<t^%OVP0N;Z5Za7_8It`;=^*aLL%1dD6PQ=PZ1eXy
zCYFa4m<;9;oDh8#nu;6&fm$`lH=b;WzO68cFQ-*<`n_}QhL1z(|37^<8FV!wTLcy}
zZ3Zl3d0Bx}&O&jV1eoB4f_Dj2`rvOd=-a0oiqgU^Qq7NW@rvv&JD_jb5FtsG?DX-T
zciBh&Vcz}6Z!ib9MqP9T+p;(uyoG-;!)Cy=0K=lT4c=qJ+%_x$(;%ybsN?Tt-!~`u
z=2WWNzHgsl%B;cQ0aIwG)eS$UiX@#r!<)a?7l@uM;9v#PIg6BVvUDr3X4oZwWdvAX
z+}6)2N~^m-^-WJ-wT`2UkQ~evHl7iu%%C4=P#%Nj#Xqi57N~-@wj?c*9U0e@nQyVo
z_#L4wU$N|pLu`F;nReq9WQrZ#PZT=Hs7&wbdAEI-aa9les6jA0<p)CC?sd6b3mY?M
z8?5snf`DBJ$(SZj32(Lo+Ds@Ws?ZO#BG6>Rzi-P!tsep*G@p5lG5%ViX1OW7sUNnL
z5M*35lVQ#tZ06_ju2JhFN7aX#;sA$xArNYH1JpWqvb+3ni`yUfqNSU}fL>#Yi7!o^
zvJHi%Y5_MZ5Fy}@L9!!-lDC^SpIR)pUqx!mzq;v0L4<W%f{9OndHnDrJ)y&lr1aXJ
zcMcl<)YcU0>Y(5_l4WQL9Om<#$eU1Nk2_)gj3`MO`Bh=#32`OkZN6JBB8*`ULSBH0
zsJn_ISQipENS(hbgiNp~5~k4zciY=o26_vus@uMS7U>nutFEsR9*Jvbie{1!TYka8
z#{`^*Xik)hZ%>zKI-D%wgi;Tn<|VO~R1DNSCPw69hSChVUY=D3-8fHeh?6sru25=`
zYvH(J*<pUo%~1fXvq>AY8<e8V6XnIz`F*YPP-1)liD4Ee9(O6%HP;?z^!o$t^Hj%p
zIYV59a*KQm=M~cq(`#-z0!&Hy7J@6Z`_Kowk3WB#)ZMVi*|_S{MKdvot*AhffU6{_
zkX*q88xLVlma=>s0kB9TJ>r4@OB7;@i<2gav#{=<FOW<?r>VppJuQs{Kyx69vO0qY
zkZkK}0&Y5_LK>Cg(j5B4Vp)f>eJ3zd;1ZybI>;`~c7R5pY$Ia^(iE?asjpwEn+XHE
zq=kcrJHwl-n$zK}@j<7GW<n5K!U<){I0x%tVqJO^NGLf*M6UWqN;7xQ2UW0g;Aa8{
zouMorYEfw6ekQz_WHT_2TIUwH5<%*qwNdc6m1hs?OsJz^6A2<nZhfyyh2mMqfc<#k
z#k)2GQ(&5CO%k}8LmIxX-V?83R5as_*gBc;($RW`z72Mb1LLUmJ6|}=pM@oOCoUkD
zg%|JG42+_7H=WJ>Zr#X@`0A5IGag`f`Q@~E;a0+nL>y|FfAO}>Kp)^b{IR}y)olSe
zl&Ar?t|GRQzQmiCh9xc}dZQ|Y7ZYs;x=`!l0`5DcJ-&NkL-EyyMKf-QEuMvm!-Lz+
zA}v;kq4*#`b3tsGB;4GCyQ{H}ypyN_D9(VgfI2daYf^6sMC=GJ#@h@upw@NdhrOGu
zCZE9Ogna>}7Eqc}o&~mIUG}+f4l7S$%V}O<)Bfu#m-vN_xA0B-4(V%dU3-~30;W$8
z5@&B;cE?rF=b@9*%=jSvx|xfJFl0iYvBv3q-^d2*z9lbVCv&izwTDo+%2q3eGgu3k
z4@6dg$co&rG8^}aqo<BXwD6Dbw>1$NV+nl0DU-$n2XavBC%<r993D@2aR+y6!1}jJ
zxsVj%sM+zbmIo>9mkxCd-LE@M^^(uNkV_~Q8R{oxI-h8KWj~ODT5rkwtXd&5o=H@x
z!Tfv{H27c(?9~*rt(tY}MaD(0i#(8;H(HjV)JFySJl^H(C%tkOh<v3p5QSPd$?H~)
z6`9U7W0YZh*HgBPsPhN2$F8tCq+9SUV!;Bs62BPd&{i-k@rP2r@e6mA<b+?EBqvFS
z+$D~l*LvGM_VDcOpxfFn&m<=u+PFg;wbttXljeCIdE@1tg=c45?rEQ-3ad~iQ&YI_
z?se|0qP1dJhy_=!rJ&~iRv~}bMVY3@b0in{0b6itl#=j_((m*0wZyTu>h9kofGf4*
z0Ghpc9{8xw|I^Y5rhbpE`+5G-2a9W)7c4vELgI<a0;a*oeK6;_strBpj;`d(+_;h%
zNkpBMF=18yyNukSP1#1VUzd3(4vN{US4MuE?=f^gf8fXY=)fK$_Zvzfw}?7Ktu@(0
zqw#}rO5dZaIlMi8tJ9-O9%Pq#bRtyl`+>@5!Yu*fW4PrTi8H*2EuySqWr9t-lH5_3
zw^Feou8w?6bb@Z2EO%u>aJ<sB*m}3P*1*OHR~<lCeOPVObIw!a;nf_z%e(_f)cR|Z
zR37e4U0yiB^Sq_l6uzpYm3=vR(VnU%#eP6m+x^h@!`~BZ_Dz@_o~j{w8SFWA+`0cu
z&xZip9?^(2%GRevPNTLpMTY3!bBH4bMa`*q$n*BG>M!M|UJ$)b?KyMY`q|#4RNEfO
zf&jQg7x&AfQ^iCt<2|=!8?kwF;e&Z6LIUarx948ydHHy9ve=u)49X~}2Iod-hFf#9
zsZQJ9>l@>IIyqP;4OOo-b8I`=_kB_udk+qg(EtgI%t=;xI0W5PMmdt`Wwqy?8G20a
zH$h#hnh6#8gP$@IFCw4ILl2OVixdn-lS-rUFvs}Y7(^XE&Ph+4oFpR|Nt{2m=MfOI
zan%QhzE~#Aj-Q#8K;i!md(sx;6f=@5qLs@-j57v8<~TACYKsB~!9r2;J@82(Yd%!)
