tworectangle

Tworectangle is a geometric term referring to the union of two closed rectangles in the plane whose interiors are disjoint and whose boundaries meet along a nonempty line segment. In this usual definition, the two rectangles touch each other along a shared side of positive length, but do not overlap in area.

If the two rectangles share a full side and lie on opposite sides of that side, their union can be a larger rectangle. In general, the resulting shape is an orthogonal polygon that may be convex only in the special case of forming a larger rectangle; otherwise the figure is typically non-convex, often resembling an L-shape or other simple orthogonal outline.

Key properties

- Area: the area of a tworectangle is the sum of the areas of its two constituent rectangles.

- Perimeter: if L denotes the length of the shared boundary segment, the outer perimeter is P = P1 + P2 − 2L, where P1 and P2 are the perimeters of the two rectangles. This reduces to the perimeter of a single larger rectangle when the union is itself a rectangle.

- Centroid: the centroid of the tworectangle is the area-weighted average of the rectangles’ centroids: C = (A1*C1 + A2*C2) / (A1 + A2), where Ai and Ci are the area and centroid of rectangle i.

- Representation: a tworectangle can be described by the coordinates of its two rectangles, or by their widths, heights, and relative position along the shared side.

Variants and usage

- Rectilinear orientation: most discussions assume axis-aligned rectangles, common in tiling and computer graphics.

- Applications include tiling problems, layout design, and computational geometry procedures for union and boundary computation. See also rectangles, polygon union, and orthogonal polygons.