Mesh Simplification Using Quadric Error Metrics Sau Yiu Introduction: My final project was to implement mesh simplification. For each triangle, find its plane equation: i.e. Your cache administrator is webmaster. Please try the request again.

Copyright © 2016 ACM, Inc. I implemented most but not all of its features. Green edges can't be collapse because it would cause a normal flip on one of the surrounding triangles. Your cache administrator is webmaster.

ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.5/ Connection to 0.0.0.5 failed. Compute the optimal contraction target for each pair. Terms of Usage Privacy Policy Code of Ethics Contact Us Useful downloads: Adobe Reader QuickTime Windows Media Player Real Player Did you know the ACM DL App is Notes on the algorithm: On average, each edge contraction eliminates 2 faces.

morefromWikipedia Tools and Resources Buy this Article Recommend the ACM DLto your organization Request Permissions TOC Service: Email RSS Save to Binder Export Formats: BibTeX EndNote ACMRef Upcoming Conference: VRCAI '16 The number of target faces in the simplified model can be set. It is not designed to fix holes and it may even enlarge the holes. morefromWikipedia Residual (numerical analysis) Loosely speaking, a residual is the error in a result.

Computing the optimal contraction target for each pair is done by inverting part of the quadric matrix: My Program My program is almost an exact implementation of the algorithm described in Then construct a 4x4 matrix K for each triangle where: | a^2 ab ac ad | | ab b^2 bc bd | | ac bc c^2 cd | | ad Heckbert Carnegie Mellon University Published in: ·Proceeding SIGGRAPH '97 Proceedings of the 24th annual conference on Computer graphics and interactive techniques Pages 209-216 ACM Press/Addison-Wesley Publishing Co. Results I am very happy with the results of simplification.

Step 4: For each valid contraction pair, calculate its error/cost of contraction. Again we construct a 4x4 matrix Q for each vertex V where Q = sum of all Kp where peP(v) Step 3: In this algorithm I only use edge contraction. v1 and v2 are a valid contraction pair if and only if (v1, v2) is an edge. Your cache administrator is webmaster.

Select all valid pairs. This is in general not desirable. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections. morefromWikipedia Surface In mathematics, specifically in topology, a surface is a two-dimensional topological manifold.

Please try the request again. When an edge is collapsed, the quadrics should be unioned but as observed by [1], addition may add some imprecision but the benefits in terms of speed outweigh unioning the quadrics. The final results resemble the initial mesh very closely. It takes about 2 minutes to simplify the bunny from 69451 to 100 faces on a 1.6GHz computer, compared to 15 seconds achieved by Garland and Heckbert.

The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R Â¿ for example, the surface of a ball. Before any mesh simplification happens, a quadric or set of quadrics associated with a vertex will evaluate to 0 if the vertex location is evaluated using the quadric. Generated Tue, 25 Oct 2016 02:36:38 GMT by s_wx1087 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.7/ Connection Place all the pairs in a data structure sorted by minimum cost.

The plane equation is ax + by + cz + d = 0 where a2 + b2 + c2 = 1. find constants a,b,c,d such that : ax + by + cz + d = 0 where a^2 + b^2 + c^2 = 1. Link: Meshshop with simplification plugin Reference: Michael Garland and Paul S. The system returned: (22) Invalid argument The remote host or network may be down.

It is implemented in OpenGL. The system returned: (22) Invalid argument The remote host or network may be down. We use this notation: (v1, v2) à w which moves vertices v1 and v2 to a new position w, connects all their incident edges to v1, and deletes the vertex v2. Generated Tue, 25 Oct 2016 02:36:38 GMT by s_wx1087 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.8/ Connection

The system returned: (22) Invalid argument The remote host or network may be down. The normal of the triangle sets the orientation of the plane and one of the vertices in the triangle is used to find the offset. The ACM Guide to Computing Literature All Tags Export Formats Save to Binder Mesh Simplification using Quadric Error Metrics California Polytechnic State University, San Luis Obispo Jeremy Seeba What Your cache administrator is webmaster.

SIGN IN SIGN UP Surface simplification using quadric error metrics Full Text: PDF Get this Article Authors: Michael Garland Carnegie Mellon University Paul S. The following is a series of simplified models from 10000 to 1000 shown in different display modes in 1000 face increments. We use this notation: P(v) = set of planes which intersect at vertex v. The same model simplified to 1500 faces and displayed using the alternate edge visualization.

The speed of my program is relatively slow. New York, NY, USA ©1997 tableofcontents ISBN:0-89791-896-7 doi>10.1145/258734.258849 1997 Article Bibliometrics ·Downloads (6 Weeks): 26 ·Downloads (12 Months): 324 ·Downloads (cumulative): 4,155 ·Citation Count: 703 Recent authors with related The quadric Kp expressed in terms of a, b, c, and d is: Quadrics are associated with vertices and every applicable quadric is added to a vertex. Test results show that this approach can handle holes better. (and will run faster) This algorithm does not work well with mesh that has holes.

Heckbert. Generated Tue, 25 Oct 2016 02:36:39 GMT by s_wx1087 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection Please try the request again.