Add spatialmath worksheet game for learning spatial transformations

[NickPPC]

Summary

Interactive CLI tool that teaches spatialmath transformations through guided exercises with 3D visualization. Inspired by the educational worksheet in a7c997a, this builds a 5-level progressive game covering Compose, PoseInverse, and PoseBetween with motion-tools visualization.

Changes

• spatialmath/worksheet/cmd/main.go: Entry point with --level N flag to jump to any level (1-5) or run all
• spatialmath/worksheet/game.go: Game engine with Question/Level types, interactive flow (show code, wait for user, reveal answer), and per-question color legend for the 3D visualizer
• spatialmath/worksheet/levels.go: 5 progressive levels:
  • Level 1: Pure translation (Compose adds vectors)
  • Level 2: Rotation from origin (orientation affects translation direction)
  • Level 3: Compose with orientations (non-commutativity, PoseBetween)
  • Level 4: Full 3D composition (multi-axis, PoseInverse)
  • Level 5: Practical robotics scenarios (forward kinematics, frame chains)
• spatialmath/worksheet/format.go: Pose/point/orientation display helpers with aggressive float rounding for clean output
• spatialmath/worksheet/visualize.go: Motion-tools integration drawing asymmetric 10x20x30 boxes (blue/green/yellow inputs, red result, white origin) so orientation is visually unambiguous

Testing

• go build ./spatialmath/worksheet/cmd compiles cleanly
• go vet ./spatialmath/worksheet/... passes
• go run ./spatialmath/worksheet/cmd — run all levels interactively
• go run ./spatialmath/worksheet/cmd --level 2 — jump to a specific level
• All answers are computed from real spatialmath calls, guaranteeing correctness
• Visualization degrades gracefully to text-only when motion-tools is not running

Claude Code Prompts Used

• "I would like to create a small Go command to play an educational game to learn about rdk's spatialmath library"
• "We should visualize all the answers using the motion-tools client. We should create a box with dimensions 10, 20, 30 so people can easily see which way the pose is pointing"
• "The game should explain which box corresponds to which situation"
• "For level 1 question 1 we seem to be giving the explanation of the answer as part of the question / For level 1 question 4 the visualizer was cleared before I could see the results"

🤖 Generated with Claude Code

[github-actions]

Availability

Scene #	viamrobotics:main	viamrobotics:worktree-spatial-math-worksheet-game	Percent Improvement	Health
1	100%	100%	0%	➖
2	100%	100%	0%	➖
3	100%	100%	0%	➖
4	100%	100%	0%	➖
5	100%	100%	0%	➖
6	100%	100%	0%	➖
7	100%	100%	0%	➖
8	100%	100%	0%	➖
9	100%	100%	0%	➖
10	100%	100%	0%	➖
11	100%	100%	0%	➖

Quality

Scene #	viamrobotics:main	viamrobotics:worktree-spatial-math-worksheet-game	Percent Improvement	Probability of Improvement	Health
1	1.31±0.00	1.31±0.00	0%	51%	➖
2	0.94±0.01	0.94±0.01	0%	56%	➖
3	6.13±0.00	6.13±0.00	-0%	50%	➖
4	1.98±0.27	1.98±0.27	0%	50%	➖
5	8.78±1.87	8.78±1.87	-0%	50%	➖
6	9.33±2.99	8.94±2.48	4%	54%	➖
7	1.95±0.38	1.95±0.38	0%	50%	➖
8	0.94±0.01	0.94±0.01	0%	55%	➖
9	4.54±0.41	4.54±0.41	-0%	50%	➖
10	12.63±0.03	12.63±0.03	-0%	50%	➖
11	0.62±0.00	0.62±0.00	-0%	49%	➖

Performance

Scene #	viamrobotics:main	viamrobotics:worktree-spatial-math-worksheet-game	Percent Improvement	Probability of Improvement	Health
1	0.02±0.00	0.02±0.00	8%	75%	➖
2	0.03±0.00	0.03±0.00	3%	57%	➖
3	0.02±0.00	0.02±0.01	-18%	37%	➖
4	0.29±0.05	0.28±0.03	6%	62%	➖
5	1.30±0.16	1.24±0.21	4%	58%	➖
6	1.54±0.40	1.51±0.41	2%	52%	➖
7	0.75±0.09	0.72±0.09	4%	60%	➖
8	0.03±0.00	0.03±0.00	16%	88%	✅
9	1.30±0.25	1.22±0.23	6%	59%	➖
10	3.53±0.39	3.54±0.41	-0%	50%	➖
11	0.61±0.06	0.56±0.08	8%	69%	➖

The above data was generated by running scenes defined in the motion-testing repository
The SHA1 for viamrobotics:main is: 34f56ff99b6db31130a351e0791da3dc0fabb01c
The SHA1 for viamrobotics:worktree-spatial-math-worksheet-game is: 34f56ff99b6db31130a351e0791da3dc0fabb01c

• 11 samples were taken for each scene