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__pycache__/
*.egg-info/
/dist/
/build/
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# CHANGELOG
## \[v0.0.1] init
- WFC
- plot WFC hitbox (x-z plot and x/z-y plot) with matplotlib toolbar
- options:
- track Mario
- show Mario as red point
- airborne or grounded
- on Yoshi
- invert X/Z
- angle dial for x/z-y plot
- Runtime
- advance by QF
- show Hitbox

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Being under the terms of the GNU General Public License version 3 only,
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LICENSES/GPL-3.0
All contributions to this software are subject to this COPYING file.

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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
Also add information on how to contact you by electronic and paper mail.
If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:
<program> Copyright (C) <year> <name of author>
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".
You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<https://www.gnu.org/licenses/>.
The GNU General Public License does not permit incorporating your program
into proprietary programs. If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library. If this is what you want to do, use the GNU Lesser General
Public License instead of this License. But first, please read
<https://www.gnu.org/licenses/why-not-lgpl.html>.

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include src/supSMSTAS/codes/*.bin

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# supSMSTAS
A tool to **sup**port **S**uper **M**ario **S**unshine **T**ool **A**ssisted **S**peedrun/Superplay.
## Installation
```
pip install supSMSTAS==0.0.1
```
## Usage
```
python -m supSMSTAS
```
## Required Gecko code
You need to add and activate the following Gecko code in Dolphin:
```
C20ECDE0 00000004
3C60817F 80631000
7C631B79 38600258
41820008 38600096
60000000 00000000
C20ED284 00000005
4E800021 3D60817F
816B1010 55608380
2800817E 4082000C
7D6803A6 4E800021
60000000 00000000
```
Make sure to disable those codes that
alter QF sync (advance by QF) or render triangle/hitbox
if you are using any of them.
If the checkboxes in the Runtime tab don't work,
try to disable all Gecko codes in Dolphin (except the *required Gecko code*).
## Execute the source code directly
To install dependencies, the easiest way is to run the following command
in the root directory of the package:
```
pip install .
```
Due to some module/script problems,
in order to start the program,
instead of using `python path/to/supSMSTAS/__main__.py` (as script),
make sure to use `python -m path.to.supSMSTAS` (as module) outside the `src/supSMSTAS/` directory.
For example, if you are in `src/` directory, you can run the following command:
```
python -m supSMSTAS
```

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[build-system]
requires = ["setuptools>=42"]
build-backend = "setuptools.build_meta"

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[metadata]
name = supSMSTAS
version = 0.0.1
author = sup39
author_email = sms@sup39.dev
description = A tool to support Super Mario Sunshine Tool Assisted Speedrun/Superplay
long_description = file: README.md
long_description_content_type = text/markdown
license_files = COPYING LICENSES/*