z6iF%uPk$wYjwDJF_vD+Q)6HFpe9WjgxZro#V*IuwYMn?ji@|Spap23q{eX5jxF67u
z`)t?eAJ>YY&*#mfDFmvBT`rGGEOSkl%6o*}>KXF3@;W%!MJDPBeTTUuIsheOBr0g9
zDz6K$Q$*YWdp>hPmuf1*ZU@-q)<gK1{PDWNfIWUh0=4c+8UyU=c_n~7S0og$-(r3P
z>_<3>&yXzT^&r5WC=++C6v<Lp59DKF{K$7X{2UB%R!@<v!@+^2dQ+zb4BR8dsmk58
zQN*b%`8~Njj3nmJ=WL=5uENdQWV+_=mK2;FtF5V}Sj}5(V2$x7FB>-SAhNs+e`}KM
zhYt#d;W2*Ug3U5L@Ie7>@a?&mjX%Q)edR0*tU}lLDZ7^z_IWo*{4+3*xNNaPM)g^N
zWHYq718ZE0QEe-59&}(#y*n0kU^Fj18c)aNq0y91**t1Ao><3h(503=l>bXVN|Tty
ztOY;S^2Ni^n)Ld-QFgHMMd9i7DEy&32Bd!@PC~ShaTv=c*8{H*-ueYx#~5^f{dm4A
zhn(~05q`-~O|gz6`CPNFBy?pGlQ&}=%yf)iGn%|v#4G@}Ea~!%!^dGveN<rQQ2$oK
znw>(cF7*S78@8VOd4Yei+Tw0Jv4G=z@{6k|M!wy{(MGLe!8%op-=n=T4>R&%t?&4f
zG}eSCJ&VL7DJErkr+#5qKN-DN*D++%tq=uno6bLbah1>PK%~~>a721Zxz8&U-aan!
z{kbyoEV!!L9E{YkQD`}e@vGr)e(p@)F-)I-y;&%zjRO<`w#<x4cx61SD~P`~1Sfa>
zs}-kTjc{{j#z_Ro$3VfwQVUjt6l32Rfr?8AFOtaxRrK|*BH(6>zgavZzp?PH)dNS>
zm1~9#T!<`Z!{4UzU#mpz`T6*vS9x9+8>LeqZ_MSx6_Ind0($}!I?8M`z^&cy2A`+$
zzcHSR>u<h{@wcz6+VA-i1h@uR?xIuT|L8i0%tNQOfBpTE?PWr50zn9c&onXRmytE}
z+`m_;4c1jN6SHQn@cjVBZ&lAYx&OHA-DKSng~fae)?cI;pV7GU#cFpFirfMn`>f|X
zQf$s^>QdiGHZ{ecdqd*FP98X>bIs6{6WmYo@iWKs;}<e8Kc;K;J*YNQxON2N*MG|R
zFT=-=|KT6krMK0WP|uIT&q&Gkx1LK89rX{KTJ1Vj)R$nxg%D3@da_Y<HFRt5$f$W=
zd0q*M!h=qTPtTC;ub<|d3b|Ho!Ah25<YIA$y*?f9@UTZOnYz$DdM+0|8vtZ|9Oaky
z9tP=UO6ArH>$-g49yh%y;?qg5m)OpTFq8ffrvJxB&(@?E&N8@#`GLQPvb0}|B_*D?
