nandi/bresenham-circle · bresenham.nim

⑂ d1c5bb86e566e9590e11c31a94f56b83e7e19c94

bresenham.nim · 342 lines · 11.8 KBNim    Blame HistoryRaw
Bresenham midpoint circle visualizer, with a zero-symmetry counterpart   1## Two ways to put a circle on a grid, side by side.
3##   left  -- Bresenham: integer decisions, one octant, mirrored 8 ways.
4##   right -- Poisson sprinkle: uniform directions snapped to cells.
6## Both land on the same lattice. The difference is the symmetry of the
7## *selection*: Bresenham's is exactly 8-fold, the sprinkle's is trivial.
9## Controls: SPACE step  A auto  R reset  UP/DOWN radius  [ ] oversample  ESC
11import raylib, std/[strformat, os, math, strutils, random, sets, hashes]
InitW = 1400
InitH = 760
PanelWant = 380
MinCell = 2
MinRadius = 2
Bg        = Color(r:  18, g:  18, b:  24, a: 255)
GridLine  = Color(r:  36, g:  36, b:  46, a: 255)
Axis      = Color(r:  70, g:  70, b:  88, a: 255)
TrueArc   = Color(r: 100, g: 100, b: 128, a: 255)
Octant    = Color(r:  88, g: 166, b: 255, a: 255)
Mirror    = Color(r:  88, g: 166, b: 255, a: 105)
Sprink    = Color(r: 118, g: 222, b: 160, a: 210)
Cursor    = Color(r: 255, g: 176, b:  64, a: 255)
Candidate = Color(r: 255, g: 176, b:  64, a:  60)
Mid       = Color(r: 255, g:  92, b:  92, a: 255)
Ink       = Color(r: 226, g: 226, b: 236, a: 255)
Dim       = Color(r: 130, g: 130, b: 148, a: 255)
HiLine    = Color(r:  40, g:  62, b:  92, a: 255)
Branch = enum brNone, brEast, brSouthEast
Cells = HashSet[(int, int)]
State = object
40
  # -- Bresenham
  x, y, d: int                 ## the entire algorithm state: three integers
  plotted: seq[(int, int)]     ## octant only; the rest is reflection
  bcells: Cells                ## all 8 octants, for counting
  branch: Branch
  lastUpdate: string
  done: bool
  # -- Poisson sprinkle
  over: int                    ## samples per Bresenham pixel
  samples: seq[(int, int)]     ## pre-rolled, revealed progressively
  revealed: int
  scells: Cells
  perStep: int
55# ---------------------------------------------------------------- algorithms --
57proc mirrors(x, y: int): array[8, (int, int)] =
## The complete symmetry group of the square lattice: D4, order 8.
[(x, y), (y, x), (y, -x), (x, -y), (-x, -y), (-y, -x), (-y, x), (-x, y)]
61proc reset(s: var State, r: int, over = -1) =
if over >= 0: s.over = over
if s.over == 0: s.over = 4
64
65
66
s.d = 1 - r            ## F(1, r - 1/2), the 1/4 dropped so d stays integral
s.plotted = @[]
s.bcells = initHashSet[(int, int)]()
s.branch = brNone
s.lastUpdate = ""
s.done = false
# Sprinkle: uniform in angle, so isotropic in distribution but with no
# exact symmetry at all. Fixed seed per radius so runs are reproducible.
var rng = initRand(0xC0FFEE + r * 7919)
let n = int(s.over.float * 4.0 * sqrt(2.0) * r.float)
s.samples = newSeqOfCap[(int, int)](n)
for _ in 1 .. n:
  let t = rng.rand(2.0 * PI)
  s.samples.add (int(round(r.float * cos(t))), int(round(r.float * sin(t))))
s.revealed = 0
s.scells = initHashSet[(int, int)]()
s.perStep = max(1, n div max(1, int(r.float / sqrt(2.0))))
86proc reveal(s: var State, k: int) =
let stop = min(s.revealed + k, s.samples.len)
while s.revealed < stop:
  s.scells.incl s.samples[s.revealed]
