TH05 has passed the 50% RE mark, with both MAIN.EXE and the
game as a whole! With that, we've also reached what -Tom-
wanted out of the project, so he's suspending his discount offer for a
bit.
Curve bullets are now officially called cheetos! 76.7% of
fans prefer this term, and it fits into the 8.3 DOS filename scheme much
better than homing lasers (as they're called in
OMAKE.TXT) or Taito
lasers (which would indeed have made sense as well).
…oh, and I managed to decompile Shinki within 2 pushes after all. That
left enough budget to also add the Stage 1 midboss on top.
So, Shinki! As far as final boss code is concerned, she's surprisingly
economical, with 📝 her background animations
making up more than ⅓ of her entire code. Going straight from TH01's
📝 final📝 bosses
to TH05's final boss definitely showed how much ZUN had streamlined
danmaku pattern code by the end of PC-98 Touhou. Don't get me wrong, there
is still room for improvement: TH05 not only
📝 reuses the same 16 bytes of generic boss state we saw in TH04 last month,
but also uses them 4× as often, and even for midbosses. Most importantly
though, defining danmaku patterns using a single global instance of the
group template structure is just bad no matter how you look at it:
The script code ends up rather bloated, with a single MOV
instruction for setting one of the fields taking up 5 bytes. By comparison,
the entire structure for regular bullets is 14 bytes large, while the
template structure for Shinki's 32×32 ball bullets could have easily been
reduced to 8 bytes.
Since it's also one piece of global state, you can easily forget to set
one of the required fields for a group type. The resulting danmaku group
then reuses these values from the last time they were set… which might have
been as far back as another boss fight from a previous stage.
And of course, I wouldn't point this out if it
didn't actually happen in Shinki's pattern code. Twice.
Declaring a separate structure instance with the static data for every
pattern would be both safer and more space-efficient, and there's
more than enough space left for that in the game's data segment.
But all in all, the pattern functions are short, sweet, and easy to follow.
The "devil"
patternis significantly more complex than the others, but still
far from TH01's final bosses at their worst. I especially like the clear
architectural separation between "one-shot pattern" functions that return
true once they're done, and "looping pattern" functions that
run as long as they're being called from a boss's main function. Not many
all too interesting things in these pattern functions for the most part,
except for two pieces of evidence that Shinki was coded after Yumeko:
The gather animation function in the first two phases contains a bullet
group configuration that looks like it's part of an unused danmaku
pattern. It quickly turns out to just be copy-pasted from a similar function
in Yumeko's fight though, where it is turned into actual
bullets.
As one of the two places where ZUN forgot to set a template field, the
lasers at the end of the white wing preparation pattern reuse the 6-pixel
width of Yumeko's final laser pattern. This actually has an effect on
gameplay: Since these lasers are active for the first 8 frames after
Shinki's wings appear on screen, the player can get hit by them in the last
2 frames after they grew to their final width.
Of course, there are more than enough safespots between the lasers.
Speaking about that wing sprite: If you look at ST05.BB2 (or
any other file with a large sprite, for that matter), you notice a rather
weird file layout:
A large sprite split into multiple smaller ones with a width of
64 pixels each? What's this, hardware sprite limitations? On my
PC-98?!
And it's not a limitation of the sprite width field in the BFNT+ header
either. Instead, it's master.lib's BFNT functions which are limited to
sprite widths up to 64 pixels… or at least that's what
MASTER.MAN claims. Whatever the restriction was, it seems to be
completely nonexistent as of master.lib version 0.23, and none of the
master.lib functions used by the games have any issues with larger
sprites.
Since ZUN stuck to the supposed 64-pixel width limit though, it's now the
game that expects Shinki's winged form to consist of 4 physical
sprites, not just 1. Any conversion from another, more logical sprite sheet
layout back into BFNT+ must therefore replicate the original number of
sprites. Otherwise, the sequential IDs ("patnums") assigned to every newly
loaded sprite no longer match ZUN's hardcoded IDs, causing the game to
crash. This is exactly what used to happen with -Tom-'s
MysticTK automation scripts,
which combined these exact sprites into a single large one. This issue has
now been fixed – just in case there are some underground modders out there
who used these scripts and wonder why their game crashed as soon as the
Shinki fight started.
And then the code quality takes a nosedive with Shinki's main function.
