Error diffusion on meshes

Alexa, Marc; Kyprianidis, Jan Eric

doi:10.1016/j.cag.2014.09.010

Cited by 5 publications

(4 citation statements)

References 28 publications

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“…The general problem of finding space-filling curves or ropes (i.e., curves of finite thickness) on surfaces has been analyzed for simple geometries like the sphere [Gerlach and von der Mosel 2011], and investigated via manual design [Delp and Thurston 2011], but few computational algorithms are known. Existing methods are mainly targeted at tasks like error diffusion [Alexa and Kyprianidis 2015] or generating coherent memory layouts [Vo et al 2012;Isenburg and Lindstrom 2005], which do not require geometric regularity or even global continuity. Pedersen and Singh [2006] generate smooth space-filling curves via regularized Brownian motion, though it is not clear how to incorporate nonlocal terms (such as distortion) into such a framework.…”

Section: Texture Mappingmentioning

confidence: 99%

Variational surface cutting

Sharp

Crane

2018

ACM Trans. Graph.

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This paper develops a global variational approach to cutting curved surfaces so that they can be flattened into the plane with low metric distortion. Such cuts are a critical component in a variety of algorithms that seek to parameterize surfaces over flat domains, or fabricate structures from flat materials. Rather than evaluate the quality of a cut solely based on properties of the curve itself ( e.g. , its length or curvature), we formulate a flow that directly optimizes the distortion induced by cutting and flattening. Notably, we do not have to explicitly parameterize the surface in order to evaluate the cost of a cut, but can instead integrate a simple evolution equation defined on the cut curve itself. We arrive at this flow via a novel application of shape derivatives to the Yamabe equation from conformal geometry. We then develop an Eulerian numerical integrator on triangulated surfaces, which does not restrict cuts to mesh edges and can incorporate user-defined data such as importance or occlusion. The resulting cut curves can be used to drive distortion to arbitrarily low levels, and have a very different character from cuts obtained via purely discrete formulations. We briefly explore potential applications to computational design, as well as connections to space filling curves and the problem of uniform heat distribution.

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Section: Texture Mappingmentioning

confidence: 99%

Variational surface cutting

Sharp

Crane

2018

ACM Trans. Graph.

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“…This issue can be mitigated by applying either error diffusion [AK15], or by building a hierarchical Laplacian forming a suspension structure and providing a better rigidity to the reconstruction [LV14]. Although both of these approaches do improve the performance of high‐pass encoding, parallelogram based approaches still provide considerably better results.…”

Section: Related Workmentioning

confidence: 99%

“…Results obtained for various static meshes. HPC stands for High-pass coding[SCOT03], Diffusion stands for Error diffusion in meshes[AK15] and WP stands for weighted parallelogram coding[VB13] RD curve for the Samba model using perceptual error measure.cian built from an average mesh that is encoded using Kirchhoff Laplacian, • Diffusion Cotan Laplacian based scheme, i.e. using a geometric Laplacian built from an average mesh that is encoded using Kirchhoff Laplacian, together with error diffusion, • Proposed Cotan Laplacian based scheme, i.e.…”

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confidence: 99%

Error propagation control in Laplacian mesh compression

Váša

Dvorak

2018

Computer Graphics Forum

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Laplacian mesh compression, also known as high‐pass mesh coding, is a popular technique for efficiently storing both static and dynamic triangle meshes that gained further recognition with the advent of perceptual mesh distortion evaluation metrics. Currently, the usual rule of thumb that drives the decision for a mesh compression algorithm is whether or not accuracy in absolute scale is required: Laplacian mesh encoding is chosen when perceptual quality is the main objective, while other techniques provide better results in terms of mechanistic error measures such as mean squared error. In this work, we present a modification of the Laplacian mesh encoding algorithm that preserves its benefits while it substantially reduces the resulting absolute error. Our approach is based on analyzing the reconstruction stage and modifying the quantization of differential coordinates, so that the decoded result stays close to the input even in areas that are distant from anchor points. In our approach, we avoid solving an overdetermined system of linear equations and thus reduce data redundancy, improve conditioning and achieve faster processing. Our approach can be directly applied to both static and dynamic mesh compression and we provide quantitative results comparing our approach with the state of the art methods.

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“…Alexa and Kyprianidis addressed error diffusion on a surface in Ref. [8], where they analyzed different path orders to better distribute the error. Brunton et al proposed an error-diffusion halftoning algorithm to produce full color with multi-jet 3D printer [9].…”

Section: Introductionmentioning

confidence: 99%

Structure-Aware Color Halftoning with Adaptive Sharpness Control

Gooran¹,

Abedini²

2022

jist

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printing are becoming increasingly popular, and consequently the demand for high quality surface reproduction is also increasing. Halftoning plays an important role in the quality of the surface reproduction. Three dimensional halftoning methods, that adapt the halftone structures to the geometrical structure of 3D surfaces or to the viewing direction, could further improve surface reproduction quality. In this paper, a 3D adaptive halftoning method is proposed, that incorporates different halftone structures on the same 3D surface. The halftone structures are firstly adapted to the 3D geometrical structure of the surface. Secondly, the halftone structures are adapted based on the normal vector to the surface at a specific voxel. Two simple approaches to approximate the normal vector are also proposed. The problem of edge artefacts that might occur in the previously proposed 3D Iterative Method Controlling the Dot Placement (IMCDP) halftoning method is discussed and a solution to reduce these artefacts is given. The results show that the proposed adaptive halftoning can combine different halftone structures on the same 3D surface with no transition artefacts between different halftone structures. It is also shown that using second-order frequency modulation (FM) halftone, in comparison to first-order FM, can result in more homogeneous appearance of 3D surfaces with undesirable structures on them.

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Error diffusion on meshes

Cited by 5 publications

References 28 publications

Variational surface cutting

Variational surface cutting

Error propagation control in Laplacian mesh compression

Structure-Aware Color Halftoning with Adaptive Sharpness Control

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Error diffusion on meshes

Cited by 5 publications

References 28 publications

Variational surface cutting

Variational surface cutting

Error propagation control in Laplacian mesh compression

Structure-Aware Color Halftoning with Adaptive Sharpness&#xA0;Control

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Structure-Aware Color Halftoning with Adaptive Sharpness Control