- 📝 Posted:
- 🚚 Summary of:
- P0184, P0185
- ⌨ Commits:
`f9d983e...f918298`

,`f918298...a21ab3d`

- 💰 Funded by:
- -Tom-, Blue Bolt, [Anonymous]
- 🏷 Tags:
- rec98+ th04+ th05+ gameplay+ louise- shinki+ bullet+ danmaku-pattern+ uth05win- blitting+

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:

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}/_{256}th 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?