Even in TH05, these boss and midboss update
functions are still very imperative:
The origin point of all bullet types used by a boss must be manually set
to the current boss/midboss position; there is no concept of a bullet type
tracking a certain entity.
The same is true for the target point of a player's homing shots…
… and updating the HP bar. At least the initial fill animation is
abstracted away rather decently.
Incrementing the phase frame variable also must be done manually. TH05
even "innovates" here by giving the boss update function exclusive ownership
of that variable, in contrast to TH04 where that ownership is given out to
the player shot collision detection (?!) and boss defeat helper
functions.
Speaking about collision detection: That is done by calling different
functions depending on whether the boss is supposed to be invincible or
not.
Timeout conditions? No standard way either, and all done with manual
if statements. In combination with the regular phase end
condition of lowering (mid)boss HP to a certain value, this leads to quite a
convoluted control flow.
The manual calls to the score bonus functions for cleared phases at least provide some sense of orientation.
One potentially nice aspect of all this imperative freedom is that
phases can end outside of HP boundaries… by manually incrementing the
phase variable and resetting the phase frame variable to 0.
The biggest WTF in there, however, goes to using one of the 16 state bytes
as a "relative phase" variable for differentiating between boss phases that
share the same branch within the switch(boss.phase)
statement. While it's commendable that ZUN tried to reduce code duplication
for once, he could have just branched depending on the actual
boss.phase variable? The same state byte is then reused in the
"devil" pattern to track the activity state of the big jerky lasers in the
second half of the pattern. If you somehow managed to end the phase after
the first few bullets of the pattern, but before these lasers are up,
Shinki's update function would think that you're still in the phase
before the "devil" pattern. The main function then sequence-breaks
right to the defeat phase, skipping the final pattern with the burning Makai
background. Luckily, the HP boundaries are far away enough to make this
impossible in practice.
The takeaway here: If you want to use the state bytes for your custom
boss script mods, alias them to your own 16-byte structure, and limit each
of the bytes to a clearly defined meaning across your entire boss script.
One final discovery that doesn't seem to be documented anywhere yet: Shinki
actually has a hidden bomb shield during her two purple-wing phases.
uth05win got this part slightly wrong though: It's not a complete
shield, and hitting Shinki will still deal 1 point of chip damage per
frame. For comparison, the first phase lasts for 3,000 HP, and the "devil"
pattern phase lasts for 5,800 HP.
And there we go, 3rd PC-98 Touhou boss
script* decompiled, 28 to go! 🎉 In case you were expecting a fix for
the Shinki death glitch: That one
is more appropriately fixed as part of the Mai & Yuki script. It also
requires new code, should ideally look a bit prettier than just removing
cheetos between one frame and the next, and I'd still like it to fit within
the original position-dependent code layout… Let's do that some other
time.
Not much to say about the Stage 1 midboss, or midbosses in general even,
except that their update functions have to imperatively handle even more
subsystems, due to the relative lack of helper functions.
The remaining ¾ of the third push went to a bunch of smaller RE and
finalization work that would have hardly got any attention otherwise, to
help secure that 50% RE mark. The nicest piece of code in there shows off
what looks like the optimal way of setting up the
📝 GRCG tile register for monochrome blitting
in a variable color:
mov ah, palette_index ; Any other non-AL 8-bit register works too.
; (x86 only supports AL as the source operand for OUTs.)
rept 4 ; For all 4 bitplanes…
shr ah, 1 ; Shift the next color bit into the x86 carry flag
sbb al, al ; Extend the carry flag to a full byte
; (CF=0 → 0x00, CF=1 → 0xFF)
out 7Eh, al ; Write AL to the GRCG tile register
endm
Thanks to Turbo C++'s inlining capabilities, the loop body even decompiles
into a surprisingly nice one-liner. What a beautiful micro-optimization, at
a place where micro-optimization doesn't hurt and is almost expected.
Unfortunately, the micro-optimizations went all downhill from there,
becoming increasingly dumb and undecompilable. Was it really necessary to
save 4 x86 instructions in the highly unlikely case of a new spark sprite
being spawned outside the playfield? That one 2D polar→Cartesian
conversion function then pointed out Turbo C++ 4.0J's woefully limited
support for 32-bit micro-optimizations. The code generation for 32-bit
📝 pseudo-registers is so bad that they almost
aren't worth using for arithmetic operations, and the inline assembler just
flat out doesn't support anything 32-bit. No use in decompiling a function
that you'd have to entirely spell out in machine code, especially if the
same function already exists in multiple other, more idiomatic C++
variations.
