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A Colour Interpolation Scheme for Topologically Unrestricted Gradient Meshes.

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Title: A Colour Interpolation Scheme for Topologically Unrestricted Gradient Meshes.
Authors: Lieng, Henrik1,2 henrik.lieng@gmail.com, Kosinka, Jiří1,3 jiri.kosinka@cl.cam.ac.uk, Shen, Jingjing1 jingjing.shen@cl.cam.ac.uk, Dodgson, Neil A.1 neil.dodgson@cl.cam.ac.uk
Source: Computer Graphics Forum. Sep2017, Vol. 36 Issue 6, p112-121. 10p.
Subjects: Topology, Vector graphics, Computer graphics, Interpolation, Approximation theory
Abstract: Gradient meshes are a 2D vector graphics primitive where colour is interpolated between mesh vertices. The current implementations of gradient meshes are restricted to rectangular mesh topology. Our new interpolation method relaxes this restriction by supporting arbitrary manifold topology of the input gradient mesh. Our method is based on the Catmull-Clark subdivision scheme, which is well-known to support arbitrary mesh topology in 3D. We adapt this scheme to support gradient mesh colour interpolation, adding extensions to handle interpolation of colours of the control points, interpolation only inside the given colour space and emulation of gradient constraints seen in related closed-form solutions. These extensions make subdivision a viable option for interpolating arbitrary-topology gradient meshes for 2D vector graphics. [ABSTRACT FROM AUTHOR]
Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Gradient meshes are a 2D vector graphics primitive where colour is interpolated between mesh vertices. The current implementations of gradient meshes are restricted to rectangular mesh topology. Our new interpolation method relaxes this restriction by supporting arbitrary manifold topology of the input gradient mesh. Our method is based on the Catmull-Clark subdivision scheme, which is well-known to support arbitrary mesh topology in 3D. We adapt this scheme to support gradient mesh colour interpolation, adding extensions to handle interpolation of colours of the control points, interpolation only inside the given colour space and emulation of gradient constraints seen in related closed-form solutions. These extensions make subdivision a viable option for interpolating arbitrary-topology gradient meshes for 2D vector graphics. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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      – SubjectFull: Computer graphics
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      – SubjectFull: Interpolation
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              M: 09
              Text: Sep2017
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