url = https://github.com/sup39/supSMSTAS
project_urls =
Bug Tracker = https://github.com/sup39/supSMSTAS/issues
classifiers =
Programming Language :: Python :: 3
License :: OSI Approved :: GNU General Public License v3 (GPLv3)
Operating System :: OS Independent
[options]
package_dir =
= src
packages = find_namespace:
include_package_data = True
python_requires = >=3.8
install_requires =
sup-dolphin-memory-lib ~= 0.1.0
matplotlib ~= 3.5
PyQt5 ~= 5.15
[options.packages.find]
where = src
[options.entry_points]
console_scripts =
supSMSTAS = supSMSTAS.__main__:main

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# SPDX-License-Identifier: GPL-3.0-only
# Copyright (c) 2022 sup39
import os
import time
## numpy
import numpy as np
from numpy import array
## matplotlib
import matplotlib as mpl
mpl.use('Qt5Agg')
from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg, NavigationToolbar2QT
from matplotlib.figure import Figure
import matplotlib.patches as patches
## PyQt5
from PyQt5.QtCore import *
from PyQt5.QtWidgets import *
## logging
import logging
## local
from .WFC import *
# add TRACE
logging.TRACE = 5
logging.addLevelName(logging.TRACE, 'TRACE')
def trace(self, message, *args, **kws):
if self.isEnabledFor(logging.TRACE):
self._log(logging.TRACE, message, args, **kws)
logging.Logger.trace = trace
# logger
logger = logging.getLogger('supSMSTAS')
# widgets utils
def layoutAddItem(ll, w):
if w is None: ll.addStretch()
elif isinstance(w, QLayout): ll.addLayout(w)
else: ll.addWidget(w)
def HBox(*children, **kwargs):
ll = QHBoxLayout(**kwargs)
for w in children: layoutAddItem(ll, w)
return ll
def VBox(*children, **kwargs):
ll = QVBoxLayout(**kwargs)
for w in children: layoutAddItem(ll, w)
return ll
class MPLCanvas(FigureCanvasQTAgg):
def __init__(self, parent=None, width=5, height=5, dpi=100):
fig = self.fig = Figure(figsize=(width, height), dpi=dpi)
self.axs = [
fig.add_subplot(121),
fig.add_subplot(122),
]
super().__init__(fig)
# Dolphin for SMS
from dolphin.memorylib import Dolphin
class SMSDolphin(Dolphin):
symbols = { # TODO
b'GMSJ01\x00\x00': {
'gpMarioOriginal': 0x8040A378,
'gpMap': 0x8040A570,
}
}
def get_symb_addr(self, name): # override
verID = self.memory.buf[:8].tobytes()
return SMSDolphin.symbols[verID][name]
def __init__(self):
super().__init__()
self.hooked = False
def hook(self):
self.hooked = False
if Dolphin.hook(self) is None:
return 'SMS is not running'
# found pid -> check game
verID = self.memory.buf[:8].tobytes()
if verID[:3] != b'GMS':
return 'Current game is not SMS'
if verID not in SMSDolphin.symbols:
return 'Only NTSJ-1.0 is supported in this version'
self.hooked = True
def checkList2list(self, ptr):
ans = []
while ptr:
ptr, data = self.read_struct(ptr+4, '>II')
ans.append(Surface(
*self.read_struct(data, '>HHBB'),
array(self.read_struct(data+0x10, '>9f'), 'f').reshape(3, 3),
n=array(self.read_struct(data+0x34, '>3f'), 'f'),
c=self.read_float(data+0x40),
))
return ans
# widgets
class WFCWidget(QWidget):
def __init__(self, dolphin, parent=None):
super().__init__(parent=parent)
self.d = dolphin
self._init_state()
self._init_layout()
def activate(self, val):
# stop timer if deactivate
self.setFPS(self.fps) if val else self.timer.stop()
def _init_state(self):
self.trackMario = Qt.Checked
self.showMario = Qt.Checked
self.airborne = Qt.Checked
self.yoshi = 0
self.fps = 4