Rounding out the third push, we got the TH04/TH05 DEMO?.REC
replay file reading code, which should finally prove that nothing about the
game's original replay system could serve as even just the foundation for
community-usable replays. Just in case anyone was still thinking that.
Next up: Back to TH01, with the Elis fight! Got a bit of room left in the
cap again, and there are a lot of things that would make a lot of
sense now:
TH04 would really enjoy a large number of dedicated pushes to catch up
with TH05. This would greatly support the finalization of both games.
Continuing with TH05's bosses and midbosses has shown to be good value
for your money. Shinki would have taken even less than 2 pushes if she
hadn't been the first boss I looked at.
Oh, and I also added Seihou as a selectable goal, for the two people out
there who genuinely like it. If I ever want to quit my day job, I need to
branch out into safer territory that isn't threatened by takedowns, after
all.
Two years after
📝 the first look at TH04's and TH05's bullets,
we finally get to finish their logic code by looking at the special motion
types. Bullets as a whole still aren't completely finished as the
rendering code is still waiting to be RE'd, but now we've got everything
about them that's required for decompiling the midboss and boss fights of
these games.
Just like the motion types of TH01's pellets, the ones we've got here really
are special enough to warrant an enum, despite all the
overlap in the "slow down and turn" and "bounce at certain edges of the
playfield" types. Sure, including them in the bitfield I proposed two years
ago would have allowed greater variety, but it wouldn't have saved any
memory. On the contrary: These types use a single global state variable for
the maximum turn count and delta speed, which a proper customizable
architecture would have to integrate into the bullet structure. Maybe it is
possible to stuff everything into the same amount of bytes, but not without
first completely rearchitecting the bullet structure and removing every
single piece of redundancy in there. Simply extending the system by adding a
new enum value for a new motion type would be way more
straightforward for modders.
Speaking about memory, TH05 already extends the bullet structure by 6 bytes
for the "exact linear movement" type exclusive to that game. This type is
particularly interesting for all the prospective PC-98 game developers out
there, as it nicely points out the precision limits of Q12.4 subpixels.
Regular bullet movement works by adding a Q12.4 velocity to a Q12.4 position
every frame, with the velocity typically being calculated only once on spawn
time from an 8-bit angle and a Q12.4 speed. Quantization errors from this
initial calculation can quickly compound over all the frames a bullet spends
moving across the playfield. If a bullet is only supposed to move on a
straight line though, there is a more precise way of calculating its
position: By storing the origin point, movement angle, and total distance
traveled, you can perform a full polar→Cartesian transformation every frame.
Out of the 10 danmaku patterns in TH05 that use this motion type, the
difference to regular bullet movement can be best seen in Louise's final
pattern:
Louise's final pattern in its original form, demonstrating
exact linear bullet movement. Note how each bullet spawns slightly
behind the delay cloud: ZUN simply forgot to shift the fixed origin
point along with it.The same pattern with standard bullet movement, corrupting
its intended appearance. No delay cloud-related oversights here though,
at least.
Not far away from the regular bullet code, we've also got the movement
function for the infamous curve / "cheeto" bullets. I would have almost
called them "cheetos" in the code as well, which surely fits more nicely
into 8.3 filenames than "curve bullets" does, but eh, trademarks…
As for hitboxes, we got a 16×16 one on the head node, and a 12×12 one on the
16 trail nodes. The latter simply store the position of the head node during
the last 16 frames, Snake style. But what you're all here for is probably
the turning and homing algorithm, right? Boiled down to its essence, it
works like this:
// [head] points to the controlled "head" part of a curve bullet entity.
// Angles are stored with 8 bits representing a full circle, providing free
// normalization on arithmetic overflow.
