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re: MCOL solved -- a closed triangle collision mesh in a uniform grid

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The 0x50 header word, which the first section of this page had dismissed as "a
large value", is two u16 counts: vertices and triangles.  They give the two
remaining blocks their stride, and every derived length is exact in 11/11 --
len(0x54) == align16(12*nv), len(0x58) == align16(6*nt), and nt equals the
bounding-sphere count decoded last iteration.

Checks that cannot pass by accident:

  * sphere i is the TIGHT bounding sphere of triangle i, 4768/4768, with
    max|v-c|/r median 0.99990 (a fixed 1.0001 epsilon), against a 1.32%
    random-triangle control;
  * the mesh is watertight -- every edge shared by exactly two triangles,
    7152/7152, zero degenerate triangles, zero unreferenced vertices;
  * the two smallest objects are 8 vertices and 12 triangles whose positions
    are the eight +-250000 corners of the map bbox: a bare bounding cube.

The cell lists are a correct broad phase: with an exact triangle/box SAT test
only 3 overlapping triangles in 18 577 entries are absent, so a query walking
one cell's list cannot miss a hit.  The 730 conservative extras bracket the
builder's own test between exact-SAT and AABB, which retires the 18 unexplained
"sphere misses" from the previous commit as that same margin.

mcol_probe.py gains `mesh` and `obj`; `verify` now runs all three checks and its
output is recorded in docs/re/data/mcol-verify.txt.
This commit is contained in:
Sylpheed RE agent
2026-08-26 09:12:36 +00:00
parent 4f0d21f50d
commit c0a7033295
4 changed files with 261 additions and 7 deletions
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21
docs/re/BACKLOG.md
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@@ -393,9 +393,24 @@ search cannot find a *schedule*.
`tools/re-capture/mcol_probe.py verify`.
⚠️ The stale ≈**0.75×** ratio I had recorded as "too consistent to be
coincidence" was **12/16** — my own wrong stride, not a fact about the data.
❔ Still open: the `0x54` and `0x58` blocks (the geometry these spheres bound;
neither has a constant stride against the sphere count), and 18 cell entries
(0.10 %) whose sphere misses its cell by 0.4–13 %.
✅✅ **`MCOL` SOLVED the same day — it is a closed triangle collision mesh.**
The `0x50` word is **two `u16` counts** (vertices, triangles), which gives the
last two blocks their stride: `len(0x54) == align16(12·nv)` and
`len(0x58) == align16(6·nt)` in **11/11**, and `nt` == the sphere count in
**11/11**. Sphere *i* is the *tight* bounding sphere of triangle *i* —
**4 768/4 768**, `max‖v−c‖/r` median 0.99990 (a fixed 1.0001 epsilon), against
a 1.32 % random-triangle control — and the mesh is **watertight**: every edge
shared by exactly two triangles, **7 152/7 152**, zero degenerates, zero
orphan vertices. The two smallest objects are 8 vertices / 12 triangles = the
map's bounding cube. The cell lists are a **correct broad phase**: only **3**
overlapping triangles in 18 577 entries are missing, and the 730 conservative
extras place the builder's test between exact-SAT and AABB — which also
explains the 18 "sphere misses" above as that same margin.
`tools/re-capture/mcol_probe.py verify` reproduces it
([`data/mcol-verify.txt`](data/mcol-verify.txt)); `mcol_probe.py obj` exports
any object as a Wavefront OBJ.
❔ Still open: the objects are **not name-resolved**, so the map each belongs
to — and the `MCOL`↔`REGN` pairing — is unknown, as is the runtime consumer.
See [`structures/mcol-collision.md`](structures/mcol-collision.md).
* 🔴 **`hidden/DefTables.pak` is NOT it** (checked 2026-08-24). The three
unnamed schemas are more **model/render** tables in the same vocabulary as the

