Drawing 3‑D Vectors on a 2‑D Page

Overview

A short animation showing how to represent three‑dimensional vectors on a flat sheet using perspective, projection lines, and shading. The viewer sees the construction steps and a concrete example vector $\mathbf{v}=\langle 2,3,4\rangle$.

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Phases

#	Phase Name	Duration	Description
1	Intro	~3s	Title fades in, camera pans to a blank 2‑D coordinate plane with faint grid lines.
2	Axes Setup	~5s	Draw three mutually orthogonal axes (x, y, z) using isometric projection: x‑axis right‑down, y‑axis right‑up, z‑axis vertical. Labels appear briefly.
3	Projection Guidelines	~5s	From the origin, draw light‑gray guide lines indicating the projection of each axis onto the page (dashed).
4	Example Vector Construction	~10s	Step‑by‑step build of $\mathbf{v}=\langle 2,3,4\rangle$:

• Highlight the x‑component (2) along the x‑axis, then project a line parallel to the y‑z plane.
• Add the y‑component (3) along the y‑axis, project a line parallel to the x‑z plane.
• Add the z‑component (4) vertically.
• Connect the tip to the origin with a bold arrow, add a small arrowhead, and shade the vector body to suggest depth.
  | 5 | Final View & Caption | ~4s | Fade in a concise caption: “3‑D vector drawn with isometric projection”. Show the vector’s coordinates as a LaTeX label near the tip. |
  | 6 | Outro | ~3s | Fade out everything, leaving only the title for a brief moment, then black screen.

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Layout

┌───────────────────────────────────────┐
│               TOP AREA                 │
├───────────────────────┬───────────────┤
│                       │               │
│       LEFT AREA       │   RIGHT AREA  │
│  (Main 3‑D sketch)    │ (Optional    │
│                       │  brief notes)│
├───────────────────────┴───────────────┤
│               BOTTOM AREA              │
└───────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Title "Drawing 3‑D Vectors on a 2‑D Page"	Fades in at start of Intro, stays until Outro
Left	Central isometric diagram: axes, guide lines, and the example vector	Primary visual focus throughout all phases
Right	Small optional bullet list summarizing the steps (appears in Phase 4)	Fades in with the step description, fades out after Phase 5
Bottom	Caption and coordinate label for the vector	Appears in Phase 5, small font, fades out with Outro

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Notes

• Keep total runtime under 30 seconds (≈30 s as listed). Adjust individual phase lengths proportionally if needed.
• Use a muted pastel palette for guide lines; the final vector should be a bold, contrasting color (e.g., deep blue).
• No textual narration is required; all information is conveyed visually.
• The single Scene class will contain all phases sequentially using self.play and self.wait calls.
• All labels use LaTeX formatting, e.g., $\mathbf{v}=\langle 2,3,4\rangle$.