def construct(self):
v = TexMobject(self.v_str)
v.highlight(YELLOW)
eq = TexMobject("=")
coords = Matrix(["x", "y", "z"])
eq2 = eq.copy()
if self.post_transform:
L, l_paren, r_paren = map(TexMobject, "L()")
parens = VMobject(l_paren, r_paren)
parens.scale(2)
parens.stretch_to_fit_height(
coords.get_height()
)
VMobject(L, l_paren, coords, r_paren).arrange_submobjects(buff = 0.1)
coords.submobjects = [L, l_paren] + coords.submobjects + [r_paren]
lin_comb = VMobject(*map(TexMobject, [
"x", self.i_str, "+",
"y", self.j_str, "+",
"z", self.k_str,
]))
lin_comb.arrange_submobjects(
RIGHT, buff = 0.1,
aligned_edge = ORIGIN if self.post_transform else DOWN
)
lin_comb_parts = np.array(lin_comb.split())
new_x, new_y, new_z = lin_comb_parts[[0, 3, 6]]
i, j, k = lin_comb_parts[[1, 4, 7]]
plusses = lin_comb_parts[[2, 5]]
i.highlight(X_COLOR)
j.highlight(Y_COLOR)
k.highlight(Z_COLOR)
everything = VMobject(v, eq, coords, eq2, lin_comb)
everything.arrange_submobjects(buff = 0.2)
everything.scale_to_fit_width(2*SPACE_WIDTH - 1)
everything.to_edge(DOWN)
if not self.post_transform:
lin_comb.shift(0.35*UP)
self.play(*map(Write, [v, eq, coords]))
self.dither()
self.play(
Transform(
coords.get_entries().copy(),
VMobject(new_x, new_y, new_z),
path_arc = -np.pi,
submobject_mode = "lagged_start"
),
Write(VMobject(*[eq2, i, j, k] + list(plusses))),
run_time = 3
)
self.dither()
def show_formula(self):
matrix = self.get_matrix()
det_text = get_det_text(matrix)
f_str = "=(a+b)(c+d)-ac-bd-2bc=ad-bc"
formula = TexMobject(f_str)
formula.next_to(det_text, RIGHT)
everyone = VMobject(det_text, matrix, formula)
everyone.scale_to_fit_width(2 * SPACE_WIDTH - 1)
everyone.next_to(DOWN, DOWN)
background_rect = BackgroundRectangle(everyone)
self.play(ShowCreation(background_rect), Write(everyone))
self.wait()
def construct(self):
matrix = Matrix(np.arange(9).reshape((3, 3)))
vect = Matrix(list("xyz"))
vect.scale_to_fit_height(matrix.get_height())
col1, col2, col3 = columns = [
Matrix(col) for col in matrix.copy().get_mob_matrix().transpose()
]
coords = x, y, z = [m.copy() for m in vect.get_entries().split()]
eq, plus1, plus2 = map(TexMobject, list("=++"))
everything = VMobject(matrix, vect, eq, x, col1, plus1, y, col2, plus2,
z, col3)
everything.arrange_submobjects(buff=0.1)
everything.scale_to_fit_width(2 * SPACE_WIDTH - 1)
result = VMobject(x, col1, plus1, y, col2, plus2, z, col3)
trips = [
(matrix, DOWN, "Transformation"),
(vect, UP, "Input vector"),
(result, DOWN, "Output vector"),
]
braces = []
for mob, direction, text in trips:
brace = Brace(mob, direction)
words = TextMobject(text)
words.next_to(brace, direction)
brace.add(words)
braces.append(brace)
matrix_brace, vect_brace, result_brace = braces
self.play(*map(Write, [matrix, vect]), run_time=2)
self.play(Write(matrix_brace, run_time=1))
self.play(Write(vect_brace, run_time=1))
sexts = zip(matrix.get_mob_matrix().transpose(), columns,
vect.get_entries().split(), coords, [eq, plus1, plus2],
[X_COLOR, Y_COLOR, Z_COLOR])
for o_col, col, start_coord, coord, sym, color in sexts:
o_col = VMobject(*o_col)
self.play(start_coord.highlight, YELLOW, o_col.highlight, color)
coord.highlight(YELLOW)
col.highlight(color)
self.play(
Write(col.get_brackets()),
Transform(o_col.copy(), col.get_entries(), path_arc=-np.pi),
Transform(start_coord.copy(), coord, path_arc=-np.pi),
Write(sym))
self.wait()
self.play(Write(result_brace, run_time=1))
self.wait()
def show_formula(self):
matrix = self.get_matrix()
det_text = get_det_text(matrix)
f_str = "=(a+b)(c+d)-ac-bd-2bc=ad-bc"
formula = TexMobject(f_str)
formula.next_to(det_text, RIGHT)
everyone = VMobject(det_text, matrix, formula)
everyone.scale_to_fit_width(2*SPACE_WIDTH - 1)
everyone.next_to(DOWN, DOWN)
background_rect = BackgroundRectangle(everyone)
self.play(
ShowCreation(background_rect),
Write(everyone)
)
self.dither()
def construct(self):
i_to = TexMobject("\\hat{\\imath} \\to").highlight(X_COLOR)
j_to = TexMobject("\\hat{\\jmath} \\to").highlight(Y_COLOR)
k_to = TexMobject("\\hat{k} \\to").highlight(Z_COLOR)
i_array = Matrix(self.col1)
j_array = Matrix(self.col2)
k_array = Matrix(self.col3)
everything = VMobject(
i_to,
i_array,
TexMobject("=").highlight(BLACK),
j_to,
j_array,
TexMobject("=").highlight(BLACK),
k_to,
k_array,
TexMobject("=").highlight(BLACK),
)
everything.arrange_submobjects(RIGHT, buff=0.1)
everything.scale_to_fit_width(2 * SPACE_WIDTH - 1)
