def get_det(self):
matrix = Matrix(np.array([
["\\hat{\\imath}", "\\hat{\\jmath}", "\\hat{k}"],
["v_%d"%d for d in range(1, 4)],
["w_%d"%d for d in range(1, 4)],
]).T)
matrix.set_column_colors(X_COLOR, V_COLOR, W_COLOR)
matrix.get_mob_matrix()[1, 0].set_color(Y_COLOR)
matrix.get_mob_matrix()[2, 0].set_color(Z_COLOR)
VGroup(*matrix.get_mob_matrix()[1, 1:]).shift(0.15*DOWN)
VGroup(*matrix.get_mob_matrix()[2, 1:]).shift(0.35*DOWN)
det_text = get_det_text(matrix)
det_text.add(matrix)
return det_text
def show_triple_cross_product(self):
colors = [WHITE, ORANGE, W_COLOR]
tex_mobs = list(map(TexMobject, get_vect_tex(*"uvw")))
u_tex, v_tex, w_tex = tex_mobs
arrays = [
Matrix(["%s_%d" % (s, d) for d in range(1, 4)]) for s in "uvw"
]
defs_equals = VGroup()
definitions = VGroup()
for array, tex_mob, color in zip(arrays, tex_mobs, colors):
array.set_column_colors(color)
tex_mob.set_color(color)
equals = TexMobject("=")
definition = VGroup(tex_mob, equals, array)
definition.arrange(RIGHT)
definitions.add(definition)
defs_equals.add(equals)
definitions.arrange(buff=MED_SMALL_BUFF)
definitions.shift(2 * DOWN)
mobs_with_targets = list(
it.chain(tex_mobs, *[a.get_entries() for a in arrays]))
for mob in mobs_with_targets:
mob.target = mob.copy()
matrix = Matrix(
np.array([[e.target for e in array.get_entries()]
for array in arrays]).T)
det_text = get_det_text(matrix, background_rect=False)
syms = times1, times2, equals = [
TexMobject(sym) for sym in (
"\\times",
"\\times",
"=",
)
]
triple_cross = VGroup(u_tex.target, times1, v_tex.target, times2,
w_tex.target, equals)
triple_cross.arrange()
final_mobs = VGroup(triple_cross, VGroup(det_text, matrix))
final_mobs.arrange()
final_mobs.next_to(self.title, DOWN, buff=MED_SMALL_BUFF)
for mob in definitions, final_mobs:
mob.set_width(FRAME_X_RADIUS - 1)
for array in arrays:
brackets = array.get_brackets()
brackets.target = matrix.get_brackets()
mobs_with_targets.append(brackets)
for def_equals in defs_equals:
def_equals.target = equals
mobs_with_targets.append(def_equals)
self.play(FadeIn(definitions, run_time=2, lag_ratio=0.5))
self.wait(2)
self.play(*[Transform(mob.copy(), mob.target) for mob in tex_mobs] + [
Write(times1),
Write(times2),
])
triple_cross.add(*self.get_mobjects_from_last_animation()[:3])
self.play(*[
Transform(mob.copy(), mob.target) for mob in mobs_with_targets
if mob not in tex_mobs
])
u_entries = self.get_mobjects_from_last_animation()[:3]
v_entries = self.get_mobjects_from_last_animation()[3:6]
w_entries = self.get_mobjects_from_last_animation()[6:9]
self.play(Write(det_text))
self.wait(2)
self.det_text = det_text
self.definitions = definitions
self.u_entries = u_entries
self.v_entries = v_entries
self.w_entries = w_entries
self.matrix = matrix
self.triple_cross = triple_cross
self.v_tex, self.w_tex = v_tex, w_tex
self.equals = equals