src/api/guide.md

# Manim Code Examples (Community v0.19.0)

## Example 1: Basic Shapes and Text

**Description:** Shows a circle and text, then fades them out.

```python
# ### MANIM CODE:
from manim import *
import numpy as np

class BasicShapes(Scene):
    def construct(self):
        circle = Circle(color=BLUE, fill_opacity=0.5)
        text = Text("Hello Manim!").next_to(circle, DOWN)
        self.play(Create(circle), Write(text), run_time=5) # Longer duration for narration
        self.wait(5) # Pause for narration
        self.play(FadeOut(circle), FadeOut(text), run_time=5)
        self.wait(15) # Fill remaining time
```

```text
# ### NARRATION:
Here we create a blue circle and display the text "Hello Manim!" below it. After a brief pause, both elements fade away.
```

## Example 2: Vector Transformation with Labels

**Description:** Creates a vector, displays a transformation matrix, applies the transformation, and labels the steps.

```python
# ### MANIM CODE:
from manim import *
import numpy as np

class VectorTransform(Scene):
    def construct(self):
        # Setup
        axes = Axes(x_range=[-5, 5, 1], y_range=[-5, 5, 1], x_length=6, y_length=6)
        vec_start = np.array([1, 1, 0])
        matrix = np.array([[0, -1], [1, 0]]) # 90 deg rotation

        # Initial vector
        vector = Arrow(ORIGIN, vec_start, buff=0, color=YELLOW)
        vec_label = MathTex("v", color=YELLOW).next_to(vector.get_end(), UR, buff=0.1)
        self.play(Create(axes), Create(vector), Write(vec_label), run_time=6) # Show initial state

        # Matrix
        matrix_tex = MathTex(r"M = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}", color=RED).to_corner(UL)
        self.play(Write(matrix_tex), run_time=4) # Introduce matrix

        # Transformation
        vec_end = np.append(np.dot(matrix, vec_start[:2]), 0)
        new_vector = Arrow(ORIGIN, vec_end, buff=0, color=GREEN)
        new_vec_label = MathTex("Mv", color=GREEN).next_to(new_vector.get_end(), UR, buff=0.1)
        transform_label = Text("Applying 90° Rotation", font_size=24).next_to(matrix_tex, DOWN, aligned_edge=LEFT)

        self.play(Write(transform_label), run_time=3) # Explain transform
        self.play(Transform(vector, new_vector), Transform(vec_label, new_vec_label), run_time=7) # Show transform

        self.wait(10) # Hold final state
```

```text
# ### NARRATION:
We start with vector v in yellow on the coordinate plane. This is the rotation matrix M we'll use. Now, we apply the matrix M to rotate vector v by 90 degrees, resulting in the green vector Mv.
```
## Example 3: BraceAnnotation

**Description:** Shows how to create braces and attach text/latex to them.

```python
# ### MANIM CODE:
from manim import *
import numpy as np

class BraceAnnotation(Scene):
    def construct(self):
        dot = Dot([-2, -1, 0])
        dot2 = Dot([2, 1, 0])
        line = Line(dot.get_center(), dot2.get_center()).set_color(ORANGE)
        b1 = Brace(line)
        b1text = b1.get_text("Horizontal distance")
        b2 = Brace(line, direction=line.copy().rotate(PI / 2).get_unit_vector())
        b2text = b2.get_tex("x-x_1")
        
        self.play(Create(line), Create(dot), Create(dot2), run_time=3)
        self.play(Create(b1), Write(b1text), run_time=3)
        self.play(Create(b2), Write(b2text), run_time=3)
        self.wait(21) # Fill remaining time
```

```text
# ### NARRATION:
Here we demonstrate how to add annotations with braces. First, we create a line between two dots. Then we add a horizontal brace with text below it showing "Horizontal distance." Finally, we add a vertical brace with mathematical notation showing the difference between x coordinates.
```