// The directions are ordered as you would expect:
// • 0x00: right (sin(0x00) = 0, cos(0x00) = +1)
// • 0x40: down (sin(0x40) = +1, cos(0x40) = 0)
// • 0x80: left (sin(0x80) = 0, cos(0x80) = -1)
// • 0xC0: up (sin(0xC0) = -1, cos(0xC0) = 0)
uint8_t angle_delta = (head->angle - player_angle_from(
head->pos.cur.x, head->pos.cur.y
));
// Stop turning if the player is 1/128ths of a circle away from this bullet
const uint8_t SNAP = 0x02;
// Else, turn either clockwise or counterclockwise by 1/256th of a circle,
// depending on what would reach the player the fastest.
if((angle_delta > SNAP) && (angle_delta < static_cast<uint8_t>(-SNAP))) {
angle_delta = (angle_delta >= 0x80) ? -0x01 : +0x01;
}
head_p->angle -= angle_delta;
5 lines of code, and not all too difficult to follow once you are familiar
with 8-bit angles… unlike what ZUN actually wrote. Which is 26 lines,
and includes an unused "friction" variable that is never set to any value
that makes a difference in the formula. uth05win
correctly saw through that all and simplified this code to something
equivalent to my explanation. Redoing that work certainly wasted a bit of my
time, and means that I now definitely need to spend another push on RE'ing
all the shared boss functions before I can start with Shinki.
So while a curve bullet's speed does get faster over time, its
angular velocity is always limited to 1/256th of a
circle per frame. This reveals the optimal strategy for dodging them:
Maximize this delta angle by staying as close to 180° away from their
current direction as possible, and let their acceleration do the rest.
At least that's the theory for dodging a single one. As a danmaku
designer, you can now of course place other bullets at these technically
optimal places to prevent a curve bullet pattern from being cheesed like
that. I certainly didn't record the video above in a single take either…
After another bunch of boring entity spawn and update functions, the
playfield shaking feature turned out as the most notable (and tricky) one to
round out these two pushes. It's actually implemented quite well in how it
simply "un-shakes" the screen by just marking every stage tile to be
redrawn. In the context of all the other tile invalidation that can take
place during a frame, that's definitely more performant than
📝 doing another EGC-accelerated memmove().
Due to these two games being double-buffered via page flipping, this
invalidation only really needs to happen for the frame after the next
one though. The immediately next frame will show the regular, un-shaken
playfield on the other VRAM page first, except during the multi-frame
shake animation when defeating a midboss, where it will also appear shifted
in a different direction… 😵 Yeah, no wonder why ZUN just always invalidates
all stage tiles for the next two frames after every shaking animation, which
is guaranteed to handle both sporadic single-frame shakes and continuous
ones. So close to good-code here.
Finally, this delivery was delayed a bit because -Tom-
requested his round-up amount to be limited to the cap in the future. Since
that makes it kind of hard to explain on a static page how much money he
will exactly provide, I now properly modeled these discounts in the website
code. The exact round-up amount is now included in both the pre-purchase
breakdown, as well as the cap bar on the main page.
With that in place, the system is now also set up for round-up offers from
other patrons. If you'd also like to support certain goals in this way, with
any amount of money, now's the time for getting in touch with me about that.
Known contributors only, though! 😛
Next up: The final bunch of shared boring boss functions. Which certainly
will give me a break from all the maintenance and research work, and speed
up delivery progress again… right?
Didn't quite get to cover background rendering for TH05's Stage 1-5
bosses in this one, as I had to reverse-engineer two more fundamental parts
involved in boss background rendering before.
First, we got the those blocky transitions from stage tiles to bomb and
boss backgrounds, loaded from BB*.BB and ST*.BB,
respectively. These files store 16 frames of animation, with every bit
corresponding to a 16×16 tile on the playfield. With 384×368 pixels to be
covered, that would require 69 bytes per frame. But since that's a very odd
number to work with in micro-optimized ASM, ZUN instead stores 512×512
pixels worth of bits, ending up with a frame size of 128 bytes, and a
per-frame waste of 59 bytes. At least it was
possible to decompile the core blitting function as __fastcall
for once.
But wait, TH05 comes with, and loads, a bomb .BB file for every character,
not just for the Reimu and Yuuka bomb transitions you see in-game… 🤔
Restoring those unused stage tile → bomb image transition
animations for Mima and Marisa isn't that trivial without having decompiled
their actual bomb animation functions before, so stay tuned!
Interestingly though, the code leaves out what would look like the most
obvious optimization: All stage tiles are unconditionally redrawn
each frame before they're erased again with the 16×16 blocks, no matter if
they weren't covered by such a block in the previous frame, or are
going to be covered by such a block in this frame. The same is true
for the static bomb and boss background images, where ZUN simply didn't
write a .CDG blitting function that takes the dirty tile array into
account. If VRAM writes on PC-98 really were as slow as the games'
README.TXT files claim them to be, shouldn't all the
optimization work have gone towards minimizing them?