  inc s.revealed
92proc step(s: var State) =
## Exactly one iteration of the Bresenham loop body, plus the sprinkle's
## proportional share of samples so the two fill at a comparable rate.
if s.done: return
if s.x > s.y:
  s.done = true
  s.branch = brNone
  s.reveal(s.samples.len)
100
s.plotted.add (s.x, s.y)
for m in mirrors(s.x, s.y): s.bcells.incl m
if s.d < 0:
  # midpoint (x+1, y-1/2) is INSIDE the circle -> East, keep y
  s.branch = brEast
  s.lastUpdate = fmt"d += 2*{s.x} + 3  =  {2 * s.x + 3}"
  s.d += 2 * s.x + 3
  # midpoint is OUTSIDE -> South-East, step y in
  s.branch = brSouthEast
  s.lastUpdate = fmt"d += 2*({s.x} - {s.y}) + 5  =  {2 * (s.x - s.y) + 5}"
  s.d += 2 * (s.x - s.y) + 5
  dec s.y
116
s.reveal(s.perStep)
if s.x > s.y:
  s.done = true
  s.reveal(s.samples.len)
123proc symmetries(c: Cells): int =
## How many of the lattice's 8 symmetries actually map this pixel set to
## itself. Bresenham: 8. A sprinkle: 1 (the identity), essentially always.
if c.len == 0: return 0
for k in 0 ..< 8:
  var ok = true
  for (x, y) in c:
    if mirrors(x, y)[k] notin c:
      ok = false
      break
  if ok: inc result
135# ------------------------------------------------------------------- layout --
137proc layout(sw, sh: int): tuple[panelW, gridW, halfW, maxR, cellCap: int] =
let panelW = clamp(PanelWant, 280, sw div 3)
let gridW = sw - panelW
let halfW = gridW div 2
let avail = max(min(halfW - 30, sh - 150), MinCell)
let maxR = max(MinRadius, (avail div MinCell - 3) div 2)
(panelW, gridW, halfW, maxR, avail)
145# ------------------------------------------------------------------ drawing --
147type View = object
ox, oy, cell, half: int
150proc cx(v: View, gx: int): int = v.ox + gx * v.cell - v.half
151proc cy(v: View, gy: int): int = v.oy - gy * v.cell - v.half
153proc drawRect(x, y, w, h: int, c: Color) =
drawRectangle(x.int32, y.int32, w.int32, h.int32, c)
156proc drawRectLines(x, y, w, h: int, c: Color) =
drawRectangleLines(x.int32, y.int32, w.int32, h.int32, c)
159proc drawLn(x1, y1, x2, y2: int, c: Color) =
drawLine(x1.int32, y1.int32, x2.int32, y2.int32, c)
162proc text(s: string, x, y, size: int, c: Color) =
drawText(s, x.int32, y.int32, size.int32, c)
