Wishful Coding

I’m trying to figure out how the serial communication between two first generation Pokemon games works.

Armed with a CPU manual and opcode summary, I’m grepping through a disassembled ROM.

Reading the section in the CPU manual about serial communication, I found that it uses two registers at addresses ff01 and ff02. Grepping the source reveals constants/hardware_constants.asm that defines rSB and rSC.

Grepping those leads me to home/serial.asm and engine/overworld/cable_club_npc.asm. I’m not sure which does what, but in the former I find a promising label called Serial_ExchangeBytes. Grepping for that leads me to engine/cable_club.asm.

The function is called 3 times in this file. Looking at the comments and at my opcode reference, it seems to be using ld to load 3 16 bit registers for the arguments. hl stores the data to send, de the data to receive, and bc the number of bytes to send.

Grepping for wSerialRandomNumberListBlock leads me to wram.asm where all 3 are defined. Looking in the manual, WRAM refers to the 8 4Kb RAM banks that can be mapped into certain address spaces. I’m assuming ds n means a data section of n bytes, but I’m not sure.

So the first command sends 17 bytes of random data, while wSerialRandomNumberListBlock is only 7, but followed by 10 bytes of wLinkBattleRandomNumberList. I could grep further, but it’s random data, so whatever. On to wSerialPlayerDataBlock

This block contains all the good stuff. We know we are looking for 424 bytes of data, but here we see them clearly labeled.

First there is a preamble, like with the random block. No idea what it’s for. Then there is space for the player name, followed by the number of Pokemon you cary and their ID. PARTY_LENGTH is just defined as 6.

Then there are 6 party_struct that contain more info about your Pokemon. I know because I found this page earlier.

I’m grepping for those bytes in the preamble. They seem to be used for a bunch of other things, completely unrelated to the player data.

I’m just randomly trying to read bit and pieces of the code and comparing with bytes coming out of the Game Boy. In the data I see a lot of FD, and in the code I found SERIAL_PREAMBLE_BYTE which so happens to be defined as FD. These seem to be for synchronisation only.

That’s it for now. There is plenty of stuff I don’t understand, but at least I know the structure of the data that is sent over the link cable.

I was reading an old book about astrology, which contained a section about how to calculate your horoscope. It used crude lookup tables for the planets, and it was only valid until 2000.

I had also wondered if two planets were still considered conjunct if they where above/below each other.

So I set out to compute my horoscope in 3D using real orbits instead of lookup tables. I read some things on Wikipedia, but nothing I could translate to running code.

Then I finally found a NASA page that contains all the orbital parameters and a PDF explaining the math.

It took me a long time to get it working for two reasons. The first was solving Kepler’s equation to obtain the eccentric anomaly.

They mix and match degrees and radians in confusing ways. While it might make sense to take the cosine of a value in degrees, it certainly does not make sense to math.cos.

I suggest any math code to convert degrees to radians at the edges, and deal with radians only. Degrees should only be used for input and display. They make sense to humans.

Once you have an approximation of Kepler’s formula solved for eccentric anomaly, it is good to verify that the original formula returns your mean anomaly.

def solve_kepler(eccentricity, mean_anomaly):
    # for the approximate formulae in the present context, tol = 10e-6 degrees is sufficient
    tolerance = 10e-6
    # E0 = M + e sin M
    eccentric_anomaly = mean_anomaly + (eccentricity * math.sin(mean_anomaly))
    # and itterate the following equations with n = 0,1,2,... unitl |delta E| <= tol
    while True:
        # delta M = M - (En - e sin En)
        delta_mean_anomaly = mean_anomaly - (eccentric_anomaly - (eccentricity * math.sin(eccentric_anomaly)))
        # delta E = delta M / (1 - e cos En)
        delta_eccentric_anomaly = delta_mean_anomaly / (1 - (eccentricity * math.cos(eccentric_anomaly)))
        # En+1 = En + delta E
        eccentric_anomaly += delta_eccentric_anomaly

        if abs(delta_eccentric_anomaly) <= tolerance:
            return eccentric_anomaly

The second problem was rotating the planet’s ellipse into the Sun’s coordinate system. Written out in Python it’s a screen full of trigonometric functions. Missing anything gives completely bogus results. It’s not hard, just tedious and error prone.

