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# On mesh

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### On mesh

1. 1. Research On MeshThenraja VettivelrajDepartment Of Computer ScienceSwansea UniversityM.Sc, Department of Computer Science, Department of Computer Science, Swansea University
2. 2. Topics Introduction “Mutual Tessellation” “Mesh Optimization” “Progressive Mesh” Energy Function Applications and Conclusion. ReferencesM.Sc, Department of Computer Science, Swansea University
3. 3. Introduction Graphics• Graphics has its necessity in all the fields and nowadays the people wantthe graphics to be so realistic.• Since it helps to analyze the data and also interact with the people itplays a vital role.• Examples in video games, cinemas, Technology Note: The centered equations and images are copied from thesource file for time consumption.M.Sc, Department of Computer Science, Swansea University
4. 4. Aim Aim• Our Ultimate aim is to construct a Mesh M from the given set of datapoints Mesh M0 scattered in three dimensions, where the topology of themesh M0 remains the same in Mesh M. The result Mesh M has to fit thedata well and also we have to reduce the number of vertices.• Concentrating on the geometry and topology of the image alone notsufficient henceforth we have to take care of the overall appearance.• In [5] they have given that how to construct a surface from the givenunorganized points. An algorithm to get the topology from theconstructed surface and from that how to get the rough geometricalsurface has been discussed in [6].M.Sc, Department of Computer Science, Swansea University
5. 5. Research On Mesh Initially Greg Turk [1] introduced the concept “Mutualtessellation”. By using this procedure we can represent thesame object in different level of detail which is very muchhelpful for achieving higher frame rates. The paper "Mesh optimization" by Hugues Hoppe et al [2]talks about minimizing the number of triangles from a initialdense triangular mesh. Goal(Mesh Optimization):Efficient, Lossless and Continuous resolution of the imagewith minimum number of triangles. Challenges(Mesh Optimization):Complex triangle meshes, Transmission bandwidth,Storing capacities and Rendering performance.M.Sc, Department of Computer Science, Swansea University
6. 6. Research On Mesh “Hugues Hoppe” [3] introducing the concept of "Progressive meshes".In addition to the mesh optimization here we are also taking care of theoverall appearance by the scalar (colour, normal and texturecoordinates) and discrete attributes (material identifier). Challenges(Progressive Mesh)• Mesh Simplification-Created meshes optimized for rendering efficiency.• Level-of-detail (LOD) approximation-To improve efficiency it isnecessary to define the different versions of the model in differentdetails• Progressive transmission-Mesh M0 is first transferred followed byincrements . Needs additional time for sending successive LOD.• Mesh Compression-Mesh Simplification and Minimize the space tostore.• Selective refinement-Details added in only desired areas.M.Sc, Department of Computer Science, Swansea University
7. 7. Research On Mesh Solution• For these drawbacks we have two solutions.First send coarser form M0 followed by n levels of detail. Inorder to refine into original mesh M=Mn.Hence the PM contains the information from M0, M1, M2,…Mn.• Preserving overall appearance by its discrete (material identifier)and scalar attributes such as colour, normal and texture coordinatesM.Sc, Department of Computer Science, Swansea University
8. 8. Mesh Optimization Definition of a Mesh• According to [4] "A graphics object that is composed entirely of polygons thathave common vertices and edges". Mesh Optimization• Mesh simplification algorithm can also be considered here because it also speaksabout the reducing in number of faces in a congested mesh while slightly disturbingthe shape with reference to Turk [7] and Schroeder et al. [8].• The exchange between geometric fit and compact representation is controlled via auser controlled parameter Crep. Increase in the value of Crep results in fewertriangles.Figure1:mesh simplification.M.Sc, Department of Computer Science, Swansea University
9. 9. Research On Mesh Meshes in computer graphics• In computer graphics we are representing the objects as trianglemeshes.• Expression for mesh M= (K, V, D, S) where K specifies the connectivityof vertices, edges, faces and where V denotes the set of vertices {V1,V2,….Vm} in the shape of the mesh R3, scalar attributes are colour (r, g, b),normal(nx, ny, nz) and texture coordinates (u, v). And discrete attributes.A corner is represented as (v,f ).Figure 2. Example of mesh representation with a single faceM.Sc, Department of Computer Science, Swansea University
