Generates synthetic datasets for triangle circumcenter construction. The agent must locate the circumcenter — the meeting point of the three perpendicular bisectors of the sides and the center of the circumscribed circle — and identify which of several candidate markers coincides with it.
Each sample pairs a task (first frame + prompt describing what needs to happen) with its ground truth solution (final frame showing the result + video demonstrating how to achieve it). This structure enables both model evaluation and training.
| Property | Value |
|---|---|
| Task ID | Multi-30 |
| Task | Triangle Circumcenter Construction |
| Category | Constructive Geometry |
| Resolution | 1024×1024 px |
| FPS | 16 fps |
| Duration | varies |
| Output | PNG images + MP4 video |
# 1. Clone the repository
git clone https://github.com/VBVR-DataFactory/Multi-30_triangle_circumcenter_construction_data-generator.git
cd Multi-30_triangle_circumcenter_construction_data-generator
# 2. Create and activate virtual environment
python3 -m venv venv
source venv/bin/activate # On Windows: venv\Scripts\activate
# 3. Install dependencies
pip install --upgrade pip
pip install -r requirements.txt
pip install -e .# Generate 50 samples
python examples/generate.py --num-samples 50
# Reproducible generation with seed
python examples/generate.py --num-samples 50 --seed 42
# Custom output directory
python examples/generate.py --num-samples 100 --output data/my_dataset
# Without videos (faster, images only)
python examples/generate.py --num-samples 50 --no-videos| Argument | Description |
|---|---|
--num-samples |
Number of tasks to generate (required) |
--output |
Output directory (default: data/questions) |
--seed |
Random seed for reproducibility |
--no-videos |
Skip video generation (images only) |
[Scenario] The image shows a triangle and five small hollow circular markers placed nearby. Each marker stands for one candidate location.
[Rules]
1. The circumcenter is the common intersection point of the perpendicular bisectors of the three sides of the triangle.
2. Exactly one of the five markers lies at the true circumcenter.
[Task] Generate a continuous video animating the drawing of the perpendicular bisectors for all three sides of the triangle. Keep the construction lines visible, and visually single out the true circumcenter marker at their intersection (e.g., with a brief highlight, fill, pulse, or zoom) without explicitly labeling options by number or word. Hold the final frame.
 |
 |
 |
| Initial Frame Triangle + 5 candidate markers |
Animation Three perpendicular bisectors drawn step by step |
Final Frame True circumcenter marker singled out |
Construct the three perpendicular bisectors of the triangle's sides and identify which of five hollow circular markers lies at their common intersection — the circumcenter, also the center of the unique circle passing through all three vertices.
- Triangle: Three labeled vertices forming an arbitrary triangle.
- Perpendicular bisectors: For each side, construct the line that passes through its midpoint at a right angle.
- Concurrence: All three bisectors meet at a single point — the circumcenter — by classical theorem.
- Candidates: Five hollow circular markers placed near the expected circumcenter (one true, four close distractors).
- Solver: Closed-form intersection of two perpendicular-bisector lines.
- Equidistance from vertices: The circumcenter is the unique point equidistant from all three vertices (radius of the circumscribed circle).
- Position varies dramatically with triangle type: Acute → inside, right → midpoint of hypotenuse, obtuse → outside the triangle.
- Three-way concurrence: A correct marker must be on all three bisectors, not just two.
- Visible construction: Each bisector renders as a separate animation phase, with the circumcenter emerging at their concurrence.
data/questions/Multi-30_triangle_circumcenter_construction_data-generator_task/Multi-30_triangle_circumcenter_construction_data-generator_00000000/
├── first_frame.png # Triangle + 5 candidate markers
├── final_frame.png # Bisectors drawn + circumcenter highlighted
├── prompt.txt # Task instruction
├── ground_truth.mp4 # Animation of stepwise construction
└── question_metadata.json # Standardized VBVR task metadata
File specifications:
- Images: 1024×1024 PNG format
- Video: MP4 format, 16 fps, H.264 + yuv420p
- Metadata: VBVR canonical schema with
task_id,vbvr_task_code,media,parameters
circumcenter perpendicular-bisector circumscribed-circle geometric-construction concurrence multiple-choice multi-step-reasoning
Part of the 36-Task Long-Horizon Multi-Step Reasoning Benchmark.