feat: /vcstatusと/cdraw

cogs/cdraw.py

@@ -0,0 +1,390 @@
+from discord.ext import commands
+from discord import app_commands
+from discord.ext import commands
+import discord
+
+import numpy as np
+from fractions import Fraction as Frac
+import matplotlib.pyplot as plt
+import matplotlib.patches as patches
+import numpy as np
+
+
+########## グラフ描画プログラム #############
+
+
+def solve(a, b, c) -> list:
+    """
+    二次方程式
+    ax^2 + b^x + c = 0
+    の解を返す
+    """
+    if a == b == c == 0:
+        return True # 恒真式なので、呼び出し元に例外処理をさせる
+    if a == b == 0:
+        return []
+    if a == 0:
+        return [-c/b]
+
+    D = b**2 - 4*a*c
+    ans = -b/(2*a)
+    if D < 0:
+        return []
+    elif D == 0:
+        return [ans]
+    else:
+        return [ans+np.sqrt(D)/(2*a), ans-np.sqrt(D)/(2*a)]
+
+
+class Curve():
+    def __init__(self, a, b, c, d, e, f):
+        """
+        二次曲線
+        a + bx + cy + dx^2 + ey^2 + fxy = 0
+        """
+        self.a = a
+        self.b = b
+        self.c = c
+        self.d = d
+        self.e = e
+        self.f = f
+        self.theta = 0
+
+        # 一次変換により xy の項が消えるような θ を設定する
+        if d == e and f != 0:
+            self.theta = np.pi / 4
+        if d != e and f != 0:
+            self.theta = np.arctan(f/(e-d)) / 2
+
+        self.phi = 0 # 一次変換してもとに戻るような角度
+
+    def __str__(self):
+        a, b, c, d, e, f = self.a, self.b, self.c, self.d, self.e, self.f
+        return f"{a} + {b}x + {c}y + {d}x^2 + {e}y^2 + {f}xy = 0"
+
+    def regularize(self) -> Curve:
+        """
+        設定した θ による一次変換
+        (X, Y) = (cosθ -sinθ, sinθ cosθ)(x, y)
+        をほどこした二次曲線
+        A + BX + CY + DX^2 + EY^2 = 0
+        を返す
+        """
+        a, b, c, d, e, f = self.a, self.b, self.c, self.d, self.e, self.f
+        COS, SIN = np.cos(self.theta), np.sin(self.theta)
+        curve = Curve(
+            a,
+            b*COS - c*SIN,
+            b*SIN + c*COS,
+            d*COS**2 + e*SIN**2 - f*SIN*COS,
+            d*SIN**2 + e*COS**2 + f*SIN*COS,
+            0
+        )
+        curve.phi = self.phi - self.theta
+        return curve
+
+
+class Area():
+    """
+    start_x <= x <= end_x かつ start_y <= y <= end_y
+    なる(x, y)長方形領域を表すクラス
+    """
+    def __init__(self, start_x:int, start_y:int, end_x:int, end_y:int):
+        if start_x > end_x:
+            start_x, end_x = end_x, start_x
+        if start_y > end_y:
+            start_y, end_y = end_y, start_y
+        self.start_x = start_x
+        self.start_y = start_y
+        self.end_x = end_x
+        self.end_y = end_y
+
+    def __contains__(self, target:Area|tuple[int, int]) -> bool:
+        """
+        領域や点(x, y)が含まれているか否か
+        """
+        if isinstance(target, tuple):
+            x, y = target
+            return self.start_x <= x <= self.end_x and self.start_y <= y <= self.end_y
+        elif isinstance(target, Area):
+            return all(
+                self.start_x <= target.start_x,
+                target.end_x <= self.end_x,
+                self.start_y <= target.start_y,
+                target.end_y <= self.end_y,
+                )
+
+    def is_painted(self, x:int, y:int, curve:Curve) -> bool:
+        """
+        (x, y)を塗るか否かを返す
+        """
+        cell = Cell(x, y)
+        return cell.is_painted(curve)
+
+    def painted_pos(self, curve:Curve) -> list[tuple[int, int]]:
+        """
+        塗る座標を返す
+        """
+        posses = []
+
+        for x in range(self.start_x, self.end_x):
+            for y in range(self.start_y, self.end_y):
+                if self.is_painted(x, y, curve):
+                    posses.append((x, y))
+
+        return posses
+
+
+class Cell(Area):
+    """
+    X <= x <= X+1 かつ Y <= y <= Y+1
