Billiard-Table Geometry: Polygonal Piecewise Path Construction

This example demonstrates a billiard-style motion path on a rectangular “table” region, where the ball’s travel is represented as a piecewise polyline produced by repeated geometric constructions (reflections/segment connections). It highlights core ideas from plane geometry, including segmented line/path building, point and segment construction, and an iterative/sequence-based generation of key points that form the overall trajectory. Construction highlights: Polygon is used to draw the table boundary, while PolyLine builds the resulting path segments; Sequence generates multiple points automatically for iterative steps (e.g., P1–P4, Q1–Q4 and other indexed points); Point objects mark all constructed vertices; additional geometric primitives (circles/lines such as c1, c2 and l, m, n, o, plus direction/auxiliary lines and vectors like l1, l2, q1–q4, L) control intersection locations and the orientation of successive segments. Suitable for high school to early undergraduate learners, and useful for teaching algorithmic geometry construction and iterative trajectory visualization.