self.updating = False
self.invertX = 0
self.invertZ = 0
self.xzAngle = 0
def _init_layout(self):
# timer
timer = self.timer = QTimer()
timer.timeout.connect(self.updatePlot)
# mcv
self.mcv = mcv = MPLCanvas(self, width=11, height=5, dpi=100)
self.updatePlot()
# toolbar
toolbar = NavigationToolbar2QT(mcv, self)
# buttons
llbtn = QHBoxLayout()
btn = QPushButton()
btn.setText('Update plot')
btn.clicked.connect(self.updatePlot)
llbtn.addWidget(btn)
# update
lbFPS = QLabel()
lbFPS.setText('fps')
sbFPS = QSpinBox()
sbFPS.setRange(0, 60)
sbFPS.setValue(self.fps)
#cbFPS.setText('fps')
sbFPS.valueChanged.connect(lambda: self.setFPS(sbFPS.value()))
self.setFPS(self.fps)
## add widget
llbtn.addWidget(lbFPS)
llbtn.addWidget(sbFPS)
for text, attr in [
('Track Mario', 'trackMario'),
('Show Mario', 'showMario'),
('Airborne', 'airborne'),
('Yoshi', 'yoshi'),
('invert X', 'invertX'),
('invert Z', 'invertZ'),
]:
cb = QCheckBox()
cb.setText(text)
cb.setCheckState(getattr(self, attr))
cb.clicked.connect((lambda attr, cb: lambda: setattr(self, attr, cb.checkState()))(attr, cb))
llbtn.addWidget(cb)
llbtn.addStretch()
# angle
lbXZAngle = QLabel()
lbXZAngle.setText('Angle')
dlXZAngle = QDial()
dlXZAngle.setWrapping(True)
#dlXZAngle.setNotchesVisible(True) # TODO
dlXZAngle.valueChanged.connect(lambda: self.setXZAngle(dlXZAngle.value()))
## angle button
llXZAngleBtns = QVBoxLayout()
for text, val in [
('X+', 75),
('X-', 25),
('Z+', 50),
('Z-', 0),
]:
btn = QPushButton()
btn.setText(text)
btn.clicked.connect((lambda val: lambda: dlXZAngle.setValue(val))(val))
llXZAngleBtns.addWidget(btn)
# footer
llFooter = HBox(
# buttons
VBox(
llbtn,
None,
),
None,
## angle
lbXZAngle,
dlXZAngle,
llXZAngleBtns,
)
# layout
self.setLayout(VBox(
toolbar,
mcv,
llFooter,
))
def toggleTimer(self, toggle):
if toggle:
self.timer.start()
else:
self.timer.stop()
def setFPS(self, fps):
self.fps = fps
if fps == 0:
self.timer.stop()
else:
self.timer.setInterval(int(1000/fps))
self.timer.start()
def setXZAngle(self, val):
self.xzAngle = val
#self.updatePlot()
def updatePlot(self):
if self.updating or not self.d.hooked: return
self.updating = True
try: self._updatePlot()
except:
import traceback
traceback.print_exc()
self.updating = False
def _updatePlot(self):
d = self.d
pos = d.read_struct(('gpMarioOriginal', 0x10), '>3f')
if pos is None: return
pos = array(pos)
x, y, z = pos
# get collision data (static collision)
colInfo = d.read_struct(('gpMap', 0x10, 0), '>ffI4x4xI')
if colInfo is None: return
xLimit, zLimit, xBlockCount, ptrStCLR = colInfo
## TBGCheckListRoot[zBlockCount][xBlockCount]
colOff = int((z+zLimit)//1024*xBlockCount + (x+xLimit)//1024)*36
## root->ground(12*2).next(4)
# mario
yoshi = self.yoshi
airborne = self.airborne
rW = 80 if yoshi else 50
t0 = time.time()
stGnds, stRoofs, stWalls = [
#data1 = [ # TODO dynamic data
d.checkList2list(d.read_uint32(ptrStCLR+colOff+4+12*j))
for j in range(3)
]
hitboxs = [
# ceiling
([
#(c, array((0, -1, 0)))
(makeRoof(tri, 82 if airborne else 2), array([0, -1, 0]))
for tri in stRoofs
#for c in makeCol(tri, airborne=airborne, yoshi=yoshi)
# if tri.maxY >= yMin
##], 1.0, 78.0 if airborne else 158.0, '#f88e', '#800'),
## FIXME: draw arrow
], 1.0, 0, '#f88e', '#800'),
([
#(c, array((0, 1, 0)))
(makeGround(tri, 0 if airborne else 0), array([0, 1, 0])) # TODO hG=100
for tri in stGnds # TODO grounded hitbox