z(AVBUDn3Zz**wxn^LY%8GEF+#4>I8W_lYG37&~84bl#8tTc0mf0FO@hYAg1|!p6X<
zY}PbJm<e+~L+t}dHS;BuFz-_r3hwGlxt=fDAjHY`7}md9;K5LRy0fMn06PIrc<f3#
zqljoH{_WPfR3dtN45en<w=}u<6HI`wYVXB<9mm0LpeYX1E}>k0uoKdZ>l}WtoBymh
z5kSaMYcQz?r+<Vj=2>spW=3yNQPT58DF%EM>_N^#o&RTr#^?=jeg^N)><!YU@X#lr
z<I&xssAT(s?5a2(wsXvcno|SrT+>z-o!90BV5`k*q1#`@+-Gb1g_y8m5Bt7a<@PY}
zRv-hq&-g#Z&$Xbs_OCx@@2u|;C)ZkK^=)|iOMv<S=)C+N+17B-FAcAA3;4nuoB^AT
z-r%hlK+|&qYqvyniXb12nHF{?N$-x_U)i=qz(~Ab-P{yu2$Md#x+kka1FmY@=RX-6
zk?v+4UN;;2HPshR|8|hU>vQ%3@Smp-A;$|ZIm8c!wq<CxwaV_O+NV-MJgfmU-Kq4a
zuO9TSc|*OyGF!peyEg*9y-@jmQ@t`AYDS#wWt}BC{jnE7J1n&Q`=%A>#yJej1q{vh
zd%(WlJ~j2)b`BQ$7Su&pXQ6>V<t(OJL9?5QDqg^r{&!aataq-_MSZI6wnM$3#}V71
zhhew;2syE#c6HTqkJ#|AlETg*FnU#BAVuebYPGF$kw2Qgzv5mgg#1DO{z@7&Tx*?G
zsZT}T5YEY}93ScGimDuj%gS~P`OJUU0&`7#(DOPaz@}4%_iB$A@#M8&!ua=2&aQRs
zR&#)AZK(PM-m5EO^v`PSq{sT7(x)+tH-S~2lfH{5JQi+-tgdiwp@@r}Q@)EU-WKgN
z_n!>O)S_YzvMk5qO#tri=Q4?Ck#rTWq15ZwC_F0i&Lae1d{T7KMn&kZ0eeoSuQ<2w
zx(<n*+=4uKI(@}ux^gH=5Ko6i2RT+aKn`PQIFF=hTTJOvk$#@`eVvl8?Ut=}D}J|n
z$hBBMQ;z3Fh*R~kldQ`nyXvxlIxtXLpcq`7U3QA$VNftWIcX~%T~IxDTm1eM|9SXS
zgvkx^;#w%Zi1xJoEA4A<*f(eE)UWO4@(bR1#nbDas#+=~Ox|vOrlX;<FcZDuL2LOY
z7z2BGs4)|F0rI?#6>8b*i&kF-Io8`Sxi$2%*hOtys^m;|yl7f{(O*uH_hTn-KfMMb
zef_me`n+J;)-`?>BMGyR*?Rlwu?|Rq@k9}aAG1|Ln|$KJ3W*X<4RouIy~5XL>wg}u
zlUSYOd*A!wiUXjhGX%ff^m%?%WvmY4+hVzO6RbYa3CTr5l@Bv+#Nx3NxRvxb*sY6H
zNhb5Hc;!y-O#|u1E63=*cX3GvAn!>Ylnr@KgLB-hGHqYX2oo2aglKwY{@#+l{Bt)%
zoe7l(LY@+JPNCdPzifw>i(9{9L;`@Xe*NmM9q@N}@)g*DxK?b2)8&)c$>h6pV2>+>
zjXV(F>RTsn-(Q-BSt#^BWdxy^4)J(&x7(X`d$?&Asq>Oj*F@9%RJZE2S0O=GHdVqY
z)_wjoqtM{sj)kfcwWmhyU}JQ>uF({{hccB*!!prvX5-VzNmH_F6w{dLvChFn`zk{P
zXW&Kn@x-B~#e+Qq=HLq0=&be`s-#q8!cdd%Qt!t<4(3T>$NH8~JKcYPh-Q(x%~l(x
z^EW?*=js%syNvdt+@F@K@PbXj@%`7De6uocNDleO>Bk6#BoLK_;QDoeBMpN#nfEv6
z@N^fu++PzR5J<dA@Q7ci3RonK?GV@(i(KGFSAPKmr!4S3(R+A5!Mpz98=dcj?5L6x
z%+u|li@~{9u5=u334cBtCydsK`RSF!b<(?Ocmn{g{C>$z%bxQ~>}A)(Ku7@2Mi{GL
z2@1&=6rLCn3`MoWK|&OYs$3ThsD_1|@by2;(*f0hiex>F?RsCr!P?RIbj`lcwu_Vg
z8aV9r%GmraW`yIm!Q`~_bp|H(tQ9ho+^a#94CV$#aDnV6ur~9{iOK*(2KyEv_aH#d
zc+|y$X4pXEwI?xvF<?@34mP|05HN7`ArQ|v$q7+qfsm>V=tjLNNXJy{8z3&ewkbwc
zdVCAWYtr!OE3IwN_}m4mL{IWULSSaStELYL9iZ^sD70>bggE@zeIv8MZB6#vT!Xe^
zJ8g5rW_2Qz5P|0*?=Opil!4eNxXwN%r@E^e;O^2T$c6wJ2K?H4F%Yx!^r<OW`K8@P
zocwvrjMBl20ZjlO8;MdY`bBDpFf>Bk$q_sG3cMTu_AVdjXpm*7O>%j|Hn5YU{7lg@
zJi6Z^Ixy5iLKON1U_7*Uq7wV(7kIJq*UuecT~D`dpijS^5B(zoJGq%f98K=kpl`{v
ziP}8K30?#f;U7a;p5PX`Xyg}iK7hUac}HH<`Yo^w9yLg|we-}ddI9si{LaC~`6s|^
zBl-f5t~wX30eu478u%wSK)c{;6m;HttsWc!0NKltufX1#tlR{DCD-=n%L3%9c$I=|
zKqR8owb`n>-X<Mjs7Wy>51SM0k|j;4Uf|WB>fQ+tEOTdq%bV_w3d#WI8rE6JGQJ59
z@XFvIgVN3MlYn7GBq&Et$PQC}!~Cqru(;hyTj#_+ha=eis_jhLX?s@NT9!*i%I%vz
zJOXR;+F^FO#j&QxUftk|NJ_SCNp_4PgjsljVIeUAV^;vW83MS&5BoL<YL%8_e$3!r
zv<ISsqe!%7*?x+WLAok|GE$0Jnm$KIR>r{^=EOU6sR0wgk(>czkN5aY9%N|xi_g7q
zq`%1ot?;U-Q3!GA9g=F&yyMk8KhhVIQR{RP&Cv@XvF<1S<%c+hfc?y~#rI|N0Wqh?