40
docs/re/data/mcol-verify.txt Normal file
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@@ -0,0 +1,40 @@
object len(0x5C) /12 /16 max u16
2cf7eb47 960 80.00 60 59 max == n-1
cbb99d34 192 16.00 12 11 max == n-1
d84a95fb 3488 290.67 * 218 217 max == n-1
db066592 12640 1053.33 * 790 789 max == n-1
db61c506 2144 178.67 * 134 133 max == n-1
dc44fe0c 2784 232.00 174 173 max == n-1
dc4b0896 14784 1232.00 924 923 max == n-1
dd89a110 18624 1552.00 1164 1163 max == n-1
df4628c2 4160 346.67 * 260 259 max == n-1
e084c13c 192 16.00 12 11 max == n-1
e16460cf 16320 1360.00 1020 1019 max == n-1
length divisible by 12: 7/11 max u16 == len/16 - 1: 11/11
referenced sphere reaches its own cell : 18559/18577 = 99.90%
random sphere, same object (control) : 2233/18577 = 12.02%
object verts tris len 0x54 len 0x58 spheres
2cf7eb47 34 60 416 368 60
cbb99d34 8 12 96 80 12
d84a95fb 111 218 1344 1312 218
db066592 405 790 4864 4752 790
db61c506 73 134 880 816 134
dc44fe0c 89 174 1072 1056 174
dc4b0896 502 924 6032 5552 924
dd89a110 632 1164 7584 6992 1164
df4628c2 134 260 1616 1568 260
e084c13c 8 12 96 80 12
e16460cf 554 1020 6656 6128 1020
len(0x54) == align16(12 * verts) : 11/11
len(0x58) == align16(6 * tris) : 11/11
triangle count == sphere count : 11/11
sphere i encloses triangle i : 4768/4768 = 100.00%
...and is tight to within 1% : 4768/4768 = 100.00%
sphere i encloses a random triangle (ctl) : 63/4768 = 1.32%
edges shared by exactly two triangles : 7152/7152 = 100.00%
PASS

111
docs/re/structures/mcol-collision.md
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@@ -375,3 +375,114 @@ rather than a decode error, but it is **not explained** and is recorded as open.
these spheres bound. Their lengths are **not** a constant multiple of the sphere
count (`0x58 / n` is ≈6.0 for the large objects but 6.13 and 6.67 for the two
smallest), so at least one of them is variable-stride or has its own count.
## ✅✅ `MCOL` is a **closed triangle collision mesh** — decoded
**2026-08-26.** The header's `0x50` word, which the first section on this page
dismissed as "a large value", is **two `u16` counts**, and they give both
remaining blocks a stride:
0x50 u16 vertex count 0x52 u16 triangle count
Every derived length is exact in **11 / 11** objects:
| | |
|---|---|
| `len(0x54) == align16(12 × vertices)` | **11 / 11** |
| `len(0x58) == align16(6 × triangles)` | **11 / 11** |
| triangle count `==` sphere count (`len(0x5C)/16`) | **11 / 11** |
| object | verts | tris | `0x54` | `0x58` | spheres |
|---|---|---|---|---|---|
| `2cf7eb47` | 34 | 60 | 416 | 368 | 60 |
| `cbb99d34` | 8 | 12 | 96 | 80 | 12 |
| `d84a95fb` | 111 | 218 | 1 344 | 1 312 | 218 |
| `db066592` | 405 | 790 | 4 864 | 4 752 | 790 |
| `db61c506` | 73 | 134 | 880 | 816 | 134 |
| `dc44fe0c` | 89 | 174 | 1 072 | 1 056 | 174 |
| `dc4b0896` | 502 | 924 | 6 032 | 5 552 | 924 |
| `dd89a110` | 632 | 1 164 | 7 584 | 6 992 | 1 164 |
| `df4628c2` | 134 | 260 | 1 616 | 1 568 | 260 |
| `e084c13c` | 8 | 12 | 96 | 80 | 12 |
| `e16460cf` | 554 | 1 020 | 6 656 | 6 128 | 1 020 |
The two smallest objects are the tell on their own: **8 vertices and 12
triangles**, and their `0x54` block is exactly the eight `±250 000` corners of
the map's bounding box. That is a cube as a triangle mesh — a map whose only
collision is its outer wall.
