Diffusion curve textures for resolution independent texture mapping

Sun, Xin; Xie, Guofu; Dong, Yue; Lin, Stephen; Xu, Weiwei; Wang, Wencheng; Tong, Xin; Guo, Baining

doi:10.1145/2185520.2185570

Cited by 35 publications

(17 citation statements)

References 37 publications

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“…In these equations, Γ represents the totality of curves bounding the domain, which includes an all-enclosing boundary curve and may include internal boundary curves, P is a point in the plane, Q is a point on a boundary curve, C(P ) is a constant which is 1 for points inside the domain and 0 for points outside the domain, n is the outward normal to the boundary and r is the distance between P and Q. [Sun et al 2012] use equation (5) as the basis for their boundary element method of rendering diffusion curve images. We use equation (6) as the basis for the boundary element method we describe in this paper for rendering biharmonic diffusion curve images.…”

Section: Biharmonic Diffusion Curvesmentioning

confidence: 99%

“…For diffusion curve images, curves inside a closed curve can be ignored when rendering outside the curve, and curves outside the closed curve can be ignored when rendering inside the curve. [Sun et al 2012] use this region independence to perform curve "culling" in their diffusion curve image rendering and they report high speed gains when it is applied in rendering particular test images. Similarly, the uniqueness property of the homogeneous biharmonic equation allows optimisations in rendering biharmonic diffusion curve images.…”

Section: Biharmonic Diffusion Curvesmentioning

confidence: 99%

“…Equation (7) with only the first two terms, i.e. with only dipole and logarithmic line segment fields, is a boundary element representation of diffusion curves without blur, similar to the solved representation of [Sun et al 2012]. The S and thin plate spline segment fields are biharmonic.…”

Section: Solved Boundary Element Representationmentioning

confidence: 99%

“…[van de Gronde 2010] describes rendering diffusion curves (without blur) using a boundary element method for solving the Laplace PDE. [Sun et al 2012] represent diffusion curves images, without blur and without gradient constraints, using a compact representation of fundamental solutions and fitted (i.e. solved) weights, which they call "diffusion curve textures".…”

Section: Introductionmentioning

confidence: 99%

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Biharmonic diffusion curve images from boundary elements

et al. 2013

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Figure 1: Boundary element rendering of biharmonic diffusion curve images. From left to right: toys image; sharp-profile (solid) and smooth-profile (dotted) curves of the toys image, with thumbnail images below showing examples of the 4 building block segment fields; car image and pumpkin image. The above images are c CiSRA; the toys image is a CiSRA re-creation of a photograph taken by C. Concolato. AbstractThere is currently significant interest in freeform, curve-based authoring of graphic images. In particular, "diffusion curves" facilitate graphic image creation by allowing an image designer to specify naturalistic images by drawing curves and setting colour values along either side of those curves. Recently, extensions to diffusion curves based on the biharmonic equation have been proposed which provide smooth interpolation through specified colour values and allow image designers to specify colour gradient constraints at curves. We present a Boundary Element Method (BEM) for rendering diffusion curve images with smooth interpolation and gradient constraints, which generates a solved boundary element image representation. The diffusion curve image can be evaluated from the solved representation using a novel and efficient line-by-line approach. We also describe "curve-aware" upsampling, in which a full resolution diffusion curve image can be upsampled from a lower resolution image using formula evaluated corrections near curves. The BEM solved image representation is compact. It therefore offers advantages in scenarios where solved image representations are transmitted to devices for rendering and where PDE solving at the device is undesirable due to time or processing constraints.

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Section: Biharmonic Diffusion Curvesmentioning

confidence: 99%

Section: Biharmonic Diffusion Curvesmentioning

confidence: 99%

Section: Solved Boundary Element Representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Biharmonic diffusion curve images from boundary elements

et al. 2013

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“…An alternative consists in performing ray tracing on the GPU via a pixel shader [Bowers et al 2011]. The approach of Sun et al [2012] avoids the explicit computation of visibility thanks to Green functions, which provide direct evaluation at individual points. Although the method is exact for closed curves, it only provides an approximation for open curves.…”

Section: Diffusion Curves: Solversmentioning

confidence: 99%

A vectorial solver for free-form vector gradients

2012

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a b c d e Figure 1: Free-form vector gradients: Our vectorial solver permits to create complex vector gradients (a). Our method is based on a triangular representation (b) that is output-insensitive and thus works with arbitrary high image resolutions. Our solver does not need to be updated for a variety of operations: (c) instancing, layering and deformation; (d) texture mapping; and even (e) environment mapping. AbstractThe creation of free-form vector drawings has been greatly improved in recent years with techniques based on (bi)-harmonic interpolation. Such methods offer the best trade-off between sparsity (keeping the number of control points small) and expressivity (achieving complex shapes and gradients). In this paper, we introduce a vectorial solver for the computation of free-form vector gradients. Based on Finite Element Methods (FEM), its key feature is to output a low-level vector representation suitable for very fast GPU accelerated rasterization and close-form evaluation. This intermediate representation is hidden from the user: it is dynamically updated using FEM during drawing when control points are edited.Since it is output-insensitive, our approach enables novel possibilities for (bi)-harmonic vector drawings such as instancing, layering, deformation, texture and environment mapping. Finally, in this paper we also generalize and extend the set of drawing possibilities. In particular, we show how to locally control vector gradients.

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Locally refinable gradient meshes supporting branching and sharp colour transitions

et al. 2018

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We present a local refinement approach for gradient meshes, a primitive commonly used in the design of vector illustrations with complex colour propagation. Local refinement allows the artist to add more detail only in the regions where it is needed, as opposed to global refinement which often clutters the workspace with undesired detail and potentially slows down the workflow. Moreover, in contrast to existing implementations of gradient mesh refinement, our approach ensures mathematically exact refinement. Additionally, we introduce a branching feature that allows for a wider range of mesh topologies, as well as a feature that enables sharp colour transitions similar to diffusion curves, which turn the gradient mesh into a more versatile and expressive vector graphics primitive.

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Diffusion curve textures for resolution independent texture mapping

Cited by 35 publications

References 37 publications

Biharmonic diffusion curve images from boundary elements

Biharmonic diffusion curve images from boundary elements

A vectorial solver for free-form vector gradients

Locally refinable gradient meshes supporting branching and sharp colour transitions

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