Tessellation. Tessellation in 2D- We introduce 2D Tessellation because it's usefulin 3D mesh processing Polygons can arrive in many different forms, andmay have to be split into more tractableprimitives, such as convex polygons, triangles orquads, this process is called tessellation. If thepolygon is split into triangles, this process iscalled triangulation(三角化)
Tessellation • Tessellation in 2D – We i d 2 ll i b i ’ f l introduce 2D Tessellation because it’s useful in 3D mesh processing – Polygons can arrive in many different forms, and may p have to be split into more tractable primitives, such as convex polygons, triangles or q,p uads this process is called tessellation. If the polygon is split into triangles, this process is called triangulation( called triangulation(三角化)
Tessellation.Various types of tessellation The leftmost polygon is not tessellated. Thenext is partitioned into convex regions, thenext is triangulated, and the rightmost isuniformly meshed
Tessellation • Various types of tessellation. • The leftmost polygon is not tessellated The The leftmost polygon is not tessellated. The next is partitioned into convex regions, the next i t i l t d d th i ht t i t is triangulated, and the rightmost is uniformly meshed
Tessellation: A basic tessellation method- Examine eachline segment between any two givenvertices on a polygon and see if it intersects oroverlaps any edge of polygon.- If it does, the line segment cannot be used to split thepolygon, so examine the next possible pair of points,else split the polygon into two parts by this segmentand triangulate the new polygons by the samemethod.inefficient
Tessellation • A basic tessellation method – Examine each line segment between any two given Examine each line segment between any two given vertices on a polygon and see if it intersects or overlaps any edge of polygon overlaps any edge of polygon. – If it does, the line segment cannot be used to split the pol gon so e amine the ne t possible pair of points polygon, so examine the next possible pair of points, else split the polygon into two parts by this segment and t i l t th l b th d triangulate the new polygons by the same method. – inefficient
Tessellation: Another tessellation method: ear clipping- First, find the ears over the polygon, that is , tolook at all triangles with vertex indices i,i+ l,i+2(mod n) and check line segment i,i+2 does notintersect any polygon edges. If so, then triangle i+1 forms an ear. Each earavailable is removed from the polygon, and thetriangles at vertices i and i+2 are re-examined tosee they are ears or not
Tessellation • Another tessellation method: ear clipping – Fi fi d h h l h i First, find the ears over the polygon, that is , to look at all triangles with vertex indices i,i+1,i+2 ( d) mo n and h k li d check line segment ii 2 , + does not intersect any polygon edges. – If so, then triangle i+1 forms an ear. Each ear available is removed from the polygon, and the triangles at vertices i and i+2 are re-examined to see they are ears or not
Tessellation T-vertices-T-vertex: Appear when joining flatsurfaces where two models' edge meet, but do notshare all vertices along them.? Even though the edges should theoretically meetperfectly, the renderer does not have enoughprecision in representing vertex locations on thescreen
Tessellation • T-vertices – T-vertex • Appear when joining flat surfaces where two models’ edge meet, but do not share all vertices along them. • Even though the edges should theoretically meet perfectly, the renderer does not have enough preci i i ti t l ti th ision in representing vertex locations on the screen