Import video pipeline as it was

1 files changed, 241 insertions, 0 deletions

diff --git a/scenes/v15_mobius.py b/scenes/v15_mobius.py
new file mode 100644
index 0000000..a921c6b
--- /dev/null
+++ b/scenes/v15_mobius.py
@@ -0,0 +1,241 @@
+# -*- coding: utf-8 -*-
+"""Cinta de Mobius renderizada como superficie reglada: se generan quads en 3D,
+se proyectan con una camara fija y se dibujan de atras hacia adelante."""
+import sys, os, math
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+from manim import *
+from tiktok import *
+
+TILT, YAW = 1.02, 0.0
+CARA_A, CARA_B = "#FFD166", "#2F6FD0"
+
+
+def geom(tau, beta, L=9.4, w=0.62, nu=170, smax=1.0):
+    """Punto central y direccion transversal de la cinta para s en [0, smax]."""
+    s = np.linspace(0.0, smax, max(int(nu * smax), 2) + 1)
+    th = max(beta * TAU, 1e-3)
+    Rr = L / th
+    ang = th * (s - 0.5)
+    p = np.stack([Rr * np.sin(ang), Rr * np.cos(ang) - Rr, np.zeros_like(ang)], axis=1)
+    N = np.stack([np.sin(ang), np.cos(ang), np.zeros_like(ang)], axis=1)
+    B = np.zeros_like(N)
+    B[:, 2] = 1.0
+    phi = tau * PI * s
+    d = np.cos(phi)[:, None] * N + np.sin(phi)[:, None] * B
+    return p, d, s
+
+
+def proj(P):
+    x, y, z = P[..., 0], P[..., 1], P[..., 2]
+    c, sn = math.cos(YAW), math.sin(YAW)
+    x2, y2 = x * c - y * sn, x * sn + y * c
+    ct, st = math.cos(TILT), math.sin(TILT)
+    return x2, y2 * ct - z * st, y2 * st + z * ct       # X, Y, profundidad
+
+
+def quads(tau, beta, L=9.4, w=0.62, nu=170, scale=1.0, center=ORIGIN):
+    """Lista de (poligono_screen, profundidad, color) sin ordenar."""
+    p, d, _ = geom(tau, beta, L, w, nu)
+    A = p - w * d
+    Bv = p + w * d
+    XA, YA, DA = proj(A)
+    XB, YB, DB = proj(Bv)
+    out = []
+    for i in range(len(p) - 1):
+        n = np.cross(Bv[i] - A[i], A[i + 1] - A[i])
+        ln = np.linalg.norm(n) + 1e-12
+        _, _, nd = proj(n / ln)
+        front = nd < 0
+        bright = 0.42 + 0.58 * abs(nd)
+        col = interpolate_color(BLACK, ManimColor(CARA_A if front else CARA_B), bright)
+        pts = [[XA[i], YA[i], 0], [XB[i], YB[i], 0],
+               [XB[i + 1], YB[i + 1], 0], [XA[i + 1], YA[i + 1], 0]]
+        pts = [list(np.array(q) * scale + center) for q in pts]
+        out.append((pts, (DA[i] + DB[i] + DA[i + 1] + DB[i + 1]) / 4.0, col))
+    return out
+
+
+def draw(items):
+    """Painter's algorithm: lo mas lejos (profundidad mayor) se dibuja primero."""
+    items = sorted(items, key=lambda t: -t[1])
+    return VGroup(*[Polygon(*pts, stroke_width=0, fill_color=col, fill_opacity=1)
+                    for pts, _, col in items])
+
+
+def cinta(tau, beta, **kw):
+    return draw(quads(tau, beta, **kw))
+
+
+def camino(tau, beta, off, smax=1.0, L=9.4, w=0.62, nu=170, scale=1.0,
+           center=ORIGIN, **kw):
+    """Poligonal sobre la cinta a distancia 'off' del centro (off en [-w, w])."""