zziKL6Ay7S)Z%PM+FFDrVFeJEIdS`m9KHKYuBqA%ra2)&nM#CPTez27>mFdy()RU-B
zg=hP+FCS#ARk~aB)#_z0WQP0i8ve@D?3;7^_ozFD)?wvE(=`i9uW^K10X>>xr@>+M
zqY=vtYJpp0h6LDJ{J7W_5s>-gGM8fvE8rKjHXqYZ?oqMXR72ifr-O*BqlT*6SNT^r
zD-f~W7{6OA^Zu!;dJSF(QSd0nSRpDb(O#LybH$c#6fZ#!L5QEYaUJu?r{2O*3_}7J
zn6WLxd)JLJ(clwJhGYC-;Pux({csm$%E87kyzMkaqhS?TsrdiyG39@H6G}F!a!8$E
U-BWuBUa!JV8=4pt>p4aK2fi4R*Z=?k

literal 0
HcmV?d00001

diff --git a/experiments/trapezoids/heart.png b/experiments/trapezoids/heart.png
new file mode 100644
index 0000000000000000000000000000000000000000..2a5f69b70fee238e797e618ec5a771d687748479
GIT binary patch
literal 4329
zcmb7IdpuO>|DSW5IHQX>GksAsjx&g;=-bX#CY`2X5M8DVvAGONQPS2%vW^<<j7u{X
zT@=fr+Ek1UU0Bk@loe63w3cC47g{3?MfyGZ{rP+SzOV1TUT2=yJkRI-yg%>f^IXp7
zJhDw2gtHCj8`5aB*&gl!5sd~ZrhlkDXrXGjztU)oQV+q}tufHh?<pJV98Iam^8%{k
zM$QGgVr%nWR|GurK*!=5E1|@;GKcjrWs;*AWznkKNt&9#X`vW{R)(Uq9SA}>z%XeH
zL3j#9Q@H-OW;Z7&EJx(|)1WKt2>;X0|Bvfc!#W+e>Fwl5ea*Zr$F)8=dzN0x6m`CS
zs2=-lIQDhM>+V1A_nw?_CUwnzOpzSv<ngtu;LSc&(Z+g<5~jja)xXbG;wtzco=jgy
z&S7MH5g=Lm<+WQ?Lj%A6*s9+r7a^g$onqtuWr?NVo|lkmg*(e+W=l(}QzlH!EPqPT
zHW(wJoB_Jo(u>M@-p>ab)A9xz$0t6fx%New!DWeOt0s+|oMdCclOMw-_pKuhlVxUl
zSzQ{XEKL!4Z+s#!wYtMJ;ZIcUIpATYmocCUIoy5r*Vm>ACC>8d4(?PtrpOXAzHdeX
z8pi#>BP5sQoSF1p7(fdNA!_Q!?K$-Uk*PI2c!XdbF>{iE)=$mjU2dOgOEAU4b2lfX
z9_D7O_h0r!Svcv$A(N|xWG*A)O#C_3n$(()^Aegdg@IRh-&s|L_6Xkhw-faKyBPDR
zevin>1yTLlv02b9OPl?(%wI8@T_fFM13Sly*8}#{Wm5r`xQ}>5bP2OjYJEzu`ag=1
z{^Jk)YjPKYdQEOa;2h|^c!V8x^fzAf7SES|zI{44G<5B+^9@PthQRAvUhT8l<rv%5
z)@H?>>TGKp_YZkNsZ?o+<ay1l6z}3jvOcg&Jb3@&Q>{;33nW|kgRXp4Vp@&Mja5^g
zrd(V(Dzwlf-7E(>-xb`~`aD!XPO%eht$^)ATkE*}o}1L!s*ihvnPv%~oXp~GCB3?*
zp7LaAHK3fTaP$K8=qD>c9h6fQ%e+X9N0@ne{N??VX+;&<$}CG*{4$ECJ-)LMaMo{W
z8}Aa00Ur(9?oHRX-5c-ndj{$&4+0nFE2nfV`$(^VN2kuJ>MeE)Q){XZnJHpgdm{gC
zUYELN$<XR4U27QW@G*LEK+9M*z&z8LC&ay4hHFFbmRG~#$>_#_zNn4A&rr2mjHzZ$
zv}bgT_vNmx|D*f1q4Yr`$A5#kPcE!5PY}LXglqe2IsVs@OcQt^#o8m1{XnUF_x+ji
zFF`c49izdy19nBD$~%WIJ$bNNws1!7wxb<p2~|IijyrprK(TRg&abouo3+OS_X6ov
zSNg}DMJ6D^dI8%O;q?|PJ=1D9Usy2KC-f(qOqBy293PqX$c>A7;*qlUY~VuKo~`vc
zaZ!(H<Z?CZj<I-hGylzaaU$hd^_=d2XDXbh_O?WlRq>=9cH9T72BF=`z7pdmeJl1M
z+drRDrU{v&uf~g$sM_V#yu=xj?~zbpw@cm)wC-o%tl)-EeV}*tS9&r7GtW3K5ab{8
z&E(U<Ta@pI5PR&T5MV;=n^S8#mzyYJ6v6g#5Ikj(u&;y*!zOI+ASigfygqPWwxP7r
zsKXD@bc5;Y=uGG<ar2&G#r~?Jvl=KE?Cl;ePN!<K;#j_9$GvK;4+l!LAG0Z?O23N(
z&?ZDR(L89)k6tZHTcbM|G5Pe$IZAcn;i-$tqReks)86tvbsG8KW+#-dDstQZ6aClR
