- Ordered sets of vertices, joined sequentially (and cyclically) by straight lines.
- Simple polygons
- convex or concave
- no line crossings
- no holes

Adding extra vertices removes the problems

- at the cost of adding degeneracies

- Polygons cover the surface of an object
- each polygon has a normal vector,
- usually pointing out
- polygonal "skin" is often called a mesh

Clipping a polygon reduces to clipping edges against

- lines in 2D
- planes in 3D

The clipping algorithm takes an ordered set of vertices [vi] and produces an ordered set of vertices [wi]. It relies on the following

- If one edge leaves the clipping region, a later edge must enter it.

The algorithm is

for each edge of clipping region for each edge of polygon // must be in sequence clip edge against region switch (result of clip) case "all inside" output leading vertex of edge case "all outside" do nothing case "cross edge leaving region" output crossing point case "cross entering region" output crossing point output leading vertex of edge

Exercise. Hand execute this algorithm on several cases to make sure that you understand exactly how it works.

Lines project to lines so projecting the vertices projects a polygon in 3D to a polygon on the view plane.

Sooner or later almost all polygons are converted to triangles

- there is not a unique way of doing so
- try to avoid long skinny triangles

Scan converting a polygon (in 2D)

sort vertices in direction perpendicular to the scan lines for each scan line if scan line contains the next vertex update and sort edge list inside = false for each pixel if on next edge inside = !inside if (inside) paint pixel

Exercise. Expand "update and sort edge list" to make this a working algorithm.

Exercise. Hand execute your expanded algorithm on a triangle to make sure that you understand how it works.

Exercise. Hand execute your expanded algorithm on a non-convex polygon.