Chap 10. Geometric Level of Detail 그래픽스 연구실 2001.11.27 김수균 Graphics Lab

Introduction Concept of LOD Sprites and Billboards Discrete Level of Detail Continuous Level of Detail Simplification Using Quadric Error Metric The algorithm Construction of the error metric Simplification at run time Selecting Surface Attribute Graphics Lab

Switching between models of varying degrees of resolution Concept of LOD Switching between models of varying degrees of resolution Faces :69,459 Faces:2,502 Faces:251 Faces:76 Graphics Lab

Concept of LOD The switching is usually associated with distance from eye point to object #F:76 #F:251 #F:2,502 #F:69,459 Graphics Lab

Sprites and Billboards Sprites (sometimes called imposters) prerendered images of three-dimensional objects Easy to spot in the rendering If they represent objects that are close to the eye point or if the eye point moves The visual anomaly associated with a moving eye point can be rectified in two ways First way is to have a set of prerendered images of the object calculated from a set of predefined eye points and orientations The second is to allow a single prerendered image to change orientation depending on eye point location and orientation (called a billboard) Graphics Lab

Discrete Level of Detail Discrete LOD advantage Simplicity of the implementation Simple programming models disadvantage Popping effect Massive CAD Models Super-detailed range scans Graphics Lab

Discrete Level of Detail Popping Effect Switch occurs during rendering it is usually noticeable and not very natural Reduce the Popping Morph between two consecutive models in the LOD sequence 2,000faces 10,000faces 50,000faces Pop Pop Graphics Lab

Continuous Level of Detail An alternative to discrete LOD is Continuous LOD CLOD algorithms Hoppe 1996 Garland and Heckbert 1997,1998 Cohen et al. 1996 Cohen, Olano, and Manocha 1998 Luebke and Erikson 1997 Lindstrom and Turk 1998 Graphics Lab

Continuous Level of Detail Advantage Reduce “Popping effect” Support progressive Progressive Meshes[Hoppe 97] Progressive Forest Split Compression[Taubin 98] Support View-dependent Graphics Lab

Continuous Level of Detail Vertex Decimation Removing a vertex and all triangles sharing it Then retriangulating the hole that produced by removal ( schroeder, Zarge, Lorensen 1992) Graphics Lab

Continuous Level of Detail Vertex Clustering Involves placing the mesh in a bounding box Partitioning that box into a lattice of small boses Collapsing all vertices in each small box into a single vertex, and removing Rossignac and Borrel 1993 Graphics Lab

Continuous Level of Detail Iterative edge contraction Replacing an edge and its two vertices by a single vertex Removing the triangles sharing that edge, and adjusting the connectivity information for the triangles adjacent to the ones removed (Hoppe 1996) Edge Contraction Graphics Lab

Continuous Level of Detail Simplification Using Quadric Error Metrics Garland and Heckbert 1997 Sum of squared distances A b c Graphics Lab

Continuous Level of Detail Quadric Form Optimal Position in the quadric Q1 Q2 Graphics Lab

Continuous Level of Detail Algorithm Select a set of candidate vertex pairs Assign a cost of contraction to each candidate Place all candidates in a heap keyed on cost with the minimum cost pair at the top Repeat until the desired approximation is reached Graphics Lab

Continuous Level of Detail Cessna Model Graphics Lab

Selecting Surface Attributes Normal vectors, texture coordinates, and colors New surface attributes must be selected for a contracted vertex Compute the barycentric coordinates of the new vertex with respect to the tetrahedron Normal vectors at contracted vertices can be computed Use the barycentric coordinate scheme By computing a weighted averages of the normals of the triangles sharing the new vertex Alternative is to view the unit-length normals as points on a sphere The minimal angle cone containing those points is computed and the axis the cone is used as the new normal a weighted averages of normals is not geometrically appealing Graphics Lab