z>z9(W4Y}7F0<R&+{+qeAaNXxhHmdIG^1mjx$Vm>m0AkV5y`&+qDI0a?oh_~WnoM1D
z>Hs_83l`&M-*hNA7l08#-mKUd1off=TAzPIiO!FJ#1(b1lTW?Ko>OlTW5)mOa>Ynm
zvgu$ZDvazwopgKU?(ZO(0Tv{H%f6>*1x!U2f|zDeSFP~c%Sfm-1i4w`_H@*75wydD
zq&Cylo-my1Np5E{g0_C{az6W2mgve@y?5Io&#XV{VsrbxfoEMBIkOvrE(4y>+5e1g
zT7d?div=xjEZdrJrudUx29DQ;i+gW<1H+pvAv@K4)Nwv!Cm^ZEsJkT)<3<`{jG*PP
zNDB003O>-EM$IKaC!|mjgS&=iU)+;zlNZ-mwmjNmqg~OHy2UvIx024&OZ_-Y8v&^q
zWcMo|HH7TEzz9+IU_i<z4Oxt!xv<EWmq);(*Rx87Pwx7q-V8xr>~wIb<dd{T1a79(
zhetP%TmmQm24}mrHW_UxKJ7vpdB^KB0dkvzRiywREpfA-0n(G?+Tdgf5*nhVrJyb6
z+X1raf05n}=9O*$iQ~?I^W%B_4AI^<>>orYDv#z4{KXEZJ}n;?J>NxY5{<Du6EKok
zAF%A{Fg!{aC;MCBGy|3*=f2+l#Yp(h;;6u+UC+ql6zy6{Qtx&;TAPUU<LxBXPFJth
zB${A(+ZHEGVcFl#v`5jFE57Lda}>>7K+f4U8wt;%%pG!R806RXVZb8)eP!u1jV$Sp
zc0dCmg-or$cP8Zb_+FP!e##dL94GC?`IQDRT>5Y5Coi65JD=)&H=^72V%Kad6y0>k
zw`0iF2b>pw<w?D0a)-u|7gpXYi!w!9D#sIJb1g2wJ*GL;&kfPq0HpAs7TGZq+S}Fz
zxbJ*+TrNxM>PFGpIY=R<6-*l+_W@($XUB`h`4vLo*a_O>#R~?G3*LPIj=!09eBg%f
z*`aOEfa47Us$jHAhuxmz&S3P|Dj8irztLlE%#+gMUdIn{4q1RP)OL$|%Z~sm2zn{t
zr30$!)M4E=Q}Hxa=^5Yf1$P|*)m8y@Ev-z4oumV*pa^B@s^ol_x$&yBb`fiAapS>H
z>N(R%%e{%i&v?y8<a)j#rDxi-08uKX6{S^xj{eg#mT5fmQo%fMm<v+SO%J6J7Qt!?
zfgn#=QY$taya(!B5#NX><#NZ!=_!o3U-#nj$vN&kEdlq>j~(L7S}+~;>%QoM--aO>
zgcG&JZh;f%Jp-V1_=@kic@E{()<80_o*nHjE_AgC1m%Ve^<_}UWRN9M%V~G{7FExH
zAhs;Y8<>+!O$qpU$WY&x&@HfKRx1?`jG$XgJ%NCVXm^=nD$E4PO)GXKUA+Lr<!9f^
z{Uwj|mW8di^M1?Q{e#7edu0ys&(mjL5LJl|W>B;M;%}BBK~;-krf16KpXh2m0uEuy
z8<2i_J3ol099Dk<f1MNpq&|44ZzVip1tmtS_#8Q1ogpS==xB3i!&{_(1`K~pNpj8Q
z;7g^6)<nzF2n&#*m;k#6FJK`)?`jg6AnsK>L)}lBh7<6|Qe8SocYt{<Z-lNkZ0G02
zD;?e0&<;!eTq$|yYW!6WZZAV`c<|a;3K;Z`6ZgswBZZWylz@jyb(>Fu1A}PM*V+n6
z!!qN#Xq((j(b17i-a$`xlUS2~Vc=HBpHSH1Mv)FSScoUd&?g?ehb+ZxDf+~fR{{37
zcDwNtj`1tojU<<;w_VT^)9zBi!OfW1iqkQX>%qn+4$RVa<WhsR{yR!*d}BiV;j$B^
zY66~6>Xb&%Z!&4Eiz;LdT*ko?_sJT50l8%N!{b9L{`?6H>};9|W(z_yh4j-1I84^y
zG`*wwc^7<bLlWSF3e#Z%e!XL2#VN|%T@bWDyW%uu?j^wGG3Fb|ML01$UwiokwUsaE
zS*h794}q6OH}aY*=jbmf%v_?2F5EH_xs{V^h$T*(4!f0Lb%&*RC`F&!u-{<{Lm4`0
z!#)hMUm1FgDL+bgzkiGkw>8ww1#QVYW(FT>cX?%lXR$ChYxX;qLSKp&U~(?%&Jjp9
zONGuzp(VlpTUD?aZZ*a7eKe2R&>ls}SZjgriXTB+-q~=1zwv7P4G(g@H8INPbz0-I
zS(x8K_CA)PUWQ&{%5`*i1A(MnDzrcfSp?r+RbT<PVp#q+n#U&4%T(#sU7E-pr{8W^
z742zPwBgOnK#g6_!21Xb^NqX@R(KARv6ngXi%}uD>R&7_mtU7IZsOEi#xoU<=%|n>
z|Ap>8Acj*=p|srSgAK07z;rh35Qbu{6ph2=(WsgfNUq5me34K`qHen?ga<FfvHay)
z(+p~sr@+>gS8t8$v9NZgTuE2=2qa%=5-FUh^5UUzok0Y_ThCj;V*DaQ<x+z)h$N68
