Calculator Inputs
Example Data Table
| Label | X | Y | Weight | Meaning |
|---|---|---|---|---|
| A | 1 | 1 | 1.0 | Base influence point near the lower left. |
| B | 4 | 2 | 1.3 | Higher weight expands its influence under weighted mode. |
| C | 2 | 5 | 0.9 | Slightly weaker influence near the upper middle. |
| D | 6 | 6 | 1.1 | Upper right point creating clipped corner regions. |
| E | 7 | 3 | 0.8 | Right-side point with modest dominance. |
Formula Used
A Voronoi region assigns each location to the nearest point under a chosen distance rule.
For site i, the region is
Rᵢ = {(x,y) : sᵢ(x,y) ≤ sⱼ(x,y) for all j}.
Distance Functions
- Euclidean:
d = √((x-xᵢ)² + (y-yᵢ)²) - Manhattan:
d = |x-xᵢ| + |y-yᵢ| - Chebyshev:
d = max(|x-xᵢ|, |y-yᵢ|)
Weighted Modes
- Unweighted:
sᵢ = dᵢ - Distance ÷ Weight:
sᵢ = dᵢ / wᵢ - Power Weighted:
sᵢ = (x-xᵢ)² + (y-yᵢ)² - wᵢ²
Grid Approximation
This calculator evaluates a regular grid inside the bounding box. Each grid-center is assigned to one site, then clipped region statistics are estimated using the winning cell count.
- Cell area:
ΔA = ((xmax-xmin)/Gx) × ((ymax-ymin)/Gy) - Region area:
Aᵢ ≈ nᵢ × ΔA - Region share:
Shareᵢ ≈ 100 × nᵢ / (Gx × Gy) - Region centroid:
Cᵢ ≈ (Σxk / nᵢ, Σyk / nᵢ)
How to Use This Calculator
- Enter at least two points, one per line.
- Add labels and weights if you want readable names or weighted influence.
- Set the X and Y bounds that clip the diagram region.
- Choose a distance metric based on your spatial model.
- Pick grid resolution. Higher values give smoother estimates but require more processing.
- Submit the form to view the region plot, area shares, centroids, neighbors, and boundary contact.
- Use the export buttons to save summary data as CSV or PDF.
Frequently Asked Questions
1. What does this calculator measure?
It estimates clipped Voronoi regions inside a selected bounding box. You get area share, centroid, nearest neighboring site, boundary contact, and an interactive plot.
2. Is this an exact polygon solver?
No. It uses a grid approximation. Higher grid counts improve smoothness and make area and centroid estimates closer to exact clipped Voronoi geometry.
3. When should I use weighted mode?
Use weights when some points should exert stronger influence than others. This is useful for service reach, facility strength, or weighted spatial competition models.
4. Which distance metric is best?
Euclidean fits ordinary geometric distance. Manhattan fits grid-like street movement. Chebyshev fits square-step movement where the largest coordinate change dominates.
5. Why do some regions touch the boundary?
The diagram is clipped to your chosen box. A region touching the box edge means its influence extends to the clipping border within the selected study area.
6. How should I choose grid resolution?
Start around 60 by 60 or 70 by 70. Increase it when you need smoother boundaries or more stable area estimates. Lower values calculate faster.
7. Can duplicate or very close points cause issues?
Yes. Duplicate points or nearly identical coordinates can create tie-heavy regions. The calculator breaks ties by first match, so distinct coordinates are recommended.
8. What do the exports include?
CSV export contains the summary table. PDF export creates a compact report with settings and region statistics, which is useful for documentation or sharing.