#for c in makeCol(tri, airborne=airborne, yoshi=yoshi)
# if tri.maxY >= yMin
## FIXME: draw arrow
], 1.0, 0, '#88fe', '#008'), # TODO
*(
([
#(c, tri.n)
(makeWall(tri, w, dy), tri.n)
for tri in stWalls
#for c in [makeCol(tri, airborne=airborne, yoshi=yoshi)[ii]]
# if tri.maxY >= yMin
# arrow size scale (0.5 if radius is 25)
], 1.0 if airborne or ii == 1 else 0.5, rW, ['#8fcc', '#8f8c'][ii], ['#084', '#080'][ii])
#], 1.0 if airborne or ii == 1 else 0.5, rW, '#8f8e', '#080')
for ii, (w, dy) in zip((1, 0), [(rW, 30), (rW, 150)] if airborne else [(rW, 60), (rW/2, 30)])
),
]
# xzAngle
theta = self.xzAngle/50*np.pi
pnXZ = (-np.sin(theta), 0, -np.cos(theta))
axesXZ = [2 if abs(pnXZ[0])>abs(pnXZ[2]) else 0, 1]
invertX = self.invertX==Qt.Checked
invertZ = self.invertZ==Qt.Checked
# ax
xzAngle = self.xzAngle
for ax, (pn, axes) in zip(self.mcv.axs, [
((0, 1, 0), [0, 2]),
(pnXZ, axesXZ),
]):
ax.patches.clear()
make_geo_plot(ax, hitboxs, pos, pn, axes)
if self.showMario:
ax.add_patch(patches.Circle(pos[axes], 25, fc='red'))
if self.trackMario:
offs = [(-1000, 1000), (-1000, 1000), (-1000, 1000)] # TODO
for f, i in zip((ax.set_xlim, ax.set_ylim), axes):
p = pos[i]
d0, d1 = offs[i]
if invertX & (i==0) | invertZ & (i==2): # invert
d0, d1 = d1, d0
f(p+d0, p+d1)
ax.grid(True)
# apply
self.mcv.fig.tight_layout()
self.mcv.draw()
logger.trace('%.2f'%((time.time()-t0)*1000))
class RuntimeWidget(QWidget):
def __init__(self, dolphin, parent=None):
super().__init__(parent=parent)
self.d = dolphin
self._init_state()
self._init_layout()
def _init_state(self):
pass
def _init_layout(self):
# QF
cbQF = QCheckBox()
cbQF.setText('Advance by QF')
cbQF.clicked.connect(lambda: self.toggleQFSync(cbQF.checkState()))
# hitbox
cbHitbox = QCheckBox()
cbHitbox.setText('Show hitbox')
cbHitbox.clicked.connect(lambda: self.toggleHitbox(cbHitbox.checkState()))
# layout
self.setLayout(VBox(
cbQF,
cbHitbox,
None,
))
def toggleQFSync(self, val):
self.d.write_uint8(0x817F1000, 1 if val else 0)
def toggleHitbox(self, val):
ptrAddr = 0x817F1010
funcAddr = 0x817E05B8 # TODO
baseAddr = 0x817E0000
if val: # TODO other scripts
baseDir = os.path.dirname(__file__)
with open(os.path.join(baseDir, 'codes/showHitbox.bin'), 'rb') as fr:
buf = fr.read()
self.d.memory.buf[baseAddr-0x80000000:baseAddr-0x80000000+len(buf)] = buf
self.d.write_uint32(ptrAddr, funcAddr)
else:
self.d.write_uint32(ptrAddr, 0)
class MainWindow(QMainWindow):
def __init__(self, dolphin=None, *args, **kwargs):
super().__init__(*args, **kwargs)
self.setWindowTitle("supSMSTAS")
self.dolphin = SMSDolphin() if dolphin is None else dolphin
self._init_layout()
self.hook()
def _init_layout(self):
# hook button bar: btHook, lbHook, (spacer)
btHook = QPushButton()
btHook.setText('Hook')
btHook.clicked.connect(self.hook)
self.lbHook = lbHook = QLabel()
lbHook.setText('')
llHook = HBox(
btHook,
lbHook,
None,
)
## tab
qtab = self.qtab = QTabWidget(self)
self.subwWFC = WFCWidget(dolphin=self.dolphin)
self.tidxWFC = qtab.addTab(self.subwWFC, 'WFC')
self.subwRuntime = RuntimeWidget(dolphin=self.dolphin)
self.tidxRuntime = qtab.addTab(self.subwRuntime, 'Runtime')
qtab.currentChanged.connect(lambda: self.onTabChanged(qtab.currentIndex()))
# dummy widget to put widgets in the center
w = QWidget()
w.setLayout(VBox(
llHook,
qtab,
None,
))
self.setCentralWidget(w)
def hook(self):