165proc backdrop(v: View, r: int) =
## Grid, axes and the ideal circle both methods are chasing.
let ext = r + 1
if v.cell >= 9:
  for i in -ext .. ext:
    drawLn(v.cx(-ext), v.cy(i) + v.half, v.cx(ext) + v.cell, v.cy(i) + v.half, GridLine)
    drawLn(v.cx(i) + v.half, v.cy(-ext) + v.cell, v.cx(i) + v.half, v.cy(ext), GridLine)
drawLn(v.cx(-ext), v.oy, v.cx(ext) + v.cell, v.oy, Axis)
drawLn(v.ox, v.cy(-ext) + v.cell, v.ox, v.cy(ext), Axis)
drawCircleLines(v.ox.int32, v.oy.int32, float32(r * v.cell), TrueArc)
176proc main =
setConfigFlags(flags(WindowResizable))
initWindow(InitW, InitH, "Bresenham vs Poisson sprinkle")
defer: closeWindow()
setWindowMinSize(900, 640)
setTargetFPS(60)
  s = State()
  auto = false
  held = 0
  tick = 0
  frames = 0
  shot = "--shot" in commandLineParams()
  shotFrame = 400
  startR = 12
for a in commandLineParams():
  if a.startsWith("--r="): startR = max(parseInt(a[4 .. ^1]), MinRadius)
  elif a.startsWith("--frame="): shotFrame = parseInt(a[8 .. ^1])
s.over = 4
s.reset(min(startR, layout(getScreenWidth().int, getScreenHeight().int).maxR))
if shot: auto = true
while not windowShouldClose():
  inc frames
    sw = getScreenWidth().int
    sh = getScreenHeight().int
    (panelW, gridW, halfW, maxR, _) = layout(sw, sh)
  if s.r > maxR: s.reset(maxR)
  # ---- input
  if isKeyPressed(Space): s.step()
  if isKeyPressed(A): auto = not auto
  if isKeyPressed(R): s.reset(s.r)
  if isKeyPressed(RightBracket) and s.over < 12: s.reset(s.r, s.over + 1)
  if isKeyPressed(LeftBracket) and s.over > 1: s.reset(s.r, s.over - 1)
  var delta = 0
  if isKeyPressed(Up): delta = 1
  elif isKeyPressed(Down): delta = -1
  elif isKeyDown(Up) or isKeyDown(Down):
    inc held
    if held > 18:
      let fast = if held > 70: 1 else: 3
      if held mod fast == 0: delta = if isKeyDown(Up): 1 else: -1
222
    held = 0
  if delta != 0:
    let want = clamp(s.r + delta, MinRadius, maxR)
    if want != s.r: s.reset(want)
  if auto and not s.done:
    inc tick
    if tick mod max(1, 10 - s.r div 8) == 0: s.step()
  # ---- both panes share a cell size so they are directly comparable
    span = 2 * s.r + 3
    cell = max(min(halfW - 30, sh - 150) div span, MinCell)
    oy = sh div 2 + 10
    left = View(ox: halfW div 2, oy: oy, cell: cell, half: cell div 2)
    right = View(ox: halfW + halfW div 2, oy: oy, cell: cell, half: cell div 2)
  drawing:
    clearBackground(Bg)
    # ================= left: Bresenham =================
    backdrop(left, s.r)
    let ext = s.r + 1
    drawLn(left.ox, left.oy, left.ox, left.cy(ext) + left.half, Axis)
    drawLn(left.ox, left.oy, left.cx(ext) + left.half, left.cy(ext) + left.half, Axis)
    for (px, py) in s.plotted:
      for k, (mx, my) in mirrors(px, py):
        drawRect(left.cx(mx), left.cy(my), cell, cell,
                 if k == 0: Octant else: Mirror)
    if not s.done:
      drawRectLines(left.cx(s.x), left.cy(s.y), cell, cell, Cursor)
      if s.x + 1 <= s.y:
        drawRect(left.cx(s.x + 1), left.cy(s.y), cell, cell, Candidate)
        drawRect(left.cx(s.x + 1), left.cy(s.y - 1), cell, cell, Candidate)
        drawCircle(int32(left.cx(s.x + 1) + left.half), int32(left.cy(s.y) + cell),
                   float32(max(3, cell div 5)), Mid)
    # ================= right: Poisson sprinkle =================
    backdrop(right, s.r)