+    なる(x, y)正方形領域（格子）を表すクラス
+    """
+    def __init__(self, X:int, Y:int):
+        super().__init__(X, Y, X+1, Y+1)
+
+    def intersections(self, curve:Curve) -> set[tuple]:
+        """
+        格子の辺と曲線の交点を返す
+        """
+        a, b, c, d, e, f = curve.a, curve.b, curve.c, curve.d, curve.e, curve.f
+        X, Y = self.start_x, self.start_y
+
+        intersection_points = set()
+
+        # 左側の辺
+        solutions = solve(e, f*X+c, d*X**2+b*X+a)
+        if solutions is True:
+            # Trueが返された場合、曲線が辺とぴったり重なってる直線の場合
+            # こうなると処理に困るので、曲線自体を微小距離下にずらして
+            # ぴったり重なってないようにする
+            curve.a += 0.0001
+            return self.intersections(curve)
+        else:
+            intersection_points |= {(X, y) for y in solutions if (X, y) in self}
+        # 右側の辺
+        solutions = solve(e, f*(X+1)+c, d*(X+1)**2+b*(X+1)+a)
+        if solutions is True:
+            curve.a += 0.0001
+            return self.intersections(curve)
+        else:
+            intersection_points |= {((X+1), y) for y in solutions if ((X+1), y) in self}
+        # 下側の辺
+        solutions = solve(d, f*Y+b, e*Y**2+c*Y+a)
+        if solutions is True:
+            curve.a += 0.0001
+            return self.intersections(curve)
+        else:
+            intersection_points |= {(x, Y) for x in solutions if (x, Y) in self}
+        # 上側の辺
+        solutions = solve(d, f*(Y+1)+b, e*(Y+1)**2+c*(Y+1)+a)
+        if solutions is True:
+            curve.a += 0.0001
+            return self.intersections(curve)
+        else:
+            intersection_points |= {(x, (Y+1)) for x in solutions if (x, (Y+1)) in self}
+
+        return intersection_points
+
+    def is_painted(self, curve:Curve) -> bool:
+        """
+        塗るか否かを返す
+        """
+        X, Y = self.start_x, self.start_y
+        points = self.intersections(curve)
+
+        # 格子を4分割し、それぞれに含まれているか否かの関数をつくる
+        is_left, is_right, is_bottom, is_top = lambda x: X <= x <= X+0.5, lambda x: X+0.5 <= x <= X+1, lambda y: Y <= y <= Y+0.5, lambda y: Y+0.5 <= y <= Y+1
+        is_right_top = lambda x, y: is_right(x) and is_top(y)
+        is_right_bottom = lambda x, y: is_right(x) and is_bottom(y)
+        is_left_top = lambda x, y: is_left(x) and is_top(y)
+        is_left_bottom = lambda x, y: is_left(x) and is_bottom(y)
+
+        funcs = [is_right_top, is_right_bottom, is_left_top, is_left_bottom]
+
+        # 分割した4部分のうち、いくつが交点を含んでいるか？(part_num)
+        part_num = len([object() for func in funcs if any(func(*point) for point in points)])
+
+        # 2部分以上なら塗る。そうでないなら塗らない。
+        return part_num >= 2
+
+
+def decide_area(curve:Curve, min_size=50, max_size=100) -> Area:
+    """
+    描画領域を出力
+    max_size : 領域の最大サイズ
+    """
+    curve = curve.regularize()
+
+    # curve:
+    # A + BX + CY + DX^2 + EY^2 = 0
+    A, B, C, D, E = curve.a, curve.b, curve.c, curve.d, curve.e
+
+    ### ひとまず曲線がすっぽり収まる領域を計算
+
+    if B == C == D == E == 0:
+        # A = 0
+        raise Exception("式 A = 0 は曲線ではありません！")
+
+    elif D == E == 0:
+        # A + BX + CY = 0 (直線)
+
+        if C == 0:
+            # Y軸に平行な直線の場合、90度回転させて
+            # X軸に平行な直線に帰着させる
+            curve.theta = np.pi / 2
+            return decide_area(curve)
+
+        # Y = (-B/C)X - A/C
+        m = Frac(-B/C) # 傾き(分数)
+        m1, m2 = m.numerator, m.denominator # 分子と分母。互いに素で m2>0
+
+        center = (0, -A/C)
+        width, height = 4*m2, 4*m1
+
+    elif D*E == 0:
+        # 放物線
+
+        if D == 0:
+            # X軸方向に開く放物線の場合、90度回転させて
+            # Y軸方向に開く放物線に帰着させる
+            curve.theta = np.pi / 2
+            return decide_area(curve)
+
+        # A + BX + CY + DX^2 = 0 (Y軸方向に開く放物線)