+    p, d, _ = geom(tau, beta, L, w, nu, smax=smax)
+    P = p + off * d
+    X, Y, _ = proj(P)
+    m = VMobject(**kw)
+    m.set_points_as_corners([list(np.array([X[i], Y[i], 0]) * scale + center)
+                             for i in range(len(X))])
+    return m
+
+
+class Mobius(TikTok):
+    NAME = "mobius"
+
+    def construct(self):
+        self.prepare()
+        chip = self.chip("Hacelo en casa", VERDE)
+        C = UP * 1.85
+        SC = 1.30
+        P = dict(L=9.4, w=0.62, nu=130, scale=SC, center=C)
+
+        tau = ValueTracker(0.0)
+        beta = ValueTracker(0.0)
+        sc = ValueTracker(0.60)          # la tira plana mide L*scale: tiene que entrar
+
+        def actual():
+            return cinta(tau.get_value(), beta.get_value(),
+                         **{**P, "scale": sc.get_value()})
+
+        banda = actual()
+
+        with self.beat(0) as b:
+            b.play(FadeIn(chip, shift=DOWN * 0.3), run_time=0.45)
+            b.play(FadeIn(banda, shift=UP * 0.2), run_time=0.7)
+
+        with self.beat(1) as b:
+            banda.add_updater(lambda m: m.become(actual()))
+            b.play(tau.animate.set_value(1.0), run_time=max(1.0, b.floor * 0.45),
+                   rate_func=smooth)
+            b.play(beta.animate.set_value(1.0), sc.animate.set_value(SC),
+                   run_time=max(1.0, b.floor * 0.45), rate_func=smooth)
+            banda.clear_updaters()
+            banda.become(cinta(1.0, 1.0, **P))
+
+        with self.beat(2) as b:
+            nom = VGroup(
+                self.fit(Text("cinta de M\u00f6bius", font=FONT, font_size=58,
+                              weight=BOLD, color=AMBAR), 8.0),
+                self.fit(Text("una sola cara", font=FONT, font_size=50,
+                              weight=BOLD, color=WHITE), 8.0),
+            ).arrange(DOWN, buff=0.3).move_to(DOWN * 2.6)
+            b.play(Write(nom[0]), run_time=0.8)
+            b.play(FadeIn(nom[1], shift=UP * 0.15), run_time=0.6)
+
+        def recorrido(off, color, prog):
+            m = camino(1.0, 1.0, off, smax=max(prog.get_value(), 0.004),
+                       stroke_color=color, stroke_width=9, **P)
+            return m
+
+        with self.beat(3) as b:
+            b.play(FadeOut(nom), run_time=0.25)
+            prog = ValueTracker(0.004)
+            traza = recorrido(0.72 * P["w"], ROSA, prog)
+            traza.add_updater(lambda m: m.become(recorrido(0.72 * P["w"], ROSA, prog)))
+            punta = Dot(radius=0.16, color=ROSA)
+            punta.add_updater(lambda m: m.move_to(traza.get_end()))
+            b.add(traza, punta)
+            b.play(prog.animate.set_value(2.0), run_time=max(1.6, b.floor - 0.5),
+                   rate_func=linear)
+            traza.clear_updaters(); punta.clear_updaters()
+
+        with self.beat(4) as b:
+            b.play(FadeOut(VGroup(traza, punta)), run_time=0.3)
+            prog2 = ValueTracker(0.004)
+            borde = recorrido(P["w"], VERDE, prog2)
+            borde.add_updater(lambda m: m.become(recorrido(P["w"], VERDE, prog2)))
+            b.add(borde)
+            b.play(prog2.animate.set_value(2.0), run_time=max(1.4, b.floor - 0.9),
+                   rate_func=linear)
+            borde.clear_updaters()
+            uno = self.fit(Text("un solo borde", font=FONT, font_size=50,
+                                weight=BOLD, color=VERDE), 8.0).move_to(DOWN * 2.6)
+            b.play(FadeIn(uno, shift=UP * 0.15), run_time=0.6)
+
+        with self.beat(5) as b:
+            b.play(FadeOut(VGroup(borde, uno)), run_time=0.3)
+            corte = camino(1.0, 1.0, 0.0, smax=1.0, stroke_color=ROSA,
+                           stroke_width=8, **P)
+            corte = DashedVMobject(corte, num_dashes=90, color=ROSA)
+            b.play(Create(corte), run_time=max(1.2, b.floor - 0.8))
+            tij = self.fit(Text("cortala al medio", font=FONT, font_size=50,
+                                weight=BOLD, color=ROSA), 8.0).move_to(DOWN * 2.6)
+            b.play(FadeIn(tij, shift=UP * 0.15), run_time=0.6)
+
+        with self.beat(6) as b:
+            b.play(FadeOut(VGroup(corte, tij)), run_time=0.3)
+            b.remove(banda)
