Hourai Jewel Bounce

Specifications

• Versions: 1.00 - 1.00a - 1.00b - 1.00c - 1.00d
• Difficulty: Easy - Normal - Hard - Lunatic - Extra - Last Word
• Mode: Main game - Practice mode - Spell Practice
• Shottype: Border Team - Magic Team - Ghost Team - Scarlet Team - Reimu - Yukari - Marisa - Alice - Youmu - Yuyuko - Sakuya - Remilia

What happens

On Kaguya's 5th spell-card, there is a chance that a bullet from below bounces upward. This comes from the initial wave the familiars shoot.

How it happens

To get this, you usually have to be unlucky. However, since there is no RNG involved there are normalised set-ups one could use to get this bug.

Why it happens

In order to understand this phenomenon, we need to take a look at the bullet's transformation properties.

Bullet transformations

Bullet transformations or transformations are special properties that are given to a bullet. The bullet could for example be immune against bombs, or the bullet could change color, or a certain sound could play when the bullet is first shot.

In the context of this glitch, there are two relevant bullet transformations at play:

• Transformation 2048 - bounce on all walls except bottom
• Transformation 128 - sets angle towards player

The bullets that use this transformation are shot by the first wave of the familiar enemies.

Bullet transformations order

The bullet transformations are applied one after the other in a specific sequence. The sequence in which the bullet transformations are applied on this attack are as follows:

Note that transformation 16384 is not relevant for the bug in this case.

Out of Bounds

A bullet is considered to be Out of Bounds or OoB from below if the bullet's position meets the criteria y > 448 + (sprite_y / 2). The rice bullets have a sprite of 16 by 16, so that means the bullet is out of bounds if y > 456.

Game frame events

On every game frame, every bullet on-screen executes a certain sequence of code. The sequence (in short) goes as follows:

1. The game checks if the bullet has an active transformation.
2. The game executes the relevant code tied to the active transformation.
3. The game updates the bullet's angle and position accordingly.
4. The game checks if the bullet is OoB.

Pseudo-code

Below is a more extensive explanation of the order of events written in pseudo-code.

if (no transform active) {
    activate next transform in list;
    reset tr_timer to 0;
}
if (transform 128 active) {
    if (tr_timer >= delay_time) {
        change bullet angle to aim towards player;
        deactivate this transform;
    }
    else {
        tr_timer += 1;
    }
}
if (transform 1024 or 2048 active) {
    if (bullet out of bounds) {
        if (transform == 2048 && y > 456) {
            don't change bullet angle;
        }
        else {
            change bullet angle;
        }
        deactivate this transform;
    }
}

update bullet position according to speed and angle;

if (bullet out of bounds) {
    if (transform 128, 1024 or 2048 active) {
        oob_timer += 1;
    }
    else if (oob_timer > 0) {
        oob_timer -= 1;
    }
    else {
        delete this bullet;
    }
}
else {
    oob_timer = 0;
}

A few notes:

• Everything that happens in a frame that is not relevant to this has been left out.
• tr_timer is a timer that counts the amount of frames a transform has been active.
• delay_time in transform 128 refers to a value set in the etEx ECL instruction. In this case, the value is equal to 1.
• oob_timer is a timer that prevents the bullet from being deleted out of bounds if it is nonzero.

Explanation

1. The bullet is shot. Transformation 2048 is active.
2. After some time, the bullet reaches one frame before it is out of bounds.
3. The next frame the bullet's position updates and it is now OoB going downward. However, since a transformation is active a counter oob_timer is increased by 1. The bullet isn't deleted.
4. The next frame transformation 2048 is still active. The bullet meets the condition y > 456. This results in the bullet not changing its angle. The transformation is then deactivated, meaning there's no transformation on the bullet. The bullet's position is updated (it still goes downward). The bullet is OoB going downward but oob_timer is equal to 1, so oob_timer decreases by 1 and now has a value of 0.
5. The next frame transform 128 is activated, setting tr_timer to 0. Since tr_timer >= delay_time is false (0 >= 1 with the value 1 being the 4th parameter of the etEx instruction), tr_timer increases by 1. The bullet is still OoB still going downward. Transformation 128 is active, so oob_timer increases by 1.
6. The next frame transformation 128 is still active, This time, the condition tr_timer >= delay_time is met. The bullet's angle changes to be toward the player. The bullet no longer has an active transformation. The bullet's position updates to go upwards. The bullet is still OoB but oob_timer is equal to 1, so oob_timer decreases by 1 and now has a value of 0.
7. The next frame transformation 16384 is applied. The bullet's position updates. However, this time the bullet no longer is OoB. The bullet has successfully done the bounce.

Below is a simple diagram of the explanation. Since the speed of the bullet is constant, the length of the vectors are the same.

However, in this diagram the bullet is coming at a very skew angle from y = 456, and the bullet is perpendicular to y = 456 once it is aimed towards the player. While this is achievable in-game (by moving the player character to be above a bottom corner), this is not what is happening in the initial image.

This diagram is more realistic as to what is happening in the initial image. The tip of the green arrow is barely above y = 456. If at step 3 the bullet was slightly farther away from y = 456, it would have meant that at step 7 the bullet is still OoB meaning it would have despawned.

Conclusion

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