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# Plotting Graphs
from manimlib.imports import *
class PlotGraphs(GraphScene):
CONFIG = {
"x_min": -5,
"x_max": 5,
"y_min": 0,
"y_max": 4,
"graph_origin": ORIGIN + 2.5* DOWN,
"x_labeled_nums": list(range(-5, 6)),
"y_labeled_nums": list(range(0, 5)),
}
def construct(self):
topic = TextMobject("Domain and Range")
topic.scale(2)
topic.set_color(YELLOW)
self.play(Write(topic))
self.play(FadeOut(topic))
self.wait(1)
scalar_func_R = TextMobject(r"Scalar Valued Functions in $\mathbb{R}$").scale(1.5).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
self.play(Write(scalar_func_R))
self.play(FadeOut(scalar_func_R))
self.wait(1)
XTD = self.x_axis_width/(self.x_max- self.x_min)
YTD = self.y_axis_height/(self.y_max- self.y_min)
self.setup_axes(animate = True)
graphobj = self.get_graph(lambda x : np.sqrt(x + 4), x_min = -4, x_max = 5)
graph_lab = self.get_graph_label(graphobj, label = r"\sqrt{x + 4}")
rangeline1 = Arrow(self.graph_origin+2.2*YTD*UP+5*XTD*LEFT, self.graph_origin+4.1*YTD*UP+5*XTD*LEFT)
rangeline2 = Arrow(self.graph_origin+1.7*YTD*UP+5*XTD*LEFT, self.graph_origin+5*XTD*LEFT)
rangeline1.set_color(RED)
rangeline2.set_color(RED)
rangeMsg = TextMobject(r"Range: $y \geq 0$")
rangeMsg.move_to(self.graph_origin+2*YTD*UP+5*XTD*LEFT)
rangeMsg.scale(0.5)
rangeMsg.set_color(YELLOW)
domainline1 = Arrow(self.graph_origin+0.6*YTD*DOWN+1.2*XTD*LEFT, self.graph_origin+0.6*YTD*DOWN + 4*XTD*LEFT, buff = 0.1)
domainline2 = Arrow(self.graph_origin+0.6*YTD*DOWN+1.1*XTD*RIGHT, self.graph_origin+0.6*YTD*DOWN + 5.3*XTD*RIGHT, buff = 0.1)
domainline1.set_color(PINK)
domainline2.set_color(PINK)
domainMsg = TextMobject(r"Domain: $x \geq -4$")
domainMsg.move_to(self.graph_origin+0.6*YTD*DOWN)
domainMsg.scale(0.5)
domainMsg.set_color(GREEN)
domain_subset = TextMobject(r"Domain $\subset \mathbb{R}$", color = PURPLE).scale(0.7).move_to(self.graph_origin+3.5*YTD*UP+2*XTD*RIGHT)
self.play(ShowCreation(graphobj))
self.play(ShowCreation(graph_lab))
self.wait(1)
self.play(GrowArrow(rangeline1))
self.play(GrowArrow(rangeline2))
self.play(Write(rangeMsg))
self.wait(1)
self.play(GrowArrow(domainline1))
self.play(GrowArrow(domainline2))
self.play(Write(domainMsg), Write(domain_subset))
self.wait(3)
class PlotSineGraphs(GraphScene):
CONFIG = {
"x_min": -8,
"x_max": 8,
"y_min": -1,
"y_max": 1,
"graph_origin": ORIGIN,
"x_labeled_nums": list(range(-8, 9)),
"y_labeled_nums": list(range(-1, 2)),
}
def construct(self):
XTD = self.x_axis_width/(self.x_max- self.x_min)
YTD = self.y_axis_height/(self.y_max- self.y_min)
self.setup_axes(animate = True)
sineobj = self.get_graph(lambda x : np.sin(x), x_min = -7, x_max = 8)
sine_lab = self.get_graph_label(sineobj, label = "\\sin(x)")
rangeline1 = Arrow(8*XTD*LEFT,1*YTD*UP+8*XTD*LEFT, buff = 0)
