Math – Exercise 10 (Analysis)

import numpy as np
import plotly.graph_objects as go

fig = go.Figure()

# --------------------------------------------------
# 1. Bottom surface: z = 0
# --------------------------------------------------

x = np.linspace(0, 2, 20)
y = np.linspace(0, 3, 20)

X, Y = np.meshgrid(x, y)

fig.add_trace(go.Surface(
    x=X,
    y=Y,
    z=np.zeros_like(X),
    opacity=0.5,
    showscale=False,
    name="z = 0"
))


# --------------------------------------------------
# 2. Top surface: z = x + y
# --------------------------------------------------

Z = X + Y

fig.add_trace(go.Surface(
    x=X,
    y=Y,
    z=Z,
    opacity=0.8,
    showscale=False,
    name="z = x + y"
))


# --------------------------------------------------
# 3. Side surface: x = 0
#    0 <= y <= 3
#    0 <= z <= y
# --------------------------------------------------

y = np.linspace(0, 3, 20)
z = np.linspace(0, 3, 20)

Y, Z = np.meshgrid(y, z)

# Keep only the region below z = y
Z = np.minimum(Z, Y)

fig.add_trace(go.Surface(
    x=np.zeros_like(Y),
    y=Y,
    z=Z,
    opacity=0.6,
    showscale=False,
    name="x = 0"
))


# --------------------------------------------------
# 4. Side surface: x = 2
#    0 <= y <= 3
#    0 <= z <= 2 + y
# --------------------------------------------------

y = np.linspace(0, 3, 20)
z = np.linspace(0, 5, 20)

Y, Z = np.meshgrid(y, z)

# Keep only the region below z = 2 + y
Z = np.minimum(Z, 2 + Y)

fig.add_trace(go.Surface(
    x=2 * np.ones_like(Y),
    y=Y,
    z=Z,
    opacity=0.6,
    showscale=False,
    name="x = 2"
))


# --------------------------------------------------
# 5. Side surface: y = 0
#    0 <= x <= 2
#    0 <= z <= x
# --------------------------------------------------

x = np.linspace(0, 2, 20)
z = np.linspace(0, 2, 20)

X, Z = np.meshgrid(x, z)

# Keep only the region below z = x
Z = np.minimum(Z, X)

fig.add_trace(go.Surface(
    x=X,
    y=np.zeros_like(X),
    z=Z,
    opacity=0.6,
    showscale=False,
    name="y = 0"
))


# --------------------------------------------------
# 6. Side surface: y = 3
#    0 <= x <= 2
#    0 <= z <= x + 3
# --------------------------------------------------

x = np.linspace(0, 2, 20)
z = np.linspace(0, 5, 20)

X, Z = np.meshgrid(x, z)

# Keep only the region below z = x + 3
Z = np.minimum(Z, X + 3)

fig.add_trace(go.Surface(
    x=X,
    y=3 * np.ones_like(X),
    z=Z,
    opacity=0.6,
    showscale=False,
    name="y = 3"
))


# --------------------------------------------------
# Layout
# --------------------------------------------------

fig.update_layout(
    title="Solid: 0 ≤ x ≤ 2, 0 ≤ y ≤ 3, 0 ≤ z ≤ x + y",

    scene=dict(
        xaxis_title="x",
        yaxis_title="y",
        zaxis_title="z",
        aspectmode="data"
    )
)

fig.show()