err = self.dolphin.hook()
self.lbHook.setText('Hooked' if err is None else err)
self.qtab.setEnabled(self.dolphin.hooked)
def onTabChanged(self, index):
self.subwWFC.activate(index==self.tidxWFC)

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# SPDX-License-Identifier: GPL-3.0-only
# Copyright (c) 2022 sup39
import numpy as np
from numpy import array
from .shape import Polyhedron
import matplotlib.patches as patches
class Surface:
def __init__(self, surtype, surpara, trntype, unk7, verts, vidxs=None, n=None, c=None):
self.surtype, self.surpara, self.trntype, self.unk7 = \
surtype, surpara, trntype, unk7
self.vidxs = vidxs
self.verts = verts
self.minY = verts[:,1].min()
self.maxY = verts[:,1].max()
self.n = normalize(np.cross(verts[1]-verts[0], verts[2]-verts[1])) if n is None else n
self.c = -np.dot(verts[0], self.n) if c is None else c
def __repr__(self):
return 'minY=%.0f maxY=%.0f n=(%5.2f, %5.2f, %5.2f)'%(
self.minY, self.maxY, *self.n,
)
makeTriPrism = lambda tri0, tri1: Polyhedron([
*tri0,
*tri1,
], [
(0, 1), (1, 2), (2, 0),
(0, 3), (1, 4), (2, 5),
(3, 4), (4, 5), (5, 3),
])
def makeGround(tri, hG=0):
vertsLow = tri.verts-(0,108,0)
ySlice = tri.minY-30
v = array(vertsLow)
vertsLow[:,1] = np.clip(vertsLow[:,1], a_min=ySlice, a_max=None)
verts = [
*vertsLow,
*(tri.verts+(0,hG,0)),
]
edges = [
# top face
(3, 4), (4, 5), (5, 3),
# vertical edge
(0, 3), (1, 4), (2, 5),
]
r = v[:, 1]-ySlice
b = r>0
bc = b.sum()
if bc in [0, 3]:
# bottom face
edges += [(0, 1), (1, 2), (2, 0)]
else:
k0 = np.where(b if bc==1 else ~b)[0][0]
k1 = (k0+1)%3
k2 = (k0+2)%3
v0, r0 = v[k0], r[k0]
v1, r1 = v[k1], r[k1]
v2, r2 = v[k2], r[k2]
verts += [
(r1*v0-r0*v1)/(-r0+r1),
(r2*v0-r0*v2)/(-r0+r2),
]
edges += [
(k0, 6), (6, k1),
(k0, 7), (7, k2),
(k1, k2), (6, 7),
]
poly = Polyhedron(verts, edges)
return poly
def makeRoof(tri, hR=82):
poly = makeTriPrism(tri.verts-(0,hR,0), tri.verts-(0,160,0))
return poly
def makeWall(tri, rW=50, dy=30):
verts = tri.verts - (0, dy, 0)
n = tri.n
off = (np.abs(rW/n[0]),0,0) if np.abs(n[0])>0.707 else (0,0,np.abs(rW/n[2]))
poly = makeTriPrism(verts-off, verts+off)
return poly
def make_geo_plot(ax, hitboxs, p0, pn, axes):
# paras
arrowWidthBase = 60
arrowWidthMul = 0.2
arrowLenMax = 80
arrowLenTher = 200
arrowLenMul1 = 0.7
arrowLenMul2 = 0.35
arrowHeadLenMul = 0.3
arrowLenMul2off = 0.025
arrowCountMax = 20
# plot
for polys, awmul, alen, facecolor, arcolor in hitboxs:
# draw wall hitboxs (draw in reverse order)
for poly, n in polys[::-1]:
# clip at y=yy and take (x, z) coordinate
verts = poly.slicePlane(p0, pn)[:,axes]
if len(verts) == 0: continue
# plot hitbox area
ax.add_patch(patches.Polygon(verts, fc=facecolor, ec='black', lw=1))
# plot arrow
n = n*(1, 0, 1) # no y arrow
n = n[axes]
nnorm = np.linalg.norm(n)
if nnorm == 0: continue # TODO
n = n/nnorm
l = array([n[1], -n[0]])
## basis matrix
B = np.vstack([n, l])
## center
C = verts.mean(axis=0)
vertsO = verts-C
## n-l coordinates
nn = np.dot(vertsO, n)
ll = np.dot(vertsO, l)
## determine arrow width and count
iminl = ll.argmin()
imaxl = ll.argmax()
minl = ll[iminl]
maxl = ll[imaxl]
dl = maxl-minl
arrowWidth = arrowWidthBase*awmul
nArrow = np.floor(dl/arrowWidth).astype('i')
if nArrow >= 1:
if nArrow>arrowCountMax: nArrow = arrowCountMax
else:
arrowWidth = dl
nArrow = 1
arrowWidth *= arrowWidthMul
## determine arrow position
vlen = len(verts)
