video/.agents/skills/manim-composer/references/scene-examples.md

Scene Examples

Example scene breakdowns from 3b1b-style videos.

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Example 1: Explaining the Dot Product

Scene 1: The Question

Duration: ~30 seconds Purpose: Hook the viewer with the mystery

Visual Elements

• Two vectors a and b drawn as arrows
• The dot product formula: a · b = |a||b|cos(θ)
• Question mark animation

Content Open on two vectors. Show the formula. Pose the question: "Why does multiplying components and adding them give you something related to the angle between vectors?"

Narration Notes Tone: curious, slightly puzzled. Emphasize that the formula seems arbitrary.

Technical Notes

• Use Arrow for vectors
• MathTex for formula
• Indicate() on the cos(θ) term

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Scene 2: Geometric Interpretation

Duration: ~90 seconds Purpose: Show projection interpretation

Visual Elements

• Vector a (horizontal, blue)
• Vector b (angled, green)
• Projection of b onto a (dashed line)
• Right angle marker
• Length labels

Content Show that a · b equals |a| times the projection of b onto a. Animate the projection dropping down. Show this equals |a||b|cos(θ) geometrically.

Narration Notes "The dot product measures how much one vector goes in the direction of another."

Technical Notes

• DashedLine for projection
• RightAngle mobject
• animate.rotate() for showing different angles

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Scene 3: Numeric Connection

Duration: ~60 seconds Purpose: Connect geometry to algebra

Visual Elements

• Coordinate grid
• Vector a = [a₁, a₂]
• Vector b = [b₁, b₂]
• Components highlighted

Content Show vectors on grid with components labeled. Demonstrate why a₁b₁ + a₂b₂ equals the geometric interpretation. Use specific numbers.

Narration Notes Walk through calculation slowly. "Let's see why the algebra matches the geometry."

Technical Notes

• NumberPlane or Axes
• Brace for component labels
• TransformMatchingTex for equation steps

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Example 2: Introduction to Fourier Series

Scene 1: The Hook

Duration: ~45 seconds Purpose: Show the surprising result

Visual Elements

• A square wave (sharp corners)
• Sum of smooth sine waves
• Morphing animation between them

Content "You can build a square wave—something with sharp corners—from perfectly smooth sine waves." Show the result first, then promise to explain how.

Narration Notes Tone: wonder, slight disbelief. This should feel surprising.

Technical Notes

• ParametricFunction for waves
• Transform animation for the morph
• Consider showing 1, 3, 5 terms building up

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Scene 2: Building Blocks

Duration: ~120 seconds Purpose: Introduce sine waves as basis

Visual Elements

• Single sine wave
• Frequency visualization (faster oscillation)
• Amplitude visualization (taller/shorter)
• Phase visualization (shifting left/right)

Content Introduce the three parameters: frequency, amplitude, phase. Show each one separately, then combine.

Narration Notes Go slow. "A sine wave has three knobs we can adjust..."

Technical Notes

• ValueTracker for animating parameters
• Updaters to make wave respond to trackers
• Labels for each parameter

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Scene 3: Superposition

Duration: ~90 seconds Purpose: Show waves can be added

Visual Elements

• Two sine waves (different colors)
• Their sum (third color)
• Point-by-point addition visualization

Content Show that adding waves means adding their heights at each point. Demonstrate with two specific frequencies combining.

Narration Notes "Adding waves is simple—at each point, just add the heights."

Technical Notes

• VGroup of three function graphs
• Vertical lines showing addition at specific x values
• Animate the addition happening

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Example 3: Matrix as Linear Transformation

Scene 1: Grid Transformation

Duration: ~60 seconds Purpose: Visual foundation

Visual Elements

• 2D coordinate grid (NumberPlane)
• Basis vectors i-hat and j-hat (colored arrows)
• Grid lines transforming

Content Show a grid. Highlight i-hat (1,0) and j-hat (0,1). Apply a transformation—watch the entire grid move while tracking where basis vectors land.

Narration Notes "Watch what happens to the grid when we apply this transformation. Notice how every point moves."

Technical Notes

• NumberPlane with visible grid lines
• apply_matrix() method
• Keep basis vectors visually distinct

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Scene 2: Basis Vectors Determine Everything

Duration: ~90 seconds Purpose: Key insight

Visual Elements

• Transformed i-hat and j-hat
• Arbitrary vector v as combination
• v = xi + yj visualization

Content Show that knowing where i-hat and j-hat land tells you where ANY vector lands. Because v = xi + yj, the transformed v = x(new i) + y(new j).

Narration Notes "Here's the key insight..." Build anticipation before the reveal.

Technical Notes

• Vector addition animation (tip-to-tail)
• Scaling animation for coefficients
• TransformMatchingShapes for the combination

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Scene Transition Patterns

Zoom Focus

Full scene → Zoom into detail → Explain → Zoom out

Side-by-Side Build

Empty left | Empty right
Add to left | Compare
Add to right | Connect them

Transform Chain

Object A → Transform → Object B → Transform → Object C
(Maintain visual continuity throughout)

Reset and Rebuild

Complex scene → Clear/fade most → Focus on one element → Build new complexity