zl-h|MUnL(<-K5sTb>48DwYJ9?>b)3qmx1xG#@8-}>vj^yV}^g&;%VpIwtV_IU|qDl
z>Fu$@wjAHnVUjx!3@^<sVGPSn31XSCwr3t(w?z<YuDSa&BDo}U|D-zMgQ82Z^lxPb
zB}_(uF(ylEcKyKUl@721tnttklLgowf0f=rI$A7szoR-)j!2#g3Ri2^(qTSEw9e7y
z&4u#MO5G!mEfHNpg}gPJlBrD>D6rgZy-C|80ha}ZOO!gOh>o6Tq#u<U_+tz%hiG6K
zRaoJXo`O>xcBD7i@s+@e>tgboP{LtHb!1be=VLar()YRYf|kN{*9D=@n!DYI<ae2S
ztmZC;NY<GzNdJk`Sa#@8RQLnCqD;TrcSkuVyLrtYpXcjI4TMa_9Bbme>O=t@{VqkS
zs_#^PO_*zA?mk8&dsQjoNJ&4pH;)VR4<r2*Qu`+Y^74kNP08vgptBrfT(Kh7s80CN
z(WlIG58mZ$YEwBFo?F~{`}S3uZ`U;;5*t;@OIu79L(W7byHXjLHqRR7Z#jBO8q+c#
z%3q14cZ`ml-Y((1F}mSKhHtNWQNd1^8r<+C!~GgD%*byczP#kVRBEuA!MNQb5~xlD
zpy=;X>4h)L<GIYoEB@fVNTOPbI$@@k0&laO$tHt-1T(_oK<1ux)1RQjBfXAJHwI!|
z20wt)R5@cOlW`l&TT{2C?11VWzZsEOs#4wu0D-kAA_*SEFl~?(T(=1<CcA1bvsc=f
zl#Zh7l1(N=(-<khWJ#qlj?19naG<^F_B7`0T{VJSe96&ocC*qzUNF2{>87<MG|-x>
ziM2_e2!cI)9;CP+GLIrS*r^VqNgMotP{85V?)y()@RDpV(s={OsU9`W$TR*=$bWJb
sFc|gfE?5UgZ*pjZ>;Jn;gIEI(*Y6Di3pXc$D-4>4>juGfe$es%0g%EZRsaA1

literal 0
HcmV?d00001

diff --git a/experiments/trapezoids/l.png b/experiments/trapezoids/l.png
new file mode 100644
index 0000000000000000000000000000000000000000..0507a7fbcdc53d64cccf19a86aec688d238cbf8f
GIT binary patch
literal 7765
zcmd5>dsGu=7N3x4f=CppfI<XBWm`p5$|FIAAigcMw)KeyO>I;ZECZ2efLOst6m7SN
z5MZpwmbR#9ECE513PoMB$xtN(c_b{AjDmnB0tp26o3QQf+0)&%+xCQW=8u{0e&6rA
z_jm8P_vYsK+hMD1C(WD$L6Gg*HK7|Jh@gicq8nu*SZU}ylLtYwT-Js%-%B7oYdIcv
zJNUKC`k6aZI`8>5lqc`twf~R<PYb!NbjajQZhkT{GQxwPO76Bs9s%OMg%UIni3U-F
z|Ie3-xi->w3hJCXik-=jIOLxw7n)jITbF1B)aCBPH~7?y(NIGWiB?Qu4A;-pMcKt6
zv$2*cUo<VzW;oBh?*HUq?La7+aRPz=6tlwAT9TaI)7v{x{wUa<sa>SZbv@ri@1rp}
zVr9Cd;HYZ>LR8zu`8{Lbh<RP(YR$k!B4w^_9h%WgVdP(5HJs=mPv%ooR-^j{{2nQu
z^Ok=x50f4y6>y`f41r8-wnOy&eS*c&QJ+?1R#sN-ksA`+I=-3&_E!{Z&*;+3N9p<6
zgdjz2BU`@OjLY%RoP*QS(kh(ER3>UTCl<vnywmM6cpR}$q|%p>Xy8rf8N#FSsl%bD
zp&qVHUBz2A_Mw~!UkOJuiYSbt5<3>BqbuX!)HsbNU+x)FJ+>wB`BEQFvKhqV$3Qns
z8cs6RT^7ZbnU5JyZClYJdSNmj;vG@uio5~vk99|?TZF)X{N_#%C$`HjpL83BZSskl
z?H<duDN9Sk3%|f&CYCJbsLjZ(DxFN2S}BpJ2PQ&ZB$HGo%l;0SV9N}0^U<;G;xzsw
zQ=~E%UI5TD5!Yk6uAd@Ai91Gi@4Pb?lg3btgky$lfN^JjHN2abV&2x9o2#D4B=c6F
zhxgi6sB_iSv5z&fn3Lwyfg-uQ!fR~rv0U}MF>&qoXX1USEeiXW69P&f0QD1ws2x2$
zJ&T%es}u9Ag6#CPsjyk?7-6nx8ctXBuHAAUaC$c8?5Az%dsM#`=hV3Be1R?pA%YXO
z)8OS}JDF|!wH{+z*<AVNF&se?odt{pKz3cS2-#N@MxQ-XO<AlB1j>b?{voL0^cc<-
zb#zv5iT7YAZSXV_BfTlg1ik}tCRrkadF#=3@0@&iCR>o-{Pa|LWo7f-yi#)E*C4`7