nbss = []
ls = np.linspace(minl, maxl, nArrow+2)[1:-1]
for step in [1, -1]:
i0 = iminl
i1 = (i0+step)%vlen
nbs = []
for lb in ls:
while ll[i1] < lb: i0, i1 = i1, (i1+step)%vlen
r0 = lb-ll[i0]
r1 = ll[i1]-lb
nbs.append((nn[i0]+nn[i1])/2 if r0+r1==0 else (nn[i0]*r1+nn[i1]*r0)/(r0+r1))
nbss.append(nbs)
nbss = array(nbss)
ncts = nbss.mean(axis=0)
nrgs = np.abs(np.diff(nbss, axis=0)[0])
# add arrow
for p, nrg in zip(
C+np.matmul(np.column_stack([ncts, ls]), B),
nrgs,
):
if nrg > arrowLenTher:
nrg = min(arrowLenMax, nrg*arrowLenMul2)
dn = n * nrg
offs = [-arrowLenMul2off, 1+arrowLenMul2off]
else:
nrg = min(arrowLenMax, nrg*arrowLenMul1)
dn = n * nrg
offs = [0.5]
arrowHeadLen = nrg*arrowHeadLenMul
for off in offs:
ax.arrow(
*(p-dn*off), *dn,
width=arrowWidth, #min(arrowWidth, nrg*0.15),
head_length=arrowHeadLen,
length_includes_head=True,
color=arcolor,
)
ax.set_xlabel('xyz'[axes[0]])
ax.set_ylabel('xyz'[axes[1]])
return axes

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# SPDX-License-Identifier: GPL-3.0-only
# Copyright (c) 2022 sup39
def main():
import os
import sys
import logging
from .UI import MainWindow
from PyQt5.QtWidgets import QApplication
# set log level
logging.basicConfig()
def try_parse_int(x):
try: return int(x)
except: return None
logLevelRaw = os.environ.get('LOG_LEVEL', 'WARNING')
logLevel = try_parse_int(logLevelRaw)
if logLevel is None: logLevel = try_parse_int(getattr(logging, logLevelRaw, None))
## logger
logger = logging.getLogger('supSMSTAS')
logger.setLevel(logging.WARNING if logLevel is None else logLevel)
# execute
app = QApplication(sys.argv)
w = MainWindow()
w.show()
sys.exit(app.exec_())
if __name__ == '__main__':
main()

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# SPDX-License-Identifier: MIT
'''
MIT License
Copyright (c) 2022 sup39[サポミク]
Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation
files (the "Software"), to deal in the Software without
restriction, including without limitation the rights to use,
copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following
conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.
'''
import numpy as np
array = np.array
import matplotlib.pyplot as plt
from matplotlib.path import Path
from matplotlib import patches
def normalize(x):
l = np.linalg.norm(x)
return x if l==0 else x/l
# 多角形
class Polygon():
def __init__(self, verts):
'''
* self.verts:
頂点の配列
Array of vertices
'''
self.verts = np.array(verts)
def clipLine(self, p, n, c):
'''
半平面 (x-p)・n >= c との共通部分を取る
Take intersection with half plane (x-p)・n >= c
* p:
直線上の一点
Any point on the line
* n:
直線の法線ベクトル
Normal vector of the line
* c:
定数
Constant
'''
p, n, c = map(array, (p, n, c))
r = np.dot(self.verts-p, n)-c
verts = []
for i in range(len(r)):
v0, r0 = self.verts[i-1], r[i-1]
v1, r1 = self.verts[i], r[i]
if r1 >= 0:
if r0 < 0: # (- +)
verts.append((r1*v0-r0*v1)/(-r0+r1))
verts.append(v1)
elif r0 >= 0: # (+ -)
verts.append((-r1*v0+r0*v1)/(r0-r1))
self.verts = np.array(verts) if len(verts) else self.verts[:0]
@property # getter
def path(self):
if self.verts.shape[0] == 0: return None
verts = self.verts
assert verts.shape[-1] == 2, 'verts should be 2D'
return Path([*verts, (0, 0)], [
Path.MOVETO,
*(Path.LINETO for _ in range(1, verts.shape[0])),
Path.CLOSEPOLY,
])
def plot(self, margin=0.05, facecolor='#2ee5b8', lw=1):
'''