Oh well, it's not like I have any idea what I'm talking about here. I'd
better stop talking about anything relating to VRAM performance on PC-98…
Second, it finally was time to solve the long-standing confusion about all
those callbacks that are supposed to render the playfield background. Given
the aforementioned static bomb background images, ZUN chose to make this
needlessly complicated. And so, we have two callback function
pointers: One during bomb animations, one outside of bomb
animations, and each boss update function is responsible for keeping the
former in sync with the latter.
Other than that, this was one of the smoothest pushes we've had in a while;
the hardest parts of boss background rendering all were part of
📝 the last push. Once you figured out that
ZUN does indeed dynamically change hardware color #0 based on the current
boss phase, the remaining one function for Shinki, and all of EX-Alice's
background rendering becomes very straightforward and understandable.
Meanwhile, -Tom- told me about his plans to publicly
release 📝 his TH05 scripting toolkit once
TH05's MAIN.EXE would hit around 50% RE! That pretty much
defines what the next bunch of generic TH05 pushes will go towards:
bullets, shared boss code, and one
full, concrete boss script to demonstrate how it's all combined. Next up,
therefore: TH04's bullet firing code…? Yes, TH04's. I want to see what I'm
doing before I tackle the undecompilable mess that is TH05's bullet firing
code, and you all probably want readable code for that feature as
well. Turns out it's also the perfect place for Blue Bolt's
pending contributions.
Y'know, I kinda prefer the pending crowdfunded workload to stay more near
the middle of the cap, rather than being sold out all the time. So to reach
this point more quickly, let's do the most relaxing thing that can be
easily done in TH05 right now: The boss backgrounds, starting with Shinki's,
📝 now that we've got the time to look at it in detail.
… Oh come on, more things that are borderline undecompilable, and
require new workarounds to be developed? Yup, Borland C++ always optimizes
any comparison of a register with a literal 0 to OR reg, reg,
no matter how many calculations and inlined function calls you replace the
0 with. Shinki's background particle rendering function contains a
CMP AX, 0 instruction though… so yeah,
📝 yet another piece of custom ASM that's worse
than what Turbo C++ 4.0J would have generated if ZUN had just written
readable C. This was probably motivated by ZUN insisting that his modified
master.lib function for blitting particles takes its X and Y parameters as
registers. If he had just used the __fastcall convention, he
also would have got the sprite ID passed as a register. 🤷
So, we really don't want to be forced into inline assembly just
because of the third comparison in the otherwise perfectly decompilable
four-comparison if() expression that prevents invisible
particles from being drawn. The workaround: Comparing to a pointer
instead, which only the linker gets to resolve to the actual value of 0.
This way, the compiler has to make room for
any 16-bit literal, and can't optimize anything.
And then we go straight from micro-optimization to
waste, with all the duplication in the code that
animates all those particles together with the zooming and spinning lines.
This push decompiled 1.31% of all code in TH05, and thanks to alignment,
we're still missing Shinki's high-level background rendering function that
calls all the subfunctions I decompiled here.
With all the manipulated state involved here, it's not at all trivial to
see how this code produces what you see in-game. Like:
If all lines have the same Y velocity, how do the other three lines in
background type B get pushed down into this vertical formation while the
top one stays still? (Answer: This velocity is only applied to the top
line, the other lines are only pushed based on some delta.)
How can this delta be calculated based on the distance of the top line
with its supposed target point around Shinki's wings? (Answer: The velocity
is never set to 0, so the top line overshoots this target point in every
frame. After calculating the delta, the top line itself is pushed down as
well, canceling out the movement. )
Why don't they get pushed down infinitely, but stop eventually?
(Answer: We only see four lines out of 20, at indices #0, #6, #12, and
#18. In each frame, lines [0..17] are copied to lines [1..18], before
anything gets moved. The invisible lines are pushed down based on the delta
as well, which defines a distance between the visible lines of (velocity *
array gap). And since the velocity is capped at -14 pixels per frame, this
also means a maximum distance of 84 pixels between the midpoints of each
line.)
And why are the lines moving back up when switching to background type
C, before moving down? (Answer: Because type C increases the
velocity rather than decreasing it. Therefore, it relies on the previous
velocity state from type B to show a gapless animation.)
