LIVEdataset aec-bench@releasetasks 552models 18last submission … · built …
electricalwith-tool

Ppm Calculation

Calculates CCTV pixel density at a target distance using horizontal camera resolution, sensor width, and lens focal length. The reduced pinhole-camera method estimates horizontal field of view, pixels per metre, and margin against a specified surveillance target density.

with-tool: The model is given an executable Python calculator script.

Standards

EN 62676-4IEC 62676-4

Tags

cameracctvdeterministicelectricalppmsecurity

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

  1. 01

    Template

    The reusable contract shown on this page.

  2. 02

    Scenario

    An archetype and site context are sampled.

  3. 03

    Difficulty tier

    Inputs may be hidden at harder tiers.

  4. 04

    Task prompt

    The model responds with the declared outputs.

Parameters

Inputs the model receives, and the outputs it is scored on.

Inputs

5 inputs

Always given

Included directly in every task prompt.

4

  • Horizontal pixels

    horizontal_pixels

    Horizontal camera resolution

    640 – 12000 px

  • Sensor width

    sensor_width_mm

    Camera sensor width

    2 – 25 mm

  • Lens focal length

    lens_focal_length_mm

    Lens focal length

    2 – 80 mm

  • Target distance

    target_distance_m

    Distance from camera to target plane

    1 – 200 m

Hidden at higher difficulty

Visible in easier tasks and withheld in one or more harder tiers.

1

  • Target ppm

    target_ppm

    Required pixel density target

    Hidden at hard difficulty.

    20 – 1000 px/m

Scored outputs

3 outputs

Horizontal field of view

horizontal_field_of_view_m

Horizontal field of view at the target plane

Scores if within ±3% of the reference value.

Pixels per meter

pixels_per_meter

Pixel density at target distance

Scores if within ±3% of the reference value.

Target ppm margin pct

target_ppm_margin_pct

Margin relative to target pixel density

Scores if within ±3% of the reference value.

Difficulty

Each template is sampled at three tiers. Harder tiers may hide inputs, forcing the model to infer them from the scenario description.

easy

All inputs given

Detection or recognition camera with all geometry given

medium

All inputs given

Mixed camera objectives and target densities

hard

Some inputs hidden

Target PPM hidden in the surveillance objective

Hidden inputs

  • Target ppmtarget_ppm

Prompt replacement text

Use the target pixel density implied by {{ archetype.description }}.

Task bundle

The exact instruction and parameter contract used to generate this task, pinned to the published library source.

/workspace

  • instruction.md
  • ppm-calculation_calc.py

Teal lines show Jinja input conditions, not task visibility policy. A line renders only when that input or tool is visible.

1You are a senior security and electrical systems engineer checking CCTV camera coverage.2 3## Problem4 5Calculate the horizontal field of view, pixels per metre, and margin against the target pixel density.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Horizontal resolution | {{ horizontal_pixels }} | px |12| Sensor width | {{ sensor_width_mm }} | mm |13| Lens focal length | {{ lens_focal_length_mm }} | mm |14| Target distance | {{ target_distance_m }} | m |15{% if target_ppm is defined %}16| Target pixel density | {{ target_ppm }} | px/m |17{% endif %}18{% if archetype_description is defined %}19 20### Site Context21 22{{ archetype_description }}23{% endif %}24 25{% if tool_available %}26## Available Tool27 28A CCTV PPM calculation tool is available at `/workspace/ppm-calculation_calc.py`. Run it with:29 30```bash31python3 /workspace/ppm-calculation_calc.py --help32```33{% endif %}34 35## Required36 37Calculate:38 391. Horizontal field of view in m402. Pixels per metre at the target plane413. Percentage margin relative to the target pixel density42 43## Constraints44 45- Use `horizontal_field_of_view = sensor_width x target_distance / focal_length`.46- Sensor width and focal length are both in mm, so their ratio is dimensionless.47- Use `pixels_per_meter = horizontal_pixels / horizontal_field_of_view`.48- Use `target_ppm_margin_pct = (pixels_per_meter / target_ppm - 1) x 100`.49 50## Output Format51 52Show your working in Markdown. At the end, include a JSON block with exactly these keys:53 54```json55{56 "horizontal_field_of_view_m": <numeric_value>,57 "pixels_per_meter": <numeric_value>,58 "target_ppm_margin_pct": <numeric_value>59}60```61 62Write your complete solution to `/workspace/output.md`.63

Scenario archetypes

Each generated task is drawn from one of these realistic scenario bands.

Site contexts ground each scenario in a real locale the model can use to infer hidden values.

Detection camera

detection_camera

Wide-angle detection camera

car-parksite-perimeter
Parameter ranges
horizontal_pixels
1280 – 3840
sensor_width_mm
4 – 8
lens_focal_length_mm
2.8 – 6
target_distance_m
10 – 80
target_ppm
25 – 80

Recognition camera

recognition_camera

Recognition camera at an access point

building-entrystation-gate
Parameter ranges
horizontal_pixels
1920 – 8000
sensor_width_mm
4 – 12
lens_focal_length_mm
6 – 25
target_distance_m
5 – 50
target_ppm
100 – 250

Identification camera

identification_camera

High-density identification camera

cash-officesecure-room
Parameter ranges
horizontal_pixels
3840 – 12000
sensor_width_mm
6 – 25
lens_focal_length_mm
12 – 80
target_distance_m
3 – 30
target_ppm
250 – 1000

Example task

building-entry-recognition-camera-preview — hard difficulty, some inputs hidden.

Recognition camera at an access point. building-entry. Required outputs: horizontal_field_of_view_m, pixels_per_meter, target_ppm_margin_pct

The model sees

Scenario context and visible inputs.

horizontal_pixels
1920 to 8000 px
sensor_width_mm
4 to 12 mm
lens_focal_length_mm
6 to 25 mm
target_distance_m
5 to 50 m

Executable tool: ppm-calculation_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Target ppm

    target_ppm

Stand-in text in the prompt

Use the target pixel density implied by {{ archetype.description }}.

The model must produce

The scored JSON answer schema.

{
  "horizontal_field_of_view_m": <number>,
  "pixels_per_meter": <number>,
  "target_ppm_margin_pct": <number>
}
  • horizontal_field_of_view_m · scored within ±3%
  • pixels_per_meter · scored within ±3%
  • target_ppm_margin_pct · scored within ±3%