zCpv|jBN)jZc(|F?$>fG_UQR%YiPM>qPvW(c)8=BqE77acZsDI1e9cM(Z|qXp#cSsC
zc@w(AW^4qJw-U`ytSlG>X3Xce$-0H3+wPnxCc0WDd5B>7N;D&zbgP~r;=>>oJeV=N
zxpMktZ|X`~!g@5nBrr1I%lHk)8GRe@4_1IUKH@l|beeu*TeS8QW${(=uB_&HnB%<8
zxUCmQQl=g*U&iO{>Y{Q*4yX6a4Y9xp@je;;VKpMt=StdqVYA6(Viz}l*&9yQ_)&~U
ztr=RqOKf^J$;1baTA0w~@>jS-lK&C$J+K07z3kfwjk;rwbFh>fnM2>q2#}^(8;>Sb
z7KjU1P!GM%=ed8V6+fZ3xN_Q|b3l*Tn3!{lF8!8boRCmy;+EK@6`mqSe2TErn+(^E
z2b8Yl^9X$228BCWHJd4cm_ZKi<o;k(A=7H_xc?|Eq!`biFX$~gLrk87apqw|Wpyr*
zKsiBGYjt>3tx4ZKalxSjUoNf-=%3er9`5%Nh@QU&ody7F(1FJzBRgdoHB<FI)AXh-
zZ0eyoeBLU4^_1OIm$OLGStO<?m$-T^#)&<A`0y9o|F*H#C143N$X=v7Xb)>Jl4%1e
zwX)Wwd;*^b$W<>~OpZQ^6lF9SxP}K#noShr42se3d;w7$iYkIp@oHJdb`Ol>hBbFw
z=4zB?aak@9uQ7{P05P}=h}(g96G*D;tvP$Z)2;wSkEGBRas(fN#G@*GP)Z&?N7qWO
zC=4xXby05}#9f7su0_Q)QSWMUtc^j|Mn4=k3}3t&E+aTFN4=Sn<uTt9DMra)=8zwS
zk&cX>Y%=`g1z{B_6okUTjV(bG<4d6NQagRxRDG9yT)HQJWD1|Rqb-`8Fc%wj!y5N+
zseS9vQ6_qIJxbUKE~6OZtr^n!%uzB^GOMVFSmkNn2cK>-SRHc1nMeC?<iTYNvo~jY
zNt4ZZAm8;BB3Zz$+fgrA0|Nu2x2)4^?DS`v3@?G^Df2LQ0LCN_Za`P?@dVm;9?2q^
zl1Ma-4|9sO@g;>J<?v@s(|6g$r7K9w=3tHOo>36XUVjE*Wi`>Ijpj9X?58D!nDQ15
zMFUX2I6^!?_-WIbtpQbd^5M<*j+7^6Y=7*TIsa$jzag~sj*L{NU4R1Jfr`BxF7<8v
z&H=zw9?<Ys5kh>3Uu`1M5Zs7fPYlBEOA2C=i>;H^phMP-U|f^7aFnngw}8k0uMqdI
zFEBsD-wSo#j@rp}PMq@T>1>eV?;S%1eBOH{kl#U%UxYAj^^#r_g6h8|{~=r6By!v7
z^!0Bu_ZP4E6^v25#F{tjoW!LUw0_#918=<`u9*J&IN~>G7FUIM=lj>Gh8b27_xGvR
zuj&-mzq~ucvQ!o5wrUQAu>~KMU*5k+dtl3?7z-;zLpG69+XG>Fue{T$&dIU-{d9J~
zcnI?yZ(=smYCIpS^AFKrdDnu$OiObm|DgRC?z~#t${Td;CCBf`nQ#26yz(2u`9Eg2
zU54+3x~%nwqS*piJx97rn0f1iP;|(`T$y4WA_o9h*M=^a^Xb~@IZ4fv-~WTM^((R}
ztciUaFN|2(j)y|s=VAqC9C#1YFj-}L1=qfBuu^^ep!A$TM!(o~*1{Er;dotYhgTSi
z^A88*O}FmmbBe8g-wOMRKKr@OKk`0O-3J1_=Jkk2P8~m-gjAPtwkSzK7A-X_7V4PZ
zN<X!@u1A?f>=Zh0IoZ71!d#VqeDp{F(1=-fsX-`;Ph4>F!la*h{A2p1|LM&U=ldL3
zuJDX~hb=hSwp?0RFfOvxt$SA8^<W;+U;ej7KW$b28!avt4JXjZa>OoofJUc9^wdsa
zs!hjP%R6t@%}a>4^Wr+y-8|@kV%)S+RGaRHfGO_Hp3T16s;4hvEKk*1)G=p|{7Lj)
zzq-9UXG?kGq849yO+O)W3SNt|rnlzNwaQIT`Yc_G9mS<AP>WT)Pgx3~F3Cpnj^%5y
zvB)dCQ<!~6KZC9JnjFaqtJ%3^HfFLgRXkgpQhS`LdpD#1B81=Vf^96U5j8@2Jqp+8
zr9;F$p>Ey!>K&GMUJ~}<k?IJAQ%8~wSyeu68mVUvs%$Xi=;p+W+472l&noOJPL(MT
zyMHPVZo_g||4NsoJ1MmTzZyD#Cv?A?(fMG=tT)muozO2d-o66bVD{#yDmz$ys^s3Y
zMV1}?m}fGu9Ly(=E@um>j}p3N<E0#%o;pNU;zg#lq4^43%iY|ASUOL=xvjqwjHQyd
zKk>?iqj&j6pBM+d)HFTt-lYboi}8t2a_r3hPtMXgam!*YoEEe<9aJ|!qB@Xd>%U)K
zQSTeL(9(_YL%Fm5F;_;9;jsO83$C5@C8!Et?I&MUL^XqAdR#K#kB^akwqMjWFtO2?