この多角形を描画し、figとaxを返す
Plot this polygon and return ``fig'' and ``ax''
* margin:
Set margin of the plot
* facecolor:
面の色
Face color
* lw:
線の太さ
Line width
'''
fig, ax = plt.subplots()
if self.verts.shape[0] == 0: return ax
# path
path = self.path
patch = patches.PathPatch(path, facecolor=facecolor, lw=lw)
ax.add_patch(patch)
verts = self.verts
xMax, yMax = verts.max(axis=0)
xMin, yMin = verts.min(axis=0)
xMg, yMg = verts.ptp(axis=0)*margin
ax.set_xlim(xMin-xMg, xMax+xMg)
ax.set_ylim(yMin-yMg, yMax+yMg)
return fig, ax
def __repr__(self):
return 'Polygon with %d vertices:\n%s'%(
len(self.verts),
array(self.verts, 'f'),
)
# 多面体
class Polyhedron:
def __init__(self, verts, edges):
'''
* self.verts:
頂点の配列
Array of vertices
* self.edges:
辺(2頂点の番号)の配列
Array of edges (indices of 2 vertices)
'''
self.verts = np.array(verts)
self.edges = np.array(edges)
def clipPlane(self, p, n, c=0):
'''
半空間 (x-p)・n >= c との共通部分を取る
Take intersection with half space (x-p)・n >= c
* p:
平面上の一点
Any point on the plane
* n:
直線の法線ベクトル
Normal vector of the plane
* c:
定数
Constant
'''
p = array(p)
n = array(n)
r = np.dot(self.verts-p, n)-c
rb = [s>=0 for s in r]
# map vertex indices old to new
io2n = {
iO: iN
for iN, iO in enumerate(iO for iO, sb in enumerate(rb) if sb)
}
# handle old vert
verts = [v for v, sb in zip(self.verts, rb) if sb]
edges = []
for i0, i1 in self.edges:
if rb[i0] and rb[i1]:
# remain
edges.append((io2n[i0], io2n[i1]))
elif rb[i0] or rb[i1]:
# new vert
v0, r0 = self.verts[i0], abs(r[i0])
v1, r1 = self.verts[i1], abs(r[i1])
vN = (r1*v0+r0*v1)/(r0+r1)
edges.append((io2n[i0 if rb[i0] else i1], len(verts)))
verts.append(vN)
# else drop edge
# add new face
nOld = len(io2n)
vNews = verts[nOld:]
if len(vNews):
assert len(vNews) >= 3
p0, p1 = vNews[:2]
# choose p1-p0 as e1
e1 = normalize(p1-p0)
# choose e2 that ⊥ n, e1
e2 = normalize(np.cross(n, e1))
# set (p0+p1)/2 as new origin, and use {e1, e2} as new basis
cNews = np.dot(vNews-(p0+p1)/2, array([e1, e2]).transpose())
# indices of new verts CCW
jNews = nOld+np.arctan2(cNews[:,0], cNews[:,1]).argsort()
# add to edge
for i in range(len(vNews)):
edges.append((jNews[i-1], jNews[i]))
# final
self.verts = array(verts)
self.edges = array(edges)
def slicePlane(self, p, n):
'''
平面 (x-p)･n=0 との共通部分(多角形)の頂点を返す
Return vertices of intersection(polygon) with plane (x-p)･n=0
* p:
平面上の一点
Any point on the plane
* n:
平面の法線ベクトル
Normal vector of the plane
'''
p = array(p)
n = array(n)
r = np.dot(self.verts-p, n)
# handle old verts
#for i0, i1 in self.edges:
# # two vertices on other side of the plane
# if np.sign(r[i0]) != np.sign(r[i1]):
# v0, r0 = self.verts[i0], abs(r[i0])
# v1, r1 = self.verts[i1], abs(r[i1])
# vN = (r1*v0+r0*v1)/(r0+r1)
# vNews.append(vN)
signr = np.sign(r[self.edges])
edgesNew = self.edges[signr[:,0]!=signr[:,1]]
vv = self.verts[edgesNew]
rr = np.abs(r[edgesNew])
vNews = ((vv[:,0]*rr[:,1,None])+(vv[:,1]*rr[:,0,None]))/rr.sum(axis=1)[:,None]
# new verts
if len(vNews):
assert len(vNews) >= 2
p0, p1 = vNews[:2]
e1 = normalize(p1-p0)
e2 = normalize(np.cross(n, e1))
cNews = np.dot(vNews-(p0+p1)/2, array([e1, e2]).transpose())
jNews = np.arctan2(cNews[:,0], cNews[:,1]).argsort()
return vNews[jNews]
else:
return vNews
def __repr__(self):
return 'Polyhedron with %d vertices and %d edges:\n%s'%(
len(self.verts), len(self.edges),
array(self.verts[self.edges], 'f')
)