+        # Y = -D/C (X + B/2D)^2 + (B^2 - 4AD)/4D
+
+        axis_X = -B/(2*D) # 放物線の軸のX座標（焦点のX座標でもある）
+        focus_Y = (B*B-4*A*D-C)/(4*D) # 焦点のY座標
+
+        center = (axis_X, focus_Y) # 焦点を描画領域の中心とする
+        width, height = np.abs(2*np.sqrt(2)*C/D), np.abs(C/D)
+
+    else:
+        # A + BX + CY + DX^2 + EY^2 = 0 (楕円 or 双曲線)
+        bunshi = B*B*E + C*C*D - 4*A*D*E
+        P_ = bunshi / (4*D*D*E)
+        Q_ = bunshi / (4*D*E*E)
+
+        if P_ < Q_:
+            # 焦点がY軸上にある楕円か双曲線の場合、90度回転させて
+            # X軸上にある場合に帰着させる
+            curve.theta = np.pi / 2
+            return decide_area(curve)
+
+        center = (-B/(2*D), C/(2*E))
+        width = 4*np.sqrt(P_ - Q_)
+        height = 4*np.sqrt(Q_*Q_/P_)
+
+    ### 領域を回転させて、xy平面での領域中心と幅と高さを計算
+
+    def linear_transform(x, y, theta):
+        COS, SIN = np.cos(theta), np.sin(theta)
+        return (COS*x-SIN*y, SIN*x+COS*y)
+
+    def expand_transform(x, y, theta):
+        COS, SIN = np.abs(np.cos(theta)), np.abs(np.sin(theta))
+        return (COS*x+SIN*y, SIN*x+COS*y)
+
+    center = linear_transform(*center, curve.phi)
+    width, height = expand_transform(width, height, curve.phi)
+
+    # 領域を正方形にする（最大幅も考慮）
+    true_width = max((min_size, width, height)) # 正方形の辺の長さ
+    true_width = min((true_width, max_size))
+
+    # 格子点処理
+    true_width = int(true_width)
+    center_x, center_y = int(center[0]), int(center[1])
+
+    start = (center_x - true_width//2, center_y - true_width//2)
+    end = (start[0] + true_width, start[1] + true_width)
+
+    return Area(*start, *end)
+
+
+def draw(curve:Curve):
+
+    # 描画領域
+    area = decide_area(curve)
+
+    fig, ax = plt.subplots(figsize=(8, 8))
+
+    # 格子目盛り
+    xticks = np.arange(area.start_x, area.end_x + 1, 1)
+    yticks = np.arange(area.start_y, area.end_y + 1, 1)
+
+    ax.set_xticks(np.arange(area.start_x, area.end_x + 1, 1))
+    ax.set_yticks(np.arange(area.start_y, area.end_y + 1, 1))
+
+    ### 目盛りラベル
+    # 5の倍数以外は非表示
+
+    # x軸ラベル
+    xlabels = []
+    for x in xticks:
+        if x % 5 == 0:
+            xlabels.append(str(x))
+        else:
+            xlabels.append("")
+
+    # y軸ラベル
+    ylabels = []
+    for y in yticks:
+        if y % 5 == 0:
+            ylabels.append(str(y))
+        else:
+            ylabels.append("")
+
+    ax.set_xticklabels(xlabels)
+    ax.set_yticklabels(ylabels)
+
+    # 格子線
+    ax.grid(True, linewidth=0.5)
+
+    # 格子の着色
+    for x, y in area.painted_pos(curve):
+        rect = patches.Rectangle(
+            (x, y),   # 左下座標
+            1,
+            1,
+            facecolor='turquoise'
+        )
+        ax.add_patch(rect)
+
+    # 表示範囲を設定
+    ax.set_xlim(area.start_x, area.end_x)
+    ax.set_ylim(area.start_y, area.end_y)
+
+    # 正方形グリッド
+    ax.set_aspect('equal')
+
+    plt.savefig("graph.png", format="png", dpi=300)
+
+
+############################## 
+
+
+class CDraw(commands.Cog):
+    def __init__(self, bot: commands.Bot):
+        self.bot = bot
+
+    @app_commands.command(name="cdraw", description="二次曲線 a+bx+cy+dx²+ey²+fxy=0 を描きます")
+    @app_commands.describe(a="a", b="b", c="c", d="d", e="e", f="f")
+    @app_commands.checks.cooldown(1, 3, key=lambda i: (i.guild_id))
+    async def ckill(
+        self, interaction: discord.Interaction,
+        a:float, b:float, c:float, d:float, e:float, f:float
+    ):
+        curve = Curve(a, b, c, d, e, f)
+        try:
+            draw(curve)
+        except Exception as error:
+            await interaction.response.send_message(str(error))
+
+        with open("graph.png", mode="rb") as file:
+            await interaction.response.send_message(fp=file)
+
+
+async def setup(bot: commands.Bot):
+    await bot.add_cog(CDraw(bot))