Generates synthetic datasets for triangle incenter construction. The agent must locate the incenter — the meeting point of the three internal angle bisectors and the center of the inscribed circle — and highlight which of several option labels 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-29 |
| Task | Triangle Incenter 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-29_triangle_incenter_construction_data-generator.git
cd Multi-29_triangle_incenter_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 displays a triangle and several labeled option markers (A, B, C, etc.).
[Rules]
1. The incenter is the point where the three internal angle bisectors of the triangle meet.
2. The incenter is also the center of the triangle's inscribed circle.
[Task] Generate a video animating the drawing of the three internal angle bisectors of the triangle to identify the incenter. Keep the construction lines visible, and animate a red highlight onto the single correct marker at their intersection. Leave all other markers unchanged and do not move the labels. Hold the final frame so only the true incenter is red.
 |
 |
 |
| Initial Frame Triangle + option labels |
Animation Three angle bisectors drawn step by step |
Final Frame Incenter found; correct option highlighted in red |
Construct the three internal angle bisectors of a given triangle and identify which of several option labels lies at their common intersection — the incenter, also the center of the largest inscribed circle.
- Triangle: Three labeled vertices forming an arbitrary triangle.
- Angle bisectors: From each vertex, draw the line bisecting the interior angle.
- Concurrence: All three bisectors meet at a single point — the incenter — by classical theorem.
- Option labels: A, B, C, D candidate points placed near the expected incenter.
- Solver: Closed-form intersection of two angle-bisector lines.
- Always interior: Unlike the orthocenter, the incenter always lies strictly inside the triangle, regardless of triangle type.
- Equidistance characterization: The incenter is the unique point equidistant from all three sides — a metric, not topological, criterion.
- Three-way concurrence: A correct selection must be at the meeting of all three bisectors, ruling out two-bisector-only positions.
- Visible construction: Each bisector renders as a separate animation phase, with the incenter emerging at their concurrence.
data/questions/Multi-29_triangle_incenter_construction_data-generator_task/Multi-29_triangle_incenter_construction_data-generator_00000000/
├── first_frame.png # Triangle + option labels
├── final_frame.png # Bisectors drawn + incenter marked
├── 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
incenter angle-bisector inscribed-circle geometric-construction concurrence multiple-choice multi-step-reasoning
Part of the 36-Task Long-Horizon Multi-Step Reasoning Benchmark.