Advanced Engineering Mathematics: Maple Computer Guide
Advanced Engineering Mathematics: Maple Computer Guide
FiberMesh: designing freeform surfaces with 3D curves
ACM SIGGRAPH 2007 papers
Diffusion curves: a vector representation for smooth-shaded images
ACM SIGGRAPH 2008 papers
A GPU Laplacian solver for diffusion curves and Poisson image editing
ACM SIGGRAPH Asia 2009 papers
Diffusion constraints for vector graphics
NPAR '10 Proceedings of the 8th International Symposium on Non-Photorealistic Animation and Rendering
Freeform vector graphics with controlled thin-plate splines
Proceedings of the 2011 SIGGRAPH Asia Conference
Diffusion curve textures for resolution independent texture mapping
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
A vectorial solver for free-form vector gradients
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Repoussé: automatic inflation of 2D artwork
SBM'08 Proceedings of the Fifth Eurographics conference on Sketch-Based Interfaces and Modeling
Computer Graphics Forum
Diffusion curves: a vector representation for smooth-shaded images
Communications of the ACM
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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.