<p>According to <a href="https://books.google.co.uk/books?id=8zX-2VRqBAkC&amp;printsec=frontcover&amp;dq=polygon%20mesh%20processing&amp;hl=en&amp;sa=X&amp;ved=0ahUKEwj6tK_o__XiAhWFY8AKHanSCBYQ6AEIKjAA#v=onepage&amp;q=polygon%20mesh%20processing&amp;f=false" rel="nofollow noreferrer">Polygon-Mesh-Processing</a>, section 7.2.2. paragraph "Error quadrics"</p>

<blockquote>
  <p>Error quadrics have major advantages regarding memory consumption and computational efficiency: each vertex <span class="math-container">$x$</span> stores a symmetric 4x4 matrix <span class="math-container">$Q$</span> only, and the error can efficiently be computed in constant time as <span class="math-container">$x^T Q x$</span> - no matter how many planes are associated to vertex <span class="math-container">$x$</span> during decimation. Because of this, error quadrics are one of the most frequently employed techniques in mesh decimation.</p>
</blockquote>

<p>The author of the reference I mentioned specifically refers to the paper you mention in your question. My interpretation is that more recent methods might be more sophisticated but resource-wise quadric errors are still better.</p>

<p>Also I'd add is relatively easy to implement anyway.</p>

CC BY-SA 4.0
2019-06-19T16:52:31.163Z
2019-06-19T16:52:31.163Z
user8469759
<p>I'm currently looking into Mesh Simplification to batch-simplify a large amount of .obj files. It is necessary for these algorithms to preserve the visual representation of a mesh as well as possible.  </p>

<p>During research I've stumbled over Garland &amp; Heckberts <a href="https://www.cs.cmu.edu/~./garland/Papers/quadrics.pdf" rel="nofollow noreferrer">Surface Simplification Using Quadric Error Metrics</a>. Most of the frameworks I've inspected are making use of this algorithm for Mesh Simplification.  </p>

<p>My question is, why are most frameworks not making use of seemingly more advanced algorithms e.g. <a href="https://mgarland.org/files/papers/quadric2.pdf" rel="nofollow noreferrer">Simplifying Surfaces with Color and Texture using Quadric Error Metrics</a> or comparable? Is the Quadric Error Metric currently state of the art concerning simplification algorithms?</p>

<mesh>
Mesh Simplification Algorithms
soultice
# Mesh Simplification Algorithms

(Asked by: username_0 on 2019-06-12)

I'm currently looking into Mesh Simplification to batch-simplify a large amount of .obj files. It is necessary for these algorithms to preserve the visual representation of a mesh as well as possible.

During research I've stumbled over Garland & Heckberts [Surface Simplification Using Quadric Error Metrics](https://www.cs.cmu.edu/~./garland/Papers/quadrics.pdf). Most of the frameworks I've inspected are making use of this algorithm for Mesh Simplification.

My question is, why are most frameworks not making use of seemingly more advanced algorithms e.g. [Simplifying Surfaces with Color and Texture using Quadric Error Metrics](https://mgarland.org/files/papers/quadric2.pdf) or comparable? Is the Quadric Error Metric currently state of the art concerning simplification algorithms?

**Tags:** mesh


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## 1 answers

### Answer by username_1 on 2019-06-19. Score: 2 | Accepted answer

According to [Polygon-Mesh-Processing](https://books.google.co.uk/books?id=8zX-2VRqBAkC&printsec=frontcover&dq=polygon%20mesh%20processing&hl=en&sa=X&ved=0ahUKEwj6tK_o__XiAhWFY8AKHanSCBYQ6AEIKjAA#v=onepage&q=polygon%20mesh%20processing&f=false), section 7.2.2. paragraph "Error quadrics"

> Error quadrics have major advantages regarding memory consumption and computational efficiency: each vertex $x$ stores a symmetric 4x4 matrix $Q$ only, and the error can efficiently be computed in constant time as $x^T Q x$ - no matter how many planes are associated to vertex $x$ during decimation. Because of this, error quadrics are one of the most frequently employed techniques in mesh decimation.

The author of the reference I mentioned specifically refers to the paper you mention in your question. My interpretation is that more recent methods might be more sophisticated but resource-wise quadric errors are still better.

Also I'd add is relatively easy to implement anyway.


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