rangeline2 = Arrow(8*XTD*LEFT,1*YTD*DOWN+8*XTD*LEFT, buff = 0)
rangeline1.set_color(RED)
rangeline2.set_color(RED)
rangeMsg = TextMobject(r"Range: $-1 \leq y \leq 1$")
rangeMsg.move_to(1.1*YTD*UP+8.5*XTD*LEFT)
rangeMsg.scale(0.5)
rangeMsg.set_color(YELLOW)
domainline1 = Arrow(1.1*YTD*DOWN+2*XTD*LEFT, 1.1*YTD*DOWN + 8.5*XTD*LEFT)
domainline2 = Arrow(1.1*YTD*DOWN+2*XTD*RIGHT, 1.1*YTD*DOWN + 8.5*XTD*RIGHT)
domainline1.set_color(PINK)
domainline2.set_color(PINK)
domainMsg = TextMobject(r"Domain: $[-\infty, \infty]$")
domainMsg.move_to(1.1*YTD*DOWN)
domainMsg.scale(0.5)
domainMsg.set_color(GREEN)
domain_subset = TextMobject(r"Domain $\subseteq \mathbb{R}$", color = PURPLE).scale(0.7).move_to(self.graph_origin+0.8*YTD*UP+4.5*XTD*RIGHT)
self.play(ShowCreation(sineobj))
self.play(ShowCreation(sine_lab))
self.wait(1)
self.play(GrowArrow(rangeline1))
self.play(GrowArrow(rangeline2))
self.play(Write(rangeMsg))
self.wait(1)
self.play(GrowArrow(domainline1))
self.play(GrowArrow(domainline2))
self.play(Write(domainMsg), Write(domain_subset))
self.wait(3)
class Paraboloid(ThreeDScene):
def construct(self):
scalar_func_R2 = TextMobject(r"Scalar Valued Functions in $\mathbb{R}^2$").scale(1.5).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
self.play(Write(scalar_func_R2))
self.play(FadeOut(scalar_func_R2))
self.wait(1)
axes = ThreeDAxes()
paraboloid = ParametricSurface(
lambda u, v: np.array([
2*np.sin(u)*np.cos(v),
2*np.sin(u)*np.sin(v),
2*2*np.sin(u)*np.sin(u)
]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E],
resolution=(15, 32)).scale(1)
domain = Polygon(np.array([-5,-5,0]),np.array([5,-5,0]),np.array([5,5,0]),np.array([-5,5,0]),np.array([-5,-5,0]), color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.2)
domain_lab = TextMobject(r"$Domain: \mathbb{R}^2$", color = YELLOW_C).scale(0.7).move_to(1*DOWN + 2*LEFT)
rangef = Line(np.array([0, 0,0]), np.array([0, 0,5]), color = RED_C)
rangef_lab = TextMobject(r"$Range: z \geq 0$", color = RED_C).scale(0.7).move_to(2*UP + 1.5*RIGHT)
func = TextMobject(r"$z = f(x,y) = x^2+y^2$").scale(0.7).move_to(3*UP + 4*LEFT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
self.set_camera_orientation(phi=60 * DEGREES, theta = 0*DEGREES)
self.begin_ambient_camera_rotation(rate=0.3)
self.add(axes)
axis = TextMobject(r"X",r"Y",r"Z")
axis[0].move_to(6*RIGHT)
axis[1].move_to(6*UP)
axis[2].move_to(np.array([0,0,3.7]))
self.add_fixed_orientation_mobjects(axis[2])
self.add_fixed_orientation_mobjects(axis[0])
self.add_fixed_orientation_mobjects(axis[1])
self.add_fixed_in_frame_mobjects(func)
self.play(Write(paraboloid))
self.play(ShowCreation(domain))
self.add_fixed_in_frame_mobjects(domain_lab)
self.wait()
self.play(ShowCreation(rangef))
self.add_fixed_in_frame_mobjects(rangef_lab)
self.wait(5)
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