Simplification（简化）. What is Mesh Simplification?- approximating a given input mesh with a lesscomplex but geometrically faithful representation
Simplification(简化 ) • What is Mesh Simplification? – approxi i i i h ih l imat ing a g iven input mes h w i t h a less complex but geometrically faithful representation
Simplification（简化）. Why do we need Mesh Simplification?- remove redundant(多余的) geometry·E.g. a flat region with many small, coplanar(共面的)triangles. Merging these triangles to large polygonscould decrease model's complexity.-reducemodel size· reduce the size to store or transmit it- improve run-time performance·simplificationcanbeessential(重要的）toefficientrendering (to be continued)
Simplification(简化 ) • Why do we need Mesh Simplification? – remove redd ( un dant (多余的 ) geometry • E.g. a flat region with many small, coplanar(共面的) triangles. Merging these triangles to large polygons could decrease model’s complexity. – reduce model size • reduce the size to store or transmit it. – improve run-time performance • simplification can be essential( simplification can be essential(重要的) to efficient ) to efficient rendering (to be continued)
Simplification（简化）generating levels of detail (LOD,层次细节)of objectsin a scene.Presenting distant(远的)objects withalower LOD and near object with a higher LODAnexample2,5022517669.451trianglestrianglestrianglestriangles1Managingmodel complexitybyvaryingthelevel ofdetallusedforrenderingsmallordistantobjectsPolygonalsimplificatlonmethodscancreatemultiplelevelsofdetallsuchasthese
Simplification(简化 ) • generating levels of detail (LOD,层次细节) of objects in a scene. Presentin g ( distant (远的 ) j ob ects with a lower LOD and near object with a higher LOD. • An example An example
Simplification（简化）·Topology(拓扑结构)- refers to the connected polygonal mesh's structure一 genus (亏格)·the number of holes in the mesh surface. For example, a sphere and a cube have a genus of zerowhile a torus(环) and a coffee cup have a genus of one- local topology of a face, edge, or vertex· refers to the connectivity of that feature's neighborhood
Simplification(简化 ) • Topology (拓扑结构 ) – ref h d l l h’ fers to t he connecte d po lygona l mesh’s structure – genus (亏格 ) • the number of holes in the mesh surface. • For example, a sphere and a cube have a genus of zero, while a torus( 环) and a coffee cup have a genus of one. – local topology of a face, edge, or vertex • refers to the connectivity of that feature’s neighborhood
Simplification(简化）·Topology(拓扑结构)- 2D manifold. if the local topology is everywhere equivalent to adisc.. In a triangle mesh manifold topology, exactly twotriangles share every edge, and every triangle sharesan edge with exactly three neighboring triangles-2Dmanifold with boundary(带边界的): permits boundary edges, which belong to only onetriangle
Simplification(简化 ) • Topology (拓扑结构 ) – 2 f ld D manifold • if the local topology is everywhere equivalent to a disc. • In a triangle mesh manifold topology, exactly two triangles share every edge, and every triangle shares an edge with exactly three neighboring triangles. – 2D manifold with boundary (带边界的 ) • permits boundary edges, which belong to only one triangle