everything.to_edge(DOWN)
i_array.highlight(X_COLOR)
j_array.highlight(Y_COLOR)
k_array.highlight(Z_COLOR)
arrays = [i_array, j_array, k_array]
matrix = Matrix(
reduce(lambda a1, a2: np.append(a1, a2, axis=1),
[m.copy().get_mob_matrix() for m in arrays]))
matrix.to_edge(DOWN)
start_entries = reduce(op.add,
map(lambda a: a.get_entries().split(), arrays))
target_entries = matrix.get_mob_matrix().transpose().flatten()
start_l_bracket = i_array.get_brackets().split()[0]
start_r_bracket = k_array.get_brackets().split()[1]
start_brackets = VMobject(start_l_bracket, start_r_bracket)
target_bracketes = matrix.get_brackets()
for mob in everything.split():
self.play(Write(mob, run_time=1))
self.wait()
self.play(
FadeOut(everything),
Transform(VMobject(*start_entries), VMobject(*target_entries)),
Transform(start_brackets, target_bracketes))
self.wait()
def construct(self):
i_to = TexMobject("\\hat{\\imath} \\to").highlight(X_COLOR)
j_to = TexMobject("\\hat{\\jmath} \\to").highlight(Y_COLOR)
k_to = TexMobject("\\hat{k} \\to").highlight(Z_COLOR)
i_array = Matrix(self.col1)
j_array = Matrix(self.col2)
k_array = Matrix(self.col3)
everything = VMobject(
i_to, i_array, TexMobject("=").highlight(BLACK),
j_to, j_array, TexMobject("=").highlight(BLACK),
k_to, k_array, TexMobject("=").highlight(BLACK),
)
everything.arrange_submobjects(RIGHT, buff = 0.1)
everything.scale_to_fit_width(2*SPACE_WIDTH-1)
everything.to_edge(DOWN)
i_array.highlight(X_COLOR)
j_array.highlight(Y_COLOR)
k_array.highlight(Z_COLOR)
arrays = [i_array, j_array, k_array]
matrix = Matrix(reduce(
lambda a1, a2 : np.append(a1, a2, axis = 1),
[m.copy().get_mob_matrix() for m in arrays]
))
matrix.to_edge(DOWN)
start_entries = reduce(op.add, map(
lambda a : a.get_entries().split(),
arrays
))
target_entries = matrix.get_mob_matrix().transpose().flatten()
start_l_bracket = i_array.get_brackets().split()[0]
start_r_bracket = k_array.get_brackets().split()[1]
start_brackets = VMobject(start_l_bracket, start_r_bracket)
target_bracketes = matrix.get_brackets()
for mob in everything.split():
self.play(Write(mob, run_time = 1))
self.dither()
self.play(
FadeOut(everything),
Transform(VMobject(*start_entries), VMobject(*target_entries)),
Transform(start_brackets, target_bracketes)
)
self.dither()
def organize_matrices(self, left, right, result):
equals = TexMobject("=")
everything = VMobject(left, right, equals, result)
everything.arrange_submobjects()
everything.scale_to_fit_width(2 * SPACE_WIDTH - 1)
self.add(everything)
def organize_matrices(self, left, right, result):
equals = TexMobject("=")
everything = VMobject(left, right, equals, result)
everything.arrange_submobjects()
everything.scale_to_fit_width(2*SPACE_WIDTH-1)
self.add(everything)
def construct(self):
matrix = Matrix(np.arange(9).reshape((3, 3)))
vect = Matrix(list("xyz"))
vect.scale_to_fit_height(matrix.get_height())
col1, col2, col3 = columns = [
Matrix(col)
for col in matrix.copy().get_mob_matrix().transpose()
]
coords = x, y, z = [m.copy() for m in vect.get_entries().split()]
eq, plus1, plus2 = map(TexMobject, list("=++"))
everything = VMobject(
matrix, vect, eq,
x, col1, plus1,
y, col2, plus2,
z, col3
)
everything.arrange_submobjects(buff = 0.1)
everything.scale_to_fit_width(2*SPACE_WIDTH-1)
result = VMobject(x, col1, plus1, y, col2, plus2, z, col3)
trips = [
(matrix, DOWN, "Transformation"),
(vect, UP, "Input vector"),
(result, DOWN, "Output vector"),
]
braces = []
for mob, direction, text in trips:
brace = Brace(mob, direction)
words = TextMobject(text)
words.next_to(brace, direction)
brace.add(words)
braces.append(brace)
matrix_brace, vect_brace, result_brace = braces
self.play(*map(Write, [matrix, vect]), run_time = 2)
self.play(Write(matrix_brace, run_time = 1))
self.play(Write(vect_brace, run_time = 1))
sexts = zip(
matrix.get_mob_matrix().transpose(),
columns,
vect.get_entries().split(),
coords,
[eq, plus1, plus2],
[X_COLOR, Y_COLOR, Z_COLOR]
)
for o_col, col, start_coord, coord, sym, color in sexts:
o_col = VMobject(*o_col)
self.play(
start_coord.highlight, YELLOW,
o_col.highlight, color
)
coord.highlight(YELLOW)
col.highlight(color)
self.play(
Write(col.get_brackets()),
Transform(
o_col.copy(), col.get_entries(),
path_arc = -np.pi
),
Transform(
start_coord.copy(), coord,
path_arc = -np.pi
),
Write(sym)
)
self.dither()
self.play(Write(result_brace, run_time = 1))
self.dither()
