Circle-Polygon Overlap Explorer

General overlap problem: Compute the overlap area between a circle of arbitrary radius and various polygon shapes (single or multiple polygons).
Drag the circle to explore. The app samples the overlap kernel A(cx, cy) = ∫1_S · 1_C(·−(cx, cy)) (i.e., the convolution of the shape and circle indicators at that offset). The 3D view is this same kernel over a grid of centers.

Touch: tap/drag the circle, pinch to zoom, two-finger pan, double-tap to finish drawing. Algorithm: compute segment–circle intersections, sum signed triangle areas for edge portions inside the circle, and add circular sector areas for arc portions inside the shape. Switch to boundary mode to sum arc lengths instead of areas—the highlighted arc labels show each contributing perimeter segment.

Shape Type:

Square Half-Side: 1.00

Rectangle Half-Width: 1.50

Rectangle Half-Height: 1.00

Polygon Radius: 1.00

Vertices (JSON):

Circle Radius (R): R = 0.50

Display Scale (Zoom): 200

Pan X: 0.00

Pan Y: 0.00

3D Resolution: 120

3D Auto-Rotate:

Show Grid:

Show Domain Regions:

Show Debug:

Calculation Mode:

Arc Length Labels:

Polygon List

Use the shape controls to edit the highlighted polygon. Add saves a new polygon with its own color.

Circle-Polygon Overlap Explorer

Per-Polygon Metrics

Interactive 2D View (Drag circle)

3D Surface Plot (Overlap vs position)