    for (mx, my) in s.scells:
      drawRect(right.cx(mx), right.cy(my), cell, cell, Sprink)
    # ---- titles and per-pane stats
267
      bSym = symmetries(s.bcells)
      sSym = symmetries(s.scells)
      rx = halfW + 24
    text("BRESENHAM", lx, 16, 20, Octant)
    text("one octant, mirrored 8 ways", lx, 40, 14, Dim)
    text("POISSON SPRINKLE", rx, 16, 20, Sprink)
    text(fmt"uniform directions, snapped ({s.over}x oversample)", rx, 40, 14, Dim)
    let by = sh - 66
    text(fmt"{s.bcells.len} cells   {s.plotted.len} computed, rest free", lx, by, 16, Ink)
    text(fmt"exact symmetries: {bSym} / 8", lx, by + 22, 16, Octant)
    text(fmt"{s.scells.len} cells   {s.revealed} samples rolled", rx, by, 16, Ink)
    text(fmt"exact symmetries: {sSym} / 8", rx, by + 22, 16, Sprink)
    drawLn(halfW, 0, halfW, sh, GridLine)
    # ================= panel =================
    let px = gridW + 24
    drawLn(gridW, 0, gridW, sh, GridLine)
    text("MIDPOINT CIRCLE", px, 20, 22, Ink)
    text(fmt"radius {s.r}  (max {maxR} at {sw}x{sh})", px, 48, 15, Dim)
    let code = [
      "x = 0;  y = r;  d = 1 - r",
      "while x <= y:",
      "    plot8(x, y)",
      "    if d < 0:          # mid inside",
      "        d += 2*x + 3",
      "    else:              # mid outside",
      "        d += 2*(x - y) + 5",
      "        y -= 1",
      "    x += 1",
    let lit =
      case s.branch
      of brEast: @[2, 3, 4, 8]
      of brSouthEast: @[2, 5, 6, 7, 8]
      of brNone: @[]
    for i, line in code:
      let ly = 84 + i * 22
      if i in lit: drawRect(px - 8, ly - 3, panelW - 32, 22, HiLine)
      text(line, px, ly, 16, if i in lit: Ink else: Dim)
    var sy = 300
    text("state", px, sy, 16, Dim); sy += 26
    text(fmt"x = {s.x}", px, sy, 20, Ink); sy += 26
    text(fmt"y = {s.y}", px, sy, 20, Ink); sy += 26
    text(fmt"d = {s.d}", px, sy, 20, (if s.d < 0: Octant else: Cursor)); sy += 32
    text(s.lastUpdate, px, sy, 15, Cursor); sy += 30
    if s.done:
      text("done -- x > y, octant closed", px, sy, 18, Octant)
    elif s.x + 1 <= s.y:
      text(fmt"testing midpoint ({s.x + 1}, {s.y}-1/2)", px, sy, 15, Mid)
    var ly = sh - 170
    text("cost of zero symmetry", px, ly, 15, Dim); ly += 24
    if s.done and s.scells.len > 0:
      let waste = s.revealed.float / s.scells.len.float
      text(fmt"{waste:.1f} samples per cell drawn", px, ly, 15, Sprink); ly += 22
      let gap = 100.0 * (s.scells.len.float / max(1, s.bcells.len).float - 1.0)
      text(fmt"{gap:+.0f}% cells vs bresenham", px, ly, 15, Sprink); ly += 30
    else:
      ly += 52
    text("SPACE step   A auto   R reset", px, ly, 15, (if auto: Cursor else: Dim)); ly += 20
    text("UP/DOWN radius (hold to scrub)", px, ly, 15, Dim); ly += 20
    text("[ ]  sprinkle oversample", px, ly, 15, Dim)
  if shot and frames == shotFrame:
    takeScreenshot("shot.png")
    break

Bresenham midpoint circle visualizer, with a zero-symmetry counterpart 3d0b0a3 nandi 17h ago	1	## Two ways to put a circle on a grid, side by side.
	2	##
	3	## left -- Bresenham: integer decisions, one octant, mirrored 8 ways.
	4	## right -- Poisson sprinkle: uniform directions snapped to cells.
	5	##
	6	## Both land on the same lattice. The difference is the symmetry of the
	7	## selection: Bresenham's is exactly 8-fold, the sprinkle's is trivial.
	8	##
	9	## Controls: SPACE step A auto R reset UP/DOWN radius [ ] oversample ESC
	10
	11	import raylib, std/[strformat, os, math, strutils, random, sets, hashes]
	12
	13	const
	14	InitW = 1400
	15	InitH = 760
	16	PanelWant = 380
	17	MinCell = 2
	18	MinRadius = 2
	19
	20	Bg = Color(r: 18, g: 18, b: 24, a: 255)
	21	GridLine = Color(r: 36, g: 36, b: 46, a: 255)
	22	Axis = Color(r: 70, g: 70, b: 88, a: 255)
	23	TrueArc = Color(r: 100, g: 100, b: 128, a: 255)
	24	Octant = Color(r: 88, g: 166, b: 255, a: 255)
	25	Mirror = Color(r: 88, g: 166, b: 255, a: 105)
	26	Sprink = Color(r: 118, g: 222, b: 160, a: 210)
	27	Cursor = Color(r: 255, g: 176, b: 64, a: 255)
	28	Candidate = Color(r: 255, g: 176, b: 64, a: 60)
	29	Mid = Color(r: 255, g: 92, b: 92, a: 255)
	30	Ink = Color(r: 226, g: 226, b: 236, a: 255)
	31	Dim = Color(r: 130, g: 130, b: 148, a: 255)
	32	HiLine = Color(r: 40, g: 62, b: 92, a: 255)
	33
	34	type
	35	Branch = enum brNone, brEast, brSouthEast
	36
	37	Cells = HashSet[(int, int)]
	38
	39	State = object
	40	r: int
	41	# -- Bresenham
	42	x, y, d: int ## the entire algorithm state: three integers
	43	plotted: seq[(int, int)] ## octant only; the rest is reflection
	44	bcells: Cells ## all 8 octants, for counting
	45	branch: Branch
	46	lastUpdate: string
	47	done: bool
	48	# -- Poisson sprinkle
	49	over: int ## samples per Bresenham pixel
	50	samples: seq[(int, int)] ## pre-rolled, revealed progressively
	51	revealed: int
	52	scells: Cells
	53	perStep: int
	54
	55	# ---------------------------------------------------------------- algorithms --
	56
	57	proc mirrors(x, y: int): array[8, (int, int)] =
	58	## The complete symmetry group of the square lattice: D4, order 8.
	59	[(x, y), (y, x), (y, -x), (x, -y), (-x, -y), (-y, -x), (-y, x), (-x, y)]
	60
	61	proc reset(s: var State, r: int, over = -1) =
	62	if over >= 0: s.over = over
	63	if s.over == 0: s.over = 4
	64	s.r = r
65	s.x = 0
66	s.y = r
67	s.d = 1 - r ## F(1, r - 1/2), the 1/4 dropped so d stays integral
68	s.plotted = @[]
69	s.bcells = initHashSet[(int, int)]()
70	s.branch = brNone
71	s.lastUpdate = ""
72	s.done = false
73
74	# Sprinkle: uniform in angle, so isotropic in distribution but with no
75	# exact symmetry at all. Fixed seed per radius so runs are reproducible.
76	var rng = initRand(0xC0FFEE + r * 7919)
77	let n = int(s.over.float * 4.0 * sqrt(2.0) * r.float)
78	s.samples = newSeqOfCap[(int, int)](n)
79	for _ in 1 .. n:
80	let t = rng.rand(2.0 * PI)
81	s.samples.add (int(round(r.float * cos(t))), int(round(r.float * sin(t))))
82	s.revealed = 0
83	s.scells = initHashSet[(int, int)]()
84	s.perStep = max(1, n div max(1, int(r.float / sqrt(2.0))))
85
86	proc reveal(s: var State, k: int) =
87	let stop = min(s.revealed + k, s.samples.len)
88	while s.revealed < stop:
89	s.scells.incl s.samples[s.revealed]
90	inc s.revealed
91
92	proc step(s: var State) =
93	## Exactly one iteration of the Bresenham loop body, plus the sprinkle's
94	## proportional share of samples so the two fill at a comparable rate.
95	if s.done: return
96	if s.x > s.y:
97	s.done = true
98	s.branch = brNone
99	s.reveal(s.samples.len)
100	return
101
102	s.plotted.add (s.x, s.y)
103	for m in mirrors(s.x, s.y): s.bcells.incl m
104
105	if s.d < 0:
106	# midpoint (x+1, y-1/2) is INSIDE the circle -> East, keep y
107	s.branch = brEast
108	s.lastUpdate = fmt"d += 2{s.x} + 3 = {2 s.x + 3}"
109	s.d += 2 * s.x + 3
110	else:
111	# midpoint is OUTSIDE -> South-East, step y in
112	s.branch = brSouthEast
113	s.lastUpdate = fmt"d += 2({s.x} - {s.y}) + 5 = {2 (s.x - s.y) + 5}"
114	s.d += 2 * (s.x - s.y) + 5
115	dec s.y
116	inc s.x
117
118	s.reveal(s.perStep)
119	if s.x > s.y:
120	s.done = true
121	s.reveal(s.samples.len)
122
123	proc symmetries(c: Cells): int =
124	## How many of the lattice's 8 symmetries actually map this pixel set to
125	## itself. Bresenham: 8. A sprinkle: 1 (the identity), essentially always.
126	if c.len == 0: return 0
127	for k in 0 ..< 8:
128	var ok = true
129	for (x, y) in c:
130	if mirrors(x, y)[k] notin c:
131	ok = false
132	break
133	if ok: inc result
134
135	# ------------------------------------------------------------------- layout --
136
137	proc layout(sw, sh: int): tuple[panelW, gridW, halfW, maxR, cellCap: int] =
138	let panelW = clamp(PanelWant, 280, sw div 3)
139	let gridW = sw - panelW
140	let halfW = gridW div 2
141	let avail = max(min(halfW - 30, sh - 150), MinCell)
142	let maxR = max(MinRadius, (avail div MinCell - 3) div 2)
143	(panelW, gridW, halfW, maxR, avail)
144
145	# ------------------------------------------------------------------ drawing --
146
147	type View = object
148	ox, oy, cell, half: int
149
150	proc cx(v: View, gx: int): int = v.ox + gx * v.cell - v.half
151	proc cy(v: View, gy: int): int = v.oy - gy * v.cell - v.half
152
153	proc drawRect(x, y, w, h: int, c: Color) =
154	drawRectangle(x.int32, y.int32, w.int32, h.int32, c)
155
156	proc drawRectLines(x, y, w, h: int, c: Color) =
157	drawRectangleLines(x.int32, y.int32, w.int32, h.int32, c)
158
159	proc drawLn(x1, y1, x2, y2: int, c: Color) =
160	drawLine(x1.int32, y1.int32, x2.int32, y2.int32, c)
161
162	proc text(s: string, x, y, size: int, c: Color) =
163	drawText(s, x.int32, y.int32, size.int32, c)
164
165	proc backdrop(v: View, r: int) =
166	## Grid, axes and the ideal circle both methods are chasing.
167	let ext = r + 1
168	if v.cell >= 9:
169	for i in -ext .. ext:
170	drawLn(v.cx(-ext), v.cy(i) + v.half, v.cx(ext) + v.cell, v.cy(i) + v.half, GridLine)
171	drawLn(v.cx(i) + v.half, v.cy(-ext) + v.cell, v.cx(i) + v.half, v.cy(ext), GridLine)
172	drawLn(v.cx(-ext), v.oy, v.cx(ext) + v.cell, v.oy, Axis)
173	drawLn(v.ox, v.cy(-ext) + v.cell, v.ox, v.cy(ext), Axis)
174	drawCircleLines(v.ox.int32, v.oy.int32, float32(r * v.cell), TrueArc)
175
176	proc main =
177	setConfigFlags(flags(WindowResizable))
178	initWindow(InitW, InitH, "Bresenham vs Poisson sprinkle")
179	defer: closeWindow()
180	setWindowMinSize(900, 640)
181	setTargetFPS(60)
182
183	var
184	s = State()
185	auto = false
186	held = 0
187	tick = 0
188	frames = 0
189	shot = "--shot" in commandLineParams()
190	shotFrame = 400
191	startR = 12
192	for a in commandLineParams():
193	if a.startsWith("--r="): startR = max(parseInt(a[4 .. ^1]), MinRadius)
194	elif a.startsWith("--frame="): shotFrame = parseInt(a[8 .. ^1])
195	s.over = 4
196	s.reset(min(startR, layout(getScreenWidth().int, getScreenHeight().int).maxR))
197	if shot: auto = true
198
199	while not windowShouldClose():
200	inc frames
201
202	let
203	sw = getScreenWidth().int
204	sh = getScreenHeight().int
205	(panelW, gridW, halfW, maxR, _) = layout(sw, sh)
206	if s.r > maxR: s.reset(maxR)
207
208	# ---- input
209	if isKeyPressed(Space): s.step()
210	if isKeyPressed(A): auto = not auto
211	if isKeyPressed(R): s.reset(s.r)
212	if isKeyPressed(RightBracket) and s.over < 12: s.reset(s.r, s.over + 1)
213	if isKeyPressed(LeftBracket) and s.over > 1: s.reset(s.r, s.over - 1)
214	var delta = 0
215	if isKeyPressed(Up): delta = 1
216	elif isKeyPressed(Down): delta = -1
217	elif isKeyDown(Up) or isKeyDown(Down):
218	inc held
219	if held > 18:
220	let fast = if held > 70: 1 else: 3
221	if held mod fast == 0: delta = if isKeyDown(Up): 1 else: -1
222	else:
223	held = 0
224	if delta != 0:
225	let want = clamp(s.r + delta, MinRadius, maxR)
226	if want != s.r: s.reset(want)
227	if auto and not s.done:
228	inc tick
229	if tick mod max(1, 10 - s.r div 8) == 0: s.step()
230
231	# ---- both panes share a cell size so they are directly comparable
232	let
233	span = 2 * s.r + 3
234	cell = max(min(halfW - 30, sh - 150) div span, MinCell)
235	oy = sh div 2 + 10
236	left = View(ox: halfW div 2, oy: oy, cell: cell, half: cell div 2)
237	right = View(ox: halfW + halfW div 2, oy: oy, cell: cell, half: cell div 2)
238
239	drawing:
240	clearBackground(Bg)
241
242	# ================= left: Bresenham =================
243	backdrop(left, s.r)
244	let ext = s.r + 1
245	drawLn(left.ox, left.oy, left.ox, left.cy(ext) + left.half, Axis)
246	drawLn(left.ox, left.oy, left.cx(ext) + left.half, left.cy(ext) + left.half, Axis)
247
248	for (px, py) in s.plotted:
249	for k, (mx, my) in mirrors(px, py):
250	drawRect(left.cx(mx), left.cy(my), cell, cell,
251	if k == 0: Octant else: Mirror)
252
253	if not s.done:
254	drawRectLines(left.cx(s.x), left.cy(s.y), cell, cell, Cursor)
255	if s.x + 1 <= s.y:
256	drawRect(left.cx(s.x + 1), left.cy(s.y), cell, cell, Candidate)
257	drawRect(left.cx(s.x + 1), left.cy(s.y - 1), cell, cell, Candidate)
258	drawCircle(int32(left.cx(s.x + 1) + left.half), int32(left.cy(s.y) + cell),
259	float32(max(3, cell div 5)), Mid)
260
261	# ================= right: Poisson sprinkle =================
262	backdrop(right, s.r)
263	for (mx, my) in s.scells:
264	drawRect(right.cx(mx), right.cy(my), cell, cell, Sprink)
265
266	# ---- titles and per-pane stats
267	let
268	bSym = symmetries(s.bcells)
269	sSym = symmetries(s.scells)
270	lx = 24
271	rx = halfW + 24
272	text("BRESENHAM", lx, 16, 20, Octant)
273	text("one octant, mirrored 8 ways", lx, 40, 14, Dim)
274	text("POISSON SPRINKLE", rx, 16, 20, Sprink)
275	text(fmt"uniform directions, snapped ({s.over}x oversample)", rx, 40, 14, Dim)
276
277	let by = sh - 66
278	text(fmt"{s.bcells.len} cells {s.plotted.len} computed, rest free", lx, by, 16, Ink)
279	text(fmt"exact symmetries: {bSym} / 8", lx, by + 22, 16, Octant)
280	text(fmt"{s.scells.len} cells {s.revealed} samples rolled", rx, by, 16, Ink)
281	text(fmt"exact symmetries: {sSym} / 8", rx, by + 22, 16, Sprink)
282
283	drawLn(halfW, 0, halfW, sh, GridLine)
284
285	# ================= panel =================
286	let px = gridW + 24
287	drawLn(gridW, 0, gridW, sh, GridLine)
288
289	text("MIDPOINT CIRCLE", px, 20, 22, Ink)
290	text(fmt"radius {s.r} (max {maxR} at {sw}x{sh})", px, 48, 15, Dim)
291
292	let code = [
293	"x = 0; y = r; d = 1 - r",
294	"while x <= y:",
295	" plot8(x, y)",
296	" if d < 0: # mid inside",
297	" d += 2*x + 3",
298	" else: # mid outside",
299	" d += 2*(x - y) + 5",
300	" y -= 1",
301	" x += 1",
302	]
303	let lit =
304	case s.branch
305	of brEast: @[2, 3, 4, 8]
306	of brSouthEast: @[2, 5, 6, 7, 8]
307	of brNone: @[]
308	for i, line in code:
309	let ly = 84 + i * 22
310	if i in lit: drawRect(px - 8, ly - 3, panelW - 32, 22, HiLine)
311	text(line, px, ly, 16, if i in lit: Ink else: Dim)
312
313	var sy = 300
314	text("state", px, sy, 16, Dim); sy += 26
315	text(fmt"x = {s.x}", px, sy, 20, Ink); sy += 26
316	text(fmt"y = {s.y}", px, sy, 20, Ink); sy += 26
317	text(fmt"d = {s.d}", px, sy, 20, (if s.d < 0: Octant else: Cursor)); sy += 32
318	text(s.lastUpdate, px, sy, 15, Cursor); sy += 30
319	if s.done:
320	text("done -- x > y, octant closed", px, sy, 18, Octant)
321	elif s.x + 1 <= s.y:
322	text(fmt"testing midpoint ({s.x + 1}, {s.y}-1/2)", px, sy, 15, Mid)
323
324	var ly = sh - 170
325	text("cost of zero symmetry", px, ly, 15, Dim); ly += 24
326	if s.done and s.scells.len > 0:
327	let waste = s.revealed.float / s.scells.len.float
328	text(fmt"{waste:.1f} samples per cell drawn", px, ly, 15, Sprink); ly += 22
329	let gap = 100.0 * (s.scells.len.float / max(1, s.bcells.len).float - 1.0)
330	text(fmt"{gap:+.0f}% cells vs bresenham", px, ly, 15, Sprink); ly += 30
331	else:
332	ly += 52
333
334	text("SPACE step A auto R reset", px, ly, 15, (if auto: Cursor else: Dim)); ly += 20
335	text("UP/DOWN radius (hold to scrub)", px, ly, 15, Dim); ly += 20
336	text("[ ] sprinkle oversample", px, ly, 15, Dim)
337
338	if shot and frames == shotFrame:
339	takeScreenshot("shot.png")
340	break
341
342	main()