## Example 4: SinAndCosFunctionPlot

**Description:** Plots sine and cosine functions on an axis with labels.

```python
# ### MANIM CODE:
from manim import *
import numpy as np

class SinAndCosFunctionPlot(Scene):
    def construct(self):
        axes = Axes(
            x_range=[-10, 10.3, 1],
            y_range=[-1.5, 1.5, 1],
            x_length=10,
            axis_config={"color": GREEN},
            x_axis_config={
                "numbers_to_include": np.arange(-10, 10.01, 2),
                "numbers_with_elongated_ticks": np.arange(-10, 10.01, 2),
            },
            tips=False,
        )
        axes_labels = axes.get_axis_labels()
        sin_graph = axes.plot(lambda x: np.sin(x), color=BLUE)
        cos_graph = axes.plot(lambda x: np.cos(x), color=RED)

        sin_label = axes.get_graph_label(
            sin_graph, "\\sin(x)", x_val=-10, direction=UP / 2
        )
        cos_label = axes.get_graph_label(cos_graph, label="\\cos(x)")

        vert_line = axes.get_vertical_line(
            axes.i2gp(TAU, cos_graph), color=YELLOW, line_func=Line
        )
        line_label = axes.get_graph_label(
            cos_graph, r"x=2\pi", x_val=TAU, direction=UR, color=WHITE
        )

        # Animation sequence
        self.play(Create(axes), Write(axes_labels), run_time=3)
        self.play(Create(sin_graph), Create(cos_graph), run_time=5)
        self.play(Write(sin_label), Write(cos_label), run_time=3)
        self.play(Create(vert_line), Write(line_label), run_time=3)
        self.wait(16) # Fill remaining time
```

```text
# ### NARRATION:
In this animation, we plot the sine and cosine functions on a coordinate plane. The sine function is shown in blue, while the cosine function is shown in red. We add labels to each curve and mark a vertical line at x equals 2π to highlight this important value. Notice how the curves oscillate between -1 and 1 as they extend across the x-axis.
```

## Example 5: PointMovingOnShapes

**Description:** Demonstrates how to animate a dot moving along paths and rotating.

```python
# ### MANIM CODE:
from manim import *
import numpy as np

class PointMovingOnShapes(Scene):
    def construct(self):
        circle = Circle(radius=1, color=BLUE)
        dot = Dot()
        dot2 = dot.copy().shift(RIGHT)
        self.add(dot)

        line = Line([3, 0, 0], [5, 0, 0])
        self.play(Create(line), run_time=2)
        self.play(GrowFromCenter(circle), run_time=2)
        self.play(Transform(dot, dot2), run_time=2)
        self.play(MoveAlongPath(dot, circle), run_time=7, rate_func=linear)
        self.play(Rotating(dot, about_point=[2, 0, 0]), run_time=7)
        self.wait(10) # Fill remaining time
```

```text
# ### NARRATION:
Here we demonstrate moving and transforming objects. We begin with a dot and create a line and circle. Then, we transform the dot by shifting it to the right. Watch as the dot moves along the circular path at a constant speed. Finally, the dot rotates around a fixed point, showing how we can create complex animations by combining different movements.
```

## Example 6: ThreeDSurfacePlot

**Description:** Creates a 3D Gaussian surface plot with colored checkerboard pattern.

```python
# ### MANIM CODE:
from manim import *
import numpy as np

class ThreeDSurfacePlot(ThreeDScene):
    def construct(self):
        resolution_fa = 24
        self.set_camera_orientation(phi=75 * DEGREES, theta=-30 * DEGREES)

        def param_gauss(u, v):
            x = u
            y = v
            sigma, mu = 0.4, [0.0, 0.0]
            d = np.linalg.norm(np.array([x - mu[0], y - mu[1]]))
            z = np.exp(-(d ** 2 / (2.0 * sigma ** 2)))
            return np.array([x, y, z])

        gauss_plane = Surface(
            param_gauss,
            resolution=(resolution_fa, resolution_fa),
            v_range=[-2, +2],
            u_range=[-2, +2]
        )

        gauss_plane.scale(2, about_point=ORIGIN)
        gauss_plane.set_style(fill_opacity=1, stroke_color=GREEN)
        gauss_plane.set_fill_by_checkerboard(ORANGE, BLUE, opacity=0.5)
        axes = ThreeDAxes()
        
        self.play(Create(axes), run_time=2)
        self.play(Create(gauss_plane), run_time=3)
        self.begin_ambient_camera_rotation(rate=0.1)
        self.wait(25) # Fill remaining time
```

```text
# ### NARRATION:
In this animation, we're creating a three-dimensional Gaussian surface plot. We first set up the camera angle to view our 3D scene properly. The surface is defined by a Gaussian function that creates a bell curve shape in three dimensions. We apply a checkerboard pattern with orange and blue colors to highlight the surface features. Notice how the ambient camera rotation helps us visualize the 3D nature of the surface from multiple angles.
```

