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from manimlib.imports import *
class text(Scene):
def construct(self):
text1 = TextMobject("For a grid, undergoing a linear transformation, all its straight lines")
text1.scale(0.9)
text2 = TextMobject("must either remain straight lines or sends to a point in the grid formed")
text2.scale(0.9)
text3 = TextMobject("Origin must remain where it was before transformation.")
text3.scale(0.9)
text1.move_to(ORIGIN+UP)
text2.move_to(ORIGIN)
text3.move_to(ORIGIN+DOWN)
self.play(Write(text1))
self.play(Write(text2))
self.play(Write(text3))
self.wait()
self.play(FadeOut(text1),FadeOut(text2),FadeOut(text3))
class LinearTransformation(LinearTransformationScene):
CONFIG = {
"basis_vector_stroke_width": 3,
"leave_ghost_vectors": True,
}
def construct(self):
self.setup()
matrix = [[0.866,-0.5],[0.5,0.866]]
self.apply_matrix(matrix)
text = TextMobject("This is a Linear","Trasformation")
text[0].move_to(DOWN+4*LEFT)
text[1].move_to(1.5*DOWN+4*LEFT)
text.add_background_rectangle()
self.play(Write(text))
self.wait()
class NonLinearTransformation(Scene):
def construct(self):
grid = NumberPlane()
self.play(ShowCreation(grid),run_time =2)
# I have taken reference from purusharth's code
NonLinearTrans = lambda coordinates : coordinates + np.array([np.sin(coordinates[1]),np.sin(coordinates[0]),0,])
grid.prepare_for_nonlinear_transform()
self.play(grid.apply_function,NonLinearTrans)
text = TextMobject("While, this is not a","Linear Trasformation")
text[0].move_to(DOWN+4*LEFT)
text[1].move_to(1.5*DOWN+4*LEFT)
text.add_background_rectangle()
self.play(Write(text))
self.wait()
class MoveOrigin(LinearTransformationScene):
CONFIG = {
"show_basis_vectors": False,
}
def construct(self):
self.wait()
dot = Dot(ORIGIN, color = YELLOW)
self.add_transformable_mobject(dot)
self.apply_nonlinear_transformation(self.func)
text = TextMobject("This is also not a linear transformation as the origin moves from its original position")
text.move_to(2*DOWN)
text.scale(0.5)
text.set_color(YELLOW)
text.add_background_rectangle()
self.play(Write(text))
self.wait()
def func(self, point):
matrix_transform = self.get_matrix_transformation([[1, -1], [1, 1]])
return matrix_transform(point) + UP+ RIGHT
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