10. 10. Mesh Representation Progressive Mesh Representation• Edge collapse is sufficient in simplifying the edges. Edge swap and the Edge splitis only in surface reconstruction and so here the Edge collapse is enough.• The Vsplit contains information about how to split the edges. By transferring intoecol we can compress the mesh and can store it in an efficient manner. Below thedescription how to make the edge collapse.Figure 4.a, b: Sequence of edge collapse and its resultM.Sc, Department of Computer Science, Swansea University
11. 11. Research On Mesh Geomorphs• In a progressive mesh representation the geomorphs can be formedbetween any two meshes.• Consider the finer Mesh Mfand a coarser Mesh Mcand this case thegeomorphs lies between 0 <= C < f <= n, where each Mfwill be having aunique mapping in Mcand this is called Surjective map Ac.• For proper resolution we will get the image slowly. Imagine an image,if we focus it then the image will keep on changing slowly until it getsthe desired image, it won’t change in quick frames. Progressive Transmission and Mesh Compression• In the progressive transmission first the compact Mesh M0 is transmittedfirst followed by vspliti records until the original mesh M is recovered.• Instead, of storing all the index vertices (si,li,ri) of vspliti just store the sialone and in the remaining 5 bits store the remaining.M.Sc, Department of Computer Science, Swansea University
12. 12. Research On Mesh Selective refinement• Supported by progressive Mesh• Details will be added only in desired areas.• Can travel in low level bandwidth.• Consider the application supply a callback function REFINE (v) that returns aBoolean function that what the neighbour mesh V supposed to do. The intialmesh Mcis refined by iterating the list (Vsplitc,…….Vsplitn-1)but only Vspliti (si,li,ri,Ai) if1) All three vertices present in the mesh {Vsi,Vli,Vri} and2) REFINE (Vsi) is trueFigure 5. Selective refinement for terrain(Using conditions 1 and 2)M.Sc, Department of Computer Science, Swansea University
13. 13. Energy Function Energy Function• The energy metric E (M) is defined as M= {K,V,D,S} with respect to the original M• E(M)=Edist(M)+Espring(M)+Escalar(M)+Edisc(M) Preserving surface geometry• Mesh M= (K,V) minimizes the energy functionE(K,V)=E dist (K,V) + E rep (K) + E spring (K,V)• The distance energy E dist is as follows• This E dist + E rep does not produce the desired result, because it produces somespike regions.Figure 6. c) Out of phase I(M0) d)Optimization without Espring.M.Sc, Department of Computer Science, Swansea University
14. 14. Energy function Scalar attributes The scalar attribute Escalar for vertices is defined as• the range constraints the (r,g,b) lies between 0 and 1. Discontinuity Curves• That is the discrete face attributes like material identifier and the scalarattributes have the problems in identifying the shadow boundaries. Theywould not be sharp in some cases which are supposed to be sharp andvice versa and we come to know that because the edge collapse we aredoing will change the topology of the mesh. Hence forth we areintroducing the new energy term Edisc which will overcome theproblems that we are facing.M.Sc, Department of Computer Science, Swansea University
15. 15. Applications and Conclusion ApplicationsThis mesh optimization, retiling polygonal model andprogressive meshes technique has given new dimensions inmedical areas, mainly in scans. And also in the graphics field ithas reduced the manual work. ConclusionAnd hence by minimizing the energy formula we are achievingour goals.M.Sc, Department of Computer Science, Swansea University
16. 16. References• [1] Greg Turk. Re-tiling polygonal surfaces. Computer Graphics (SIGGRAPH ’92Proceedings), 26(2):55–64, July 1992.• [2] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle. Surfacereconstruction from unorganized points. Computer Graphics (SIGGRAPH ’92Proceedings), 26(2):71–78, July 1992.• [3] Hugues Hoppe, Progressive Meshes, Microsoft Research.• [4]Computer graphics dictionary By Roger T. Stevens.• [5] T. DeRose, H. Hoppe, T. Duchamp, J. McDonald, and W.Stuetzle.Fitting ofsurfaces to scattered data. SPIE, 1830:212–220, 1992• [6] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle. Surfacereconstruction from unorganized points. Computer Graphics (SIGGRAPH ’92Proceedings), 26(2):71–78, July 1992.• [7] Greg Turk. Re-tiling polygonal surfaces. Computer Graphics (SIGGRAPH ’92Proceedings), 26(2):55–64, July 1992.• [8] William Schroeder, Jonathan Zarge, and William Lorensen. Decimation oftriangle meshes. Computer Graphics (SIGGRAPH ’92 Proceedings), 26(2):65–70,July 1992.M.Sc, Department of Computer Science, Swansea University
17. 17. Thank YouM.Sc, Department of Computer Science, Swansea University