Colour interpolants for polygonal gradient meshes

Hettinga, Gerben J.; Brals, René; Kosinka, Jiří

doi:10.1016/j.cagd.2019.101769

Cited by 8 publications

(6 citation statements)

References 25 publications

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“…Beatson et al [10] then extended the domain to piecewise quadratic boundaries, where they proposed the Hermite mean value interpolation technique for polygons. Hettinga et al [53] further adjusted the interpolation schemes from generalized Bézier patches [125] and Charrot-Gregory corner interpolation patches [22] (both are multi-sided parametric patches) such that the interpolation scheme can be used for 2D gradient meshes. By using the algorithm from Chiyokura and Kimura [25], they achieved at least G 1 continuity for the color.…”

Section: Irregular Meshesmentioning

confidence: 99%

“…Fig. 5: Patches of arbitrary shape, filled with constant color.al [53]. investigated several schemes to interpolate the values and gradients of color from boundary conditions, including the approach for topologically unrestricted gradient meshes by Lieng et al[86], the cubic mean value coordinates by Li et al[81], and two newly-proposed interpolation methods based on the Gregory generalized Bézier patch and the Charrot-Gregory corner interpolator.…”

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confidence: 99%

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A Survey of Smooth Vector Graphics: Recent Advances in Repr esentation, Creation, Rasterization, and Image Vectorization

Tian

Günther

2024

IEEE Trans. Visual. Comput. Graphics

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The field of smooth vector graphics explores the representation, creation, rasterization, and automatic generation of light-weight image representations, frequently used for scalable image content. Over the past decades, several conceptual approaches on the representation of images with smooth gradients have emerged that each led to separate research threads, including the popular gradient meshes and diffusion curves. As the computational models matured, the mathematical descriptions diverged and papers started to focus more narrowly on subproblems, such as on the representation and creation of vector graphics, or the automatic vectorization from raster images. Most of the work concentrated on a specific mathematical model only. With this survey, we describe the established computational models in a consistent notation to spur further knowledge transfer, leveraging the recent advances in each field. We therefore categorize vector graphics papers from the last decades based on their underlying mathematical representations as well as on their contribution to the vector graphics content creation pipeline, comprising representation, creation, rasterization, and automatic image vectorization. This survey is meant as an entry point for both artists and researchers. We conclude this survey with an outlook on promising research directions and challenges to overcome in the future.

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Section: Irregular Meshesmentioning

confidence: 99%

mentioning

confidence: 99%

A Survey of Smooth Vector Graphics: Recent Advances in Repr esentation, Creation, Rasterization, and Image Vectorization

Tian

Günther

2024

IEEE Trans. Visual. Comput. Graphics

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“…However, the regular topology requirement and lack of support for local refinement limit its usability and expressiveness, mostly due to an extensive number of patches that are generated. The regular topology restriction has been addressed and alleviated by using either generalised barycentric coordinates [LJH13, HBK19], loop subdivision surfaces [Loo87] or Catmull–Clark subdivision surfaces [LKSD17]. The latter approach, often called the subdivision gradient mesh , is especially useful as it has basically the same functionality as traditional gradient meshes, but with the added advantage of unstructured topology and increased smoothness.…”

Section: Related Workmentioning

confidence: 99%

Feature‐Adaptive and Hierarchical Subdivision Gradient Meshes

Zhou

Hettinga

Houwink

et al. 2022

Computer Graphics Forum

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Gradient meshes, an advanced vector graphics primitive, are widely used by designers for creating scalable vector graphics. Traditional variants require a regular rectangular topology, which is a severe design restriction. The more advanced subdivision gradient mesh allows for an arbitrary manifold topology and is based on subdivision techniques to define the resulting colour surface. This also allows the artists to manipulate the geometry and colours at various levels of subdivision. Recent advances allow for the interpolation of both geometry and colour, local detail following edits at coarser subdivision levels and sharp colour transitions. A shortcoming of all existing methods is their dependence on global refinement, which makes them unsuitable for real‐time (commercial) design applications. We present a novel method that incorporates the idea of feature‐adaptive subdivision and uses approximating patches suitable for hardware tessellation with real‐time performance. Further novel features include multiple interaction mechanisms and self‐intersection prevention during interactive design/editing.

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“…Image vectorization based on gradient mesh [17,18] is also available. To prove it, there are some studies that discovered color operations by gradient mesh [19][20][21][22].…”

Section: Related Workmentioning

confidence: 99%

A Novel Approach to Transform Bitmap to Vector Image for Data Reliable Visualization considering the Image Triangulation and Color Selection

Han

Chi

et al. 2020

Security and Communication Networks

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Vector image is a type of image composed of many geometric primitives. Compared with bitmaps, vector images have the ability to save memory as well as to enlarge without distortion. Meanwhile, it has been commonly adopted in data visualization (image data) because it can be scaled to multiple sizes to fit different scenes. For instance, it can be applied for the illustrations in newspapers and magazines, the logo on the web, the background for poster, the design of text, and traffic signs. However, transforming a bitmap to vector image is still a challenging problem because of the complicated content of a bitmap, which tends to consist of more than just simple geometry. Aiming at this issue, there is a new approach proposed to transform from bitmaps to vector images, which is based on triangle units and consists of three steps. In detail, firstly, there is an initial mesh constructed for one image in pixel level after detecting features. Then, the initial mesh will be simplified by collapsing two vertices as the initial mesh is too dense to represent one image. Specifically, there are two main parts in this step, which are collapse conditions and collapse influences. In the step of collapsing, issues such as overlap and sharp triangles can be conquered by a sort-edge method (which will be illustrated specifically later). The final step is to select one color for each triangle, since it is helpful to save the memory and speed up the process of this method. In addition, one color will represent one triangle; hence, in the final step, the four-triangle sample method will be applied in order to prevent a vector image from generating too large color discontinuity. Once the pretest proceeds without mistake, the method above is able to work for the general bitmaps. Note that our method can be applied to information security and privacy, since one image can be encoded to some triangles and colors.

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Colour interpolants for polygonal gradient meshes

Cited by 8 publications

References 25 publications

A Survey of Smooth Vector Graphics: Recent Advances in Repr esentation, Creation, Rasterization, and Image Vectorization

A Survey of Smooth Vector Graphics: Recent Advances in Repr esentation, Creation, Rasterization, and Image Vectorization

Feature‐Adaptive and Hierarchical Subdivision Gradient Meshes

A Novel Approach to Transform Bitmap to Vector Image for Data Reliable Visualization considering the Image Triangulation and Color Selection

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