Documentation

Filling Rules

Filling rules determine how the interior of a shape is defined. iOverlay supports 4 filling rules:

  • Even-Odd: A point is inside the shape if a ray drawn from the point crosses the shape's edges an odd number of times.
  • Non-Zero: A point is inside the shape if the total winding number around the point is non-zero.
  • Positive: Only regions with a positive winding number are considered inside.
  • Negative: Only regions with a negative winding number are considered inside.

Overlay Rules

Overlay rules define how two shapes interact during Boolean operations:

  • Union (A ∪ B): Combines the areas of both shapes.
  • Intersection (A ∩ B): Retains only the overlapping area of both shapes.
  • Difference (A - B): Subtracts the area of shape B from shape A.
  • Exclusion (A ⊕ B): Combines the areas of both shapes but excludes the overlapping region.

Contours

Contours represent the boundaries of shapes and are categorized as:

  • Outer Contours: Define the external boundary of a shape, ordered in a counterclockwise direction.
  • Inner Contours (Holes): Define holes within a shape, ordered in a clockwise direction.

Overlay Graph

The overlay graph is a data structure that represents the intersections and overlays of two geometric objects. It is constructed by dividing all segments of the object contours into non-intersecting parts, where segments can only touch at their endpoints. Each segment in the graph contains information about its association with the original shapes, facilitating efficient Boolean operations.

Extract Shapes

After applying Boolean operations, the resulting shapes are extracted through a series of steps:

  1. Build Contour: Starting from the leftmost node, the algorithm traverses connected segments to form contours, marking each segment as visited to prevent duplication.
  2. Define Contour: Determines whether a contour is outer or inner based on its orientation and position.
  3. Matching Contours: Associates inner contours with their corresponding outer contours by analyzing spatial relationships.