+            larga = cinta(4.0, 1.0, L=18.0, w=0.30, nu=260, scale=0.92, center=C)
+            b.play(FadeIn(larga), run_time=0.7)
+            t = VGroup(
+                self.fit(Text("no salen dos", font=FONT, font_size=50,
+                              weight=BOLD, color=WHITE), 8.0),
+                self.fit(Text("sale UNA, el doble de larga", font=FONT, font_size=46,
+                              weight=BOLD, color=AMBAR), 8.2),
+            ).arrange(DOWN, buff=0.3).move_to(DOWN * 2.6)
+            b.play(FadeIn(t[0], shift=UP * 0.15), run_time=0.5)
+            b.play(FadeIn(t[1], shift=UP * 0.15), run_time=0.6)
+
+        with self.beat(7) as b:
+            b.play(FadeOut(t), run_time=0.3)
+            dc = VGroup(
+                self.fit(Text("y esa ya tiene", font=FONT, font_size=48,
+                              weight=BOLD, color=WHITE), 8.0),
+                self.fit(Text("DOS caras", font=FONT, font_size=62,
+                              weight=BOLD, color=CELESTE), 8.0),
+            ).arrange(DOWN, buff=0.28).move_to(DOWN * 2.7)
+            b.play(FadeIn(dc[0], shift=UP * 0.15), run_time=0.5)
+            b.play(FadeIn(dc[1], scale=0.75), run_time=0.7)
+
+        with self.beat(8) as b:
+            b.play(FadeOut(VGroup(larga, dc)), run_time=0.35)
+            c1 = DashedVMobject(camino(1.0, 1.0, P["w"] / 3, stroke_color=VERDE,
+                                   stroke_width=7, **P),
+                                num_dashes=80, color=VERDE)
+            c2 = DashedVMobject(camino(1.0, 1.0, -P["w"] / 3, stroke_color=VERDE,
+                                   stroke_width=7, **P),
+                                num_dashes=80, color=VERDE)
+            b.play(FadeIn(banda), run_time=0.35)
+            b.play(Create(c1), Create(c2), run_time=max(1.1, b.floor - 1.1))
+            tt = self.fit(Text("ahora cortá a 1/3 del borde", font=FONT, font_size=44,
+                               weight=BOLD, color=VERDE), 8.2).move_to(DOWN * 2.7)
+            b.play(FadeIn(tt, shift=UP * 0.15), run_time=0.55)
+
+        with self.beat(9) as b:
+            b.play(FadeOut(VGroup(c1, c2, tt)), run_time=0.3)
+            b.remove(banda)
+            q1 = quads(1.0, 1.0, L=9.4, w=0.22, nu=170, scale=0.95,
+                       center=C + LEFT * 1.15)
+            q2 = quads(4.0, 1.0, L=18.0, w=0.22, nu=260, scale=0.72,
+                       center=C + RIGHT * 1.15)
+            r1, r2 = draw(q1), draw(q2)
+            dep = np.array([q[1] for q in q1])
+            med = float(np.median(dep))
+            frente = draw([q for q in q1                       # eslabon que pasa encima
+                           if np.mean([pt[0] for pt in q[0]]) > C[0] - 1.15
+                           and q[1] < med])
+            cadena = VGroup(r1, r2, frente)
+            b.play(FadeIn(cadena), run_time=0.8)
+            t2 = VGroup(
+                self.fit(Text("dos cintas distintas", font=FONT, font_size=48,
+                              weight=BOLD, color=WHITE), 8.2),
+                self.fit(Text("y quedan enganchadas", font=FONT, font_size=48,
+                              weight=BOLD, color=AMBAR), 8.2),
+            ).arrange(DOWN, buff=0.3).move_to(DOWN * 2.7)
+            b.play(FadeIn(t2[0], shift=UP * 0.15), run_time=0.5)
+            b.play(FadeIn(t2[1], shift=UP * 0.15), run_time=0.6)
+
+        with self.beat(10) as b:
+            b.play(FadeOut(VGroup(cadena, t2)), run_time=0.4)
+            cta = VGroup(
+                self.fit(Text("una hoja y cinta", font=FONT, font_size=52,
+                              weight=BOLD, color=WHITE), 8.0),
+                self.fit(Text("hacelo ahora", font=FONT, font_size=66,
+                              weight=BOLD, color=VERDE), 8.0),
+                self.fit(Text("contame cómo te fue", font=FONT, font_size=42,
+                              weight=BOLD, color=WHITE), 8.0),
+            ).arrange(DOWN, buff=0.32).move_to(UP * 1.4)
+            b.play(FadeIn(cta[0], shift=UP * 0.12), run_time=0.5)
+            b.play(Write(cta[1]), run_time=0.8)
+            b.play(FadeIn(cta[2], shift=UP * 0.12), run_time=0.5)
+
+        self.finish()