def ecliptic_coordinates(orbit_x, orbit_y, perihelion, longitude_ascending, inclination):
    term1 = math.cos(perihelion) * math.cos(longitude_ascending)
    term2 = math.sin(perihelion) * math.sin(longitude_ascending) * math.cos(inclination)
    term3 = math.sin(perihelion) * math.cos(longitude_ascending)
    term4 = math.cos(perihelion) * math.sin(longitude_ascending) * math.cos(inclination)
    x = (term1 - term2) * orbit_x + (-term3 - term4) * orbit_y

    term1 = math.cos(perihelion) * math.sin(longitude_ascending)
    term2 = math.sin(perihelion) * math.cos(longitude_ascending) * math.cos(inclination)
    term3 = math.sin(perihelion) * math.sin(longitude_ascending)
    term4 = math.cos(perihelion) * math.cos(longitude_ascending) * math.cos(inclination)
    y = (term1 + term2) * orbit_x + (-term3 + term4) * orbit_y

    term1 = math.sin(perihelion) * math.sin(inclination)
    term2 = math.cos(perihelion) * math.sin(inclination)
    z = term1 * orbit_x + term2 * orbit_y

    return x, y, z

And in the end I did not even use this code. Once I started using Processing, I also wanted to draw the orbits themselves. This should not be hard, given the semi-major axis and eccentricity.

I again hit two problems. The first is that Processing’s ellipse function takes a center point, height and width. But I solved this using Wikipedia and math I can understand.

def planet_ellipse(planet, jd):
    eccentricity = planet.eccentricity(jd)
    smajor = planet.semi_major_axis(jd)
    sminor = smajor * math.sqrt(1 - (eccentricity ** 2))
    center = smajor * eccentricity
    return smajor * 2, sminor * 2, center

The tougher problem is rotating the ellipse to match the planet. While I successfully translated the math to code, I had no idea what is going on. I still have no clue how this pile of trigonometry works.

Instead I substituted the function arguments to ecliptic_coordinates for mouseX and mouseY to experiment what is going on. After some failed experiments I found some rotation commands that would align the ellipse with the planet. Then I removed the trigonometric mess and simply drew the planet in the same plane as the ellipse.

def planet_rotation(planet, jd):
    perihelion = planet.longitude_perhelion(jd) - planet.longitude_ascending(jd)
    rotateZ(-planet.longitude_ascending(jd))
    rotateX(planet.inclination(jd))
    rotateZ(-perihelion)

That’s it. The rest is mostly just drawing code. You can run the code for yourself.

I really like how it turned out. If you pan around you can clearly see that Pluto might not be as conjunct as it looks in 2D. If you let things rotate, you can visually see Mercury speed up near the sun. It’s also intuitively clear how retrograde motion works.

The only thing missing is the moon. I could not find orbital parameters for it.

I’ve been putting off writing this post for far to long, because I’m to busy hacking on other things. So here are the video, slides, and code. Enjoy.

Slides

import usb.core
import binascii
import re

dev = usb.core.find(idProduct=0x001e, idVendor=0x0b0c)
dev.set_configuration()

def hex_print(s):
    print(binascii.hexlify(s).decode(), re.sub("[^a-zA-Z0-9]", ".", str(s, 'ascii', 'replace')))

def write(data):
    s = binascii.unhexlify(data)
    hex_print(s)
    dev.write(0x02, s)

def read(t=100):
    try:
        while True:
            s = dev.read(0x81, 8, t)
            hex_print(s)
            t = 100
    except usb.core.USBError:
        pass
    print('---')

def message(data, display=0x01):
    #write = print
    data = chr(display).encode() + chr(len(data)).encode() + data
    write(b"010305" + binascii.hexlify(chr(len(data)).encode()) + b"00000000")
    for i in range(int(len(data)/6)):
        s = data[i*6:i*6+6]
        b = binascii.hexlify(s)
        write(b"0006" + b)

    i += 1
    s = data[i*6:i*6+6]
    b = binascii.hexlify(s.ljust(6))
    write(b'0004' + b)

# always the same lenth
def confirm_login(data, lang='nl'):
    data = b'\x03' + data
    write(b"0103081500000000")
    for i in range(3):
        s = data[i*6:i*6+6]
        b = binascii.hexlify(s.ljust(6))
        write(b"0006" + b)

    write(b'000300' + binascii.hexlify(lang) + b'000000')

if __name__ == '__main__':
    write(b"0209000000000000") # shield
    read()
    write(b"0103020000000000") # version
    read()
    write(b"0103010200000000") # insert card
    write(b"00026e6c00000000")
    read(10000)
    write(b"0103030000000000") # card info
    read()
    write(b"0103040000000000") # ask pin
    read(60000)
    message(b'abbalalalala', 0x00) # sign data
    read()

    message(b"Never gonna give you up Never gonna let you down                    ")
    read(10000)

    write(b"0103060000000000") # cryptogram
    read()

    confirm_login(b'You where drunk', b'en')
    read()