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calesthioandHanzo Dev 7ffb943132 Initial release — OpenMontage: the first open-source agentic video production system

11 production pipelines, 47 tools, 124 agent skills.
Supports cloud APIs (fal.ai, OpenAI, ElevenLabs, Suno, HeyGen, Runway) and
free local providers (diffusers, Piper TTS, WAN 2.1, Hunyuan, CogVideo).

Co-authored-by: Hanzo Dev <[email protected]>

2026-03-29 08:25:17 -07:00

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Integration Visualization - Reference Guide

Example file: examples/integration_visualization.py

User Query Scenarios

This example addresses queries like:

"Show the area under a curve"
"Visualize Riemann sums converging to integral"
"Animate definite integral accumulation"
"Show integral of e^(-x) equals 1"

Scene Thinking Process (3b1b Style)

1. Core Concept

Definite Integral: The integral ∫f(x)dx represents accumulated area under curve f(x). Riemann sums with shrinking rectangles converge to the true integral.

2. Technical Implementation

Animated Area Fill (Using Polygon)

def get_area_polygon():
    t = t_tracker.get_value()
    xs = np.linspace(0, t, 50)
    # Points along curve
    points = [axes.c2p(x, f(x)) for x in xs]
    # Close the polygon along x-axis
    points.append(axes.c2p(t, 0))
    points.append(axes.c2p(0, 0))
    poly = Polygon(*points)
    poly.set_fill(BLUE_E, opacity=0.5)
    poly.set_stroke(width=0)
    return poly

area = always_redraw(get_area_polygon)

Key insight: ManimGL doesn't have axes.get_area(), so build polygons manually from curve points.

Riemann Sum Rectangles

for i in range(n):
    x = start + i * dx
    height = f(x)
    rect = Rectangle(
        width=dx * axes.x_axis.get_unit_size(),
        height=height * axes.y_axis.get_unit_size(),
    )
    rect.move_to(axes.c2p(x + dx/2, height/2))

3. Scene Variants

Scene	Purpose
`AreaUnderCurve`	Basic accumulating area animation
`RiemannSums`	Rectangles converging (n=4,8,16,32)
`ExponentialDecay`	∫e^(-x)dx = 1 with live area counter

Key Patterns

Pattern: Live Value Display

value_label = Tex(r"\text{Area} \approx 0.00")
value_num = value_label.make_number_changeable("0.00")
value_num.add_updater(lambda m: m.set_value(computed_area))

Pattern: Progressive Rectangle Refinement

for n in [4, 8, 16, 32]:
    new_rects = create_rectangles(n)
    self.play(ReplacementTransform(current_rects, new_rects))
    current_rects = new_rects

Run Commands

manimgl integration_visualization.py AreaUnderCurve -w
manimgl integration_visualization.py RiemannSums -w
manimgl integration_visualization.py ExponentialDecay -w

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