So yeah, it's a nice-looking effect, just very hard to understand. 😵
With the amount of effort I'm putting into this project, I typically
gravitate towards more descriptive function names. Here, however,
uth05win's simple and seemingly tiny-brained "background type A/B/C/D" was
quite a smart choice. It clearly defines the sequence in which these
animations are intended to be shown, and as we've seen with point 4
from the list above, that does indeed matter.
Next up: At least EX-Alice's background animations, and probably also the
high-level parts of the background rendering for all the other TH05 bosses.
… and just as I explained 📝 in the last post
how decompilation is typically more sensible and efficient than ASM-level
reverse-engineering, we have this push demonstrating a counter-example.
The reason why the background particles and lines in the Shinki and
EX-Alice battles contributed so much to position dependence was simply
because they're accessed in a relatively large amount of functions, one
for each different animation. Too many to spend the remaining precious
crowdfunded time on reverse-engineering or even decompiling them all,
especially now that everyone anticipates 100% PI for TH05's
MAIN.EXE.
Therefore, I only decompiled the two functions of the line structure that
also demonstrate best how it works, which in turn also helped with RE.
Sadly, this revealed that we actually can't📝 overload operator =() to get
that nice assignment syntax for 12.4 fixed-point values, because one of
those new functions relies on Turbo C++'s built-in optimizations for
trivially copyable structures. Still, impressive that this abstraction
caused no other issues for almost one year.
As for the structures themselves… nope, nothing to criticize this time!
Sure, one good particle system would have been awesome, instead of having
separate structures for the Stage 2 "starfield" particles and the one used
in Shinki's battle, with hardcoded animations for both. But given the
game's short development time, that was quite an acceptable compromise,
I'd say.
And as for the lines, there just has to be a reason why the game
reserves 20 lines per set, but only renders lines #0, #6, #12, and #18.
We'll probably see once we get to look at those animation functions more
closely.
This was quite a 📝 TH03-style RE push,
which yielded way more PI% than RE%. But now that that's done, I can
finally not get distracted by all that stuff when looking at the
list of remaining memory references. Next up: The last few missing
structures in TH05's MAIN.EXE!
To finish this TH05 stretch, we've got a feature that's exclusive to TH05
for once! As the final memory management innovation in PC-98 Touhou, TH05
provides a single static (64 * 26)-byte array for storing up to 64
entities of a custom type, specific to a stage or boss portion.
(Edit (2023-05-29): This system actually debuted in
📝 TH04, where it was used for much simpler
entities.)
TH05 uses this array for
the Stage 2 star particles,
Alice's puppets,
the tip of curve ("jello") bullets,
Mai's snowballs and Yuki's fireballs,
Yumeko's swords,
and Shinki's 32×32 bullets,
which makes sense, given that only one of those will be active at any
given time.
On the surface, they all appear to share the same 26-byte structure, with
consistently sized fields, merely using its 5 generic fields for different
purposes. Looking closer though, there actually are differences in
the signedness of certain fields across the six types. uth05win chose to
declare them as entirely separate structures, and given all the semantic
differences (pixels vs. subpixels, regular vs. tiny master.lib sprites,
…), it made sense to do the same in ReC98. It quickly turned out to be the
only solution to meet my own standards of code readability.
Which blew this one up to two pushes once again… But now, modders can
trivially resize any of those structures without affecting the other types
within the original (64 * 26)-byte boundary, even without full position
independence. While you'd still have to reduce the type-specific
number of distinct entities if you made any structure larger, you
could also have more entities with fewer structure members.
As for the types themselves, they're full of redundancy once again – as
you might have already expected from seeing #4, #5, and #6 listed as
unrelated to each other. Those could have indeed been merged into a single
32×32 bullet type, supporting all the unique properties of #4
(destructible, with optional revenge bullets), #5 (optional number of
twirl animation frames before they begin to move) and #6 (delay clouds).
The *_add(), *_update(), and *_render()
functions of #5 and #6 could even already be completely
reverse-engineered from just applying the structure onto the ASM, with the
ones of #3 and #4 only needing one more RE push.
But perhaps the most interesting discovery here is in the curve bullets:
TH05 only renders every second one of the 17 nodes in a curve
bullet, yet hit-tests every single one of them. In practice, this is an
acceptable optimization though – you only start to notice jagged edges and
gaps between the fragments once their speed exceeds roughly 11 pixels per
second:
And that brings us to the last 20% of TH05 position independence! But
first, we'll have more cheap and fast TH01 progress.