### Sphere *i* bounds triangle *i*, and it is tight
The algebraic test, which cannot pass by accident:
| | |
|---|---|
| all three vertices of triangle *i* inside sphere *i* | **4 768 / 4 768 = 100.00 %** |
| …and the sphere is **tight** (`max‖v−c‖ / r` within 1 %) | **4 768 / 4 768 = 100.00 %** |
| sphere *i* encloses a *random* triangle (control) | 63 / 4 768 = **1.32 %** |
`max‖v−c‖ / r` has median **0.99990** across every triangle of every object, so
the radius is the enclosing radius times a fixed **1.0001** epsilon. That is the
same 1.0001 visible by hand on the cube, where the sphere of a box-face triangle
came out as `250 000·√2 × 1.0001`.
### And the mesh is closed
| | |
|---|---|
| edges shared by exactly two triangles | **7 152 / 7 152 = 100.00 %** |
| degenerate triangles | **0** |
| vertices never referenced by a triangle | **0** |
A watertight manifold with no orphans — which is what a collision hull must be,
and a result that a wrong stride or a wrong index width could not produce.
`cbb99d34` has Euler characteristic `V − E + F = 8 − 18 + 12 = 2` (one closed
surface, the box); `2cf7eb47` has 4, i.e. two closed components.
### The cell lists are a correct broad phase
Re-running the completeness test with the *actual triangles* instead of their
bounding spheres, using a separating-axis triangle/box test:
| | |
|---|---|
| cells whose `u16` list is exactly the overlapping triangle set | 3 973 / 4 488 = **88.52 %** |
| triangles overlapping a cell but **absent** from its list | **3** |
| triangles listed but not overlapping | 730 (3.9 % of 18 577 entries) |
Three misses in 18 577 entries: the lists are **complete**, which is the property
a broad phase must have — a collision query that walks one cell's list cannot
miss a triangle it should have hit. The 730 extras are conservative and harmless.
Their size identifies the builder's own test as sitting **between** an exact
triangle/box test and a cheap AABB one: replacing the SAT test with "triangle
AABB overlaps cell" gives **0** listed-but-not-overlapping (so every listed
triangle's AABB does reach its cell) but 7 913 missing, so the builder is
stricter than AABB and looser than exact — an exact test with a margin. This
also explains the **18 sphere misses** left open in the section above: they were
never sphere-vs-cell facts, they are that same margin.
### The full format
0x00 magic 'MCOL'
0x04 data size (POF0 table at data_size + 16)
0x10 bbox min f32[4] 0x20 bbox max f32[4] 0x30 extent f32[4]
0x40 cell size f32[3]
0x50 u16 vertex count 0x52 u16 triangle count
0x54 → vertex array f32[3] × nv, padded to 16
0x58 → triangle array u16[3] × nt, padded to 16
0x5C → bounding spheres {centre f32[3], radius f32} × nt (= 0x80)
0x74 → grid cell array 32-byte A records, pointer at +8
position → cell → A {cell index (x,y,z,1), count 1, →B, bounding sphere}
→ B {u32 count, →u16[n] at +4}
→ n triangle indices
Reproduce with `tools/re-capture/mcol_probe.py verify` (recorded in
[`../data/mcol-verify.txt`](../data/mcol-verify.txt)); `mcol_probe.py obj` writes
any object out as a Wavefront OBJ.
❔ Still open: `MCOL` objects are **not name-resolved**, so which map each one
belongs to — and the object-to-object pairing with `REGN` that the header
distributions only hint at — is still unknown. And the runtime consumer has not
been found, the same gap `REGN` has.