zTP(t09^${1t$*(JB2Cnm27&4H)xEY4H<K@nK1yN{z>Hdr_(rg3(aZE*sa9YZow{0y
zq{f$jhF)!^f=?5qL{sAfwqcD2Nt!4=FER>}FuHy9U1bnBD`7@C1<mT8YKSi&3_c<%
YL)iTd@!=uh?_y}}%COKYA(8yQ1I^Zv2LJ#7

literal 0
HcmV?d00001

diff --git a/experiments/trapezoids/rect.png b/experiments/trapezoids/rect.png
new file mode 100644
index 0000000000000000000000000000000000000000..36f2913c76ef3d004960747655f1eeac488fa6ca
GIT binary patch
literal 921
zcmeAS@N?(olHy`uVBq!ia0vp^CqS5k4M?tyST~P>fjPm`#WAFU@$H?1Tulxl4i^u}
z%kSTl5xYmBE3b_2j9W;_oNn%eZ;N)uh<&(FcDss6PKbktg^9WGfP;d80BxBCF3Zbr
zUW<AitKPg=5UW)dJ_^r2|J?F^x8Tg?#WnSIJ__4g9orp}SS~3|kZ9b(q2i{X%hW08
z(LI1dd&Ev?rblP5y%V}O;r@5=zDL1)o7S)#O6O2HCcVT}!H_9a(4)s8ibY6yf>`4b
zj=?Xq??p-e+S2_W*>hhjly7?fo8Rw$p=?SdXUlm3j~?@Z3F|!mBM~z#ExHc>nJsST
zNFZhY*(mIvo4xjHiT;mZrp88x1O)*J4i+|=Fk=`W_Evt~7N?vB%yJB#u6{1-oD!M<
DoJS3<

literal 0
HcmV?d00001

diff --git a/experiments/trapezoids/rhombus.png b/experiments/trapezoids/rhombus.png
new file mode 100644
index 0000000000000000000000000000000000000000..5f7e184311673bfeaf92b1eeb164f833da0420df
GIT binary patch
literal 1260
zcmeAS@N?(olHy`uVBq!ia0vp^CqS5k4M?tyST~P>fn~F&i(^Oy<J;S(`<fLb8UknU
z+fn<;?*z}x=-=DJ1h}57<n=i2sYzV?{PowW*v8rCGT$@ZQ4!$aU}0ivY;aIepe-}e
z#ar`vY3%i&=7Sk5OpJ{V4hjMS94u(ek|!lry3<dmek^phXSviV;;uHSj$;Y4{o@lZ
zm)ILk%C!4@RNitfS*QV|b2*nxOn(HF=yQ;|Ap}%u#!|E)94Js^(<qbSFEi7lPjy1`
zln!O#lZ7lr4U-B}lq}mEv{nlOmHuK03Os9JH1Ue+1g}1z3Qt?6l@CsU1QaJ6iaIi}
zbBRr($Q2`?EvcMKCddH|4eE2?dZ7st;7D062XxP-`3_|-EP(>QIi9$_7XTW1o%0Fn
zdytc_bEGUT?*ZCd#&q++T#(vchj}JWKo`wZpP=3YQu3VRNuwZ8=F<!ZCgtN3J5|&s
zSf_!UTFbOEahb&?JEh27#c|h5-{yt!&h=Z~mY)B*Xs1qG`+b&AhtB|g^3zu#{>VpP
zmHRB4bRO++RGGhw|H!Gr`5x1DG7BD0-t2DlmP@Jc`B|BhQyM#xcSkDE)DtM&lXuKx
z8JCO9@3UejO&U8E&zY$-Q%Rt3in+JSVRogys<e)j7Y;`P@4uMHBi&)qXI!M>%%;@$
zxL4|A0Z{c^L1jrTfx<23Q7VU7l=|v=L{1tsE{S)&+`Mq_>#w)!gj#uoJ(MPWbL#@C
zo8Y4Iwnxm}C`O^vqt84^=H!G%6(!4aD+*N(vrXz)vTx#Jk2XFPK~LMo$0zd01GRku
zdVZ!7P}|cpLheSsKyBY<YxbqAauAxhCvTg@q?b&dE}QQ56siOR^*^cHd~BkRG*H{|
zv_9pTRzPjv&&s(Q)dIEs6F#oqSR;7Sys$?21iw<`k&o>T|7KVUX&<i#hU_tqBZada
z-p$YyD!ijU;Q-G>k<Mhv>y@$BOYfY%t$%mk>8G3O7x2Zdzs{F_RlLzA@rcKfk1~xm
znM;7QO=FIMlggtTZVJ+Si-EMCf_}wuptw}yo)>eK1dqRF*>u?2MX9frWmE9^i5<!I
zjUpG4RUT<LE3|$Q>9jZ{=;3G!l-|S=6mi<)NZ>pNtqj3Vi&p|3s_t&U&}Rv{C^)fW
zv0h_Hn6Xgd74-?sS2|o|jtiV{^a4sh=6K?u3bbS+Fpb+z?08(kl=)z)$B~O|4pKLT
zIxTJqdN`j48orI?QUuVhTf!dfd9F%*b{tED?Ue=Hfq7}7i07>r?S!+r+O`iDfZ_4=
mVW5E~j!cR@>yjaA$FSn!qrD58?B4@RF$PapKbLh*2~7a5W6zxc

literal 0
HcmV?d00001