Journal ArticleDOI
Biharmonic diffusion curve images from boundary elements
Peter Ilbery,Luke Kendall,Cyril Concolato,Michael McCosker +3 more
- Vol. 32, Iss: 6, pp 219
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TLDR
A Boundary Element Method (BEM) for rendering diffusion curve images with smooth interpolation and gradient constraints, which generates a solved boundary element image representation that is compact and 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.Abstract:
There 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 orrections 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.read more
Citations
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Complex variables and applications
TL;DR: In this article, Cauchy-Goursat Theorem 2.1.1 was extended to include the point at infinity and the point of infinity at infinity in the definition of differentiability of analytical functions.
Journal ArticleDOI
Fast winding numbers for soups and clouds
TL;DR: A tree-based algorithm is proposed to reduce the asymptotic complexity of generalized winding number computation, while closely approximating the exact value of the winding number.
Journal ArticleDOI
Hierarchical diffusion curves for accurate automatic image vectorization
TL;DR: This work automatically generates sparse diffusion curve vectorizations of raster images by fitting curves in the Laplacian domain, which captures both sharp and smooth image features, across scales, more robustly than previous image- and gradient-domain fitting strategies.
Journal ArticleDOI
Fast multipole representation of diffusion curves and points
TL;DR: This work proposes a new algorithm for random-access evaluation of diffusion curve images (DCIs) using the fast multipole method, which achieves real-time performance for rasterization and texture-mapping DCIs of up to millions of curves.
Proceedings ArticleDOI
Interactive Vectorization
TL;DR: This work proposes interactive vectorization tools that offer more local control than automatic systems, but are more powerful and high-level than simple curve editing.
References
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Book
Advanced Engineering Mathematics
TL;DR: This book discusses ODEs, Partial Differential Equations, Fourier Series, Integrals, and Transforms, and Numerics for ODE's and PDE's, as well as numerical analysis and potential theory, and more.
Journal ArticleDOI
Complex Variables and Applications
Book
Advanced engineering mathematics
Dennis G. Zill,Michael R. Cullen +1 more
TL;DR: Zill's writing style has been highly praised by reviewers as easy-to-read, understandable and helpful to readers as discussed by the authors, and has been described as "easy to read, understandable, and helpful".
Book
Complex Variables and Applications
TL;DR: In this paper, Cauchy-Goursat Theorem 2.1.1 was extended to include the point at infinity and the point of infinity at infinity in the definition of differentiability of analytical functions.