## Example 7: MovingAngle

**Description:** Shows an animated angle that changes based on a ValueTracker.

```python
# ### MANIM CODE:
from manim import *
import numpy as np

class MovingAngle(Scene):
    def construct(self):
        rotation_center = LEFT

        theta_tracker = ValueTracker(110)
        line1 = Line(LEFT, RIGHT)
        line_moving = Line(LEFT, RIGHT)
        line_ref = line_moving.copy()
        line_moving.rotate(
            theta_tracker.get_value() * DEGREES, about_point=rotation_center
        )
        a = Angle(line1, line_moving, radius=0.5, other_angle=False)
        tex = MathTex(r"\theta").move_to(
            Angle(
                line1, line_moving, radius=0.5 + 3 * SMALL_BUFF, other_angle=False
            ).point_from_proportion(0.5)
        )

        self.play(Create(line1), Create(line_moving), run_time=2)
        self.play(Create(a), Write(tex), run_time=2)
        self.wait(2)

        line_moving.add_updater(
            lambda x: x.become(line_ref.copy()).rotate(
                theta_tracker.get_value() * DEGREES, about_point=rotation_center
            )
        )

        a.add_updater(
            lambda x: x.become(Angle(line1, line_moving, radius=0.5, other_angle=False))
        )
        tex.add_updater(
            lambda x: x.move_to(
                Angle(
                    line1, line_moving, radius=0.5 + 3 * SMALL_BUFF, other_angle=False
                ).point_from_proportion(0.5)
            )
        )

        self.play(theta_tracker.animate.set_value(40), run_time=3)
        self.play(theta_tracker.animate.increment_value(140), run_time=3)
        self.play(tex.animate.set_color(RED), run_time=1)
        self.play(theta_tracker.animate.set_value(350), run_time=7)
        self.wait(10) # Fill remaining time
```

```text
# ### NARRATION:
This animation demonstrates how to create a dynamic angle that updates as values change. We start with two lines forming an angle of 110 degrees. Using updaters and a ValueTracker, we can animate the angle changing smoothly. Watch as we decrease the angle to 40 degrees, then increase it by 140 degrees. As the angle continues to change, we also highlight the theta symbol in red before completing a full rotation to 350 degrees.
```

## Example 8: GraphAreaPlot

**Description:** Demonstrates how to show areas between curves and Riemann rectangles.

```python
# ### MANIM CODE:
from manim import *
import numpy as np

class GraphAreaPlot(Scene):
    def construct(self):
        ax = Axes(
            x_range=[0, 5],
            y_range=[0, 6],
            x_axis_config={"numbers_to_include": [2, 3]},
            tips=False,
        )

        labels = ax.get_axis_labels()

        curve_1 = ax.plot(lambda x: 4 * x - x ** 2, x_range=[0, 4], color=BLUE_C)
        curve_2 = ax.plot(
            lambda x: 0.8 * x ** 2 - 3 * x + 4,
            x_range=[0, 4],
            color=GREEN_B,
        )

        line_1 = ax.get_vertical_line(ax.input_to_graph_point(2, curve_1), color=YELLOW)
        line_2 = ax.get_vertical_line(ax.i2gp(3, curve_1), color=YELLOW)

        riemann_area = ax.get_riemann_rectangles(
            curve_1, x_range=[0.3, 0.6], dx=0.03, color=BLUE, fill_opacity=0.5
        )
        area = ax.get_area(
            curve_2, [2, 3], bounded_graph=curve_1, color=GREY, opacity=0.5
        )

        self.play(Create(ax), Write(labels), run_time=3)
        self.play(Create(curve_1), Create(curve_2), run_time=4)
        self.play(Create(line_1), Create(line_2), run_time=3)
        self.play(FadeIn(riemann_area), run_time=3) 
        self.play(FadeIn(area), run_time=3)
        self.wait(14) # Fill remaining time
```

```text
# ### NARRATION:
In this animation, we visualize areas between curves using Manim's plotting capabilities. We create two functions, shown in blue and green, and mark two vertical lines at x equals 2 and x equals 3. The small blue rectangles demonstrate Riemann sums, which approximate the area under a curve. The gray shaded region shows the area between both curves from x equals 2 to x equals 3. These visualizations are powerful tools for understanding calculus concepts like integration and area between curves.
```