Diffusion Curves - Revision history

Kris: /* Mathematical Definition */

2011-12-11T17:35:22Z

Mathematical Definition

← Older revision		