96
tools/re-capture/mcol_probe.py
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@@ -4,9 +4,11 @@
`MCOL` (`hidden/MiscBin.pak`, 11 objects) shares `REGN`'s container, so the
`POF0` reader is imported from `regn_decode.py` rather than duplicated.
./mcol_probe.py stride <MiscBin.pak> # the 0x5C block is stride 16, not 12
./mcol_probe.py cells <MiscBin.pak> # the u16s name spheres in their cell
./mcol_probe.py verify <MiscBin.pak> # both, with pass/fail
./mcol_probe.py stride <MiscBin.pak> # the 0x5C block is stride 16, not 12
./mcol_probe.py cells <MiscBin.pak> # the u16s name spheres in their cell
./mcol_probe.py mesh <MiscBin.pak> # vertices, triangles, bounding spheres
./mcol_probe.py obj <MiscBin.pak> <hash> <out.obj>
./mcol_probe.py verify <MiscBin.pak> # all checks, with pass/fail
The `cells` check is the powered one: a `u16` is reached *through* a specific
grid cell, so the sphere it names must reach that cell. A bound-check ("is it
@@ -24,9 +26,16 @@ sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
from regn_decode import pak_entries, pof0_pointer_slots, FIXUP_BASE
SPHERE = 16 # stride of the 0x5C record: centre f32[3] then radius f32
VERTEX = 12 # stride of the 0x54 record: f32[3]
TRI = 6 # stride of the 0x58 record: u16[3]
def align16(n):
return (n + 15) // 16 * 16
def u32(b, o): return struct.unpack_from(">I", b, o)[0]
def u16(b, o): return struct.unpack_from(">H", b, o)[0]
def f32(b, o): return struct.unpack_from(">f", b, o)[0]
def ptr(b, o): return u32(b, o) + FIXUP_BASE
@@ -42,9 +51,19 @@ class Mcol:
for o in (0x54, 0x58, 0x5C, 0x74))
self.sphere_bytes = self.p54 - self.p5c
self.n = self.sphere_bytes // SPHERE
self.nv = u16(blob, 0x50) # vertex count
self.nt = u16(blob, 0x52) # triangle count == sphere count
self.bbox_min = [f32(blob, 0x10 + 4 * i) for i in range(3)]
self.cell_size = [f32(blob, 0x40 + 4 * i) for i in range(3)]
def vertex(self, i):
o = self.p54 + VERTEX * i
return [f32(self.b, o + 4 * k) for k in range(3)]
def triangle(self, i):
o = self.p58 + TRI * i
return [u16(self.b, o + 2 * k) for k in range(3)]
def sphere(self, i):
o = self.p5c + SPHERE * i
return [f32(self.b, o + 4 * k) for k in range(3)], f32(self.b, o + 12)
@@ -120,6 +139,69 @@ def cmd_cells(pak, seed=12345):
return hit / tot > 0.99 and ctl / tot < 0.25
def cmd_mesh(pak):
"""The 0x50 counts give both blocks a stride, and sphere i bounds triangle i."""
import collections
print(f"{'object':>8} {'verts':>6} {'tris':>6} {'len 0x54':>9} {'len 0x58':>9} {'spheres':>8}")
n = sv = st = ss = 0
enc = tight = ctl = tri_total = 0
edges2 = edges = 0
random.seed(7)
for h, blob in objects(pak):
m = Mcol(blob)
l54, l58 = m.p58 - m.p54, m.p74 - m.p58
n += 1
sv += align16(VERTEX * m.nv) == l54
st += align16(TRI * m.nt) == l58
ss += m.nt == m.n
print(f"{h:08x} {m.nv:6d} {m.nt:6d} {l54:9d} {l58:9d} {m.n:8d}")
V = [m.vertex(i) for i in range(m.nv)]
T = [m.triangle(i) for i in range(m.nt)]
ec = collections.Counter()
for i, t in enumerate(T):
c, r = m.sphere(i)
far = max(math.dist(V[j], c) for j in t)
tri_total += 1
enc += far <= r * 1.0001
tight += abs(far / r - 1) < 0.01
tj = T[random.randrange(m.nt)]
ctl += max(math.dist(V[j], c) for j in tj) <= r * 1.0001
for k in range(3):
a, b_ = t[k], t[(k + 1) % 3]
ec[(min(a, b_), max(a, b_))] += 1
edges += len(ec)
edges2 += sum(1 for v in ec.values() if v == 2)
print(f"\nlen(0x54) == align16(12 * verts) : {sv}/{n}")
print(f"len(0x58) == align16(6 * tris) : {st}/{n}")
print(f"triangle count == sphere count : {ss}/{n}")
print(f"sphere i encloses triangle i : {enc}/{tri_total} = {100*enc/tri_total:.2f}%")
print(f" ...and is tight to within 1% : {tight}/{tri_total} = {100*tight/tri_total:.2f}%")
print(f"sphere i encloses a random triangle (ctl) : {ctl}/{tri_total} = {100*ctl/tri_total:.2f}%")
print(f"edges shared by exactly two triangles : {edges2}/{edges} = {100*edges2/edges:.2f}%")
return (sv == st == ss == n and enc == tri_total and edges2 == edges
and ctl / tri_total < 0.10)
def cmd_obj(pak, want, out):
"""Export one object as a Wavefront OBJ, so the decode can be looked at."""
want = int(want, 16)
for h, blob in objects(pak):
if h != want:
continue
m = Mcol(blob)
with open(out, "w") as fh:
fh.write(f"# MCOL {h:08x} -- {m.nv} vertices, {m.nt} triangles\n")
for i in range(m.nv):
fh.write("v %.4f %.4f %.4f\n" % tuple(m.vertex(i)))
for i in range(m.nt):
a, b_, c = m.triangle(i)
fh.write(f"f {a+1} {b_+1} {c+1}\n")
print(f"{out}: {m.nv} vertices, {m.nt} triangles")
return True
raise SystemExit(f"no MCOL object {want:08x}")
def main():
if len(sys.argv) < 3:
raise SystemExit(__doc__)
@@ -128,11 +210,17 @@ def main():
ok = cmd_stride(pak)
elif cmd == "cells":
ok = cmd_cells(pak)
elif cmd == "mesh":
ok = cmd_mesh(pak)
elif cmd == "obj":
ok = cmd_obj(pak, sys.argv[3], sys.argv[4])
elif cmd == "verify":
a = cmd_stride(pak)
print()
b = cmd_cells(pak)
ok = a and b
print()
c = cmd_mesh(pak)
ok = a and b and c
else:
raise SystemExit(__doc__)
print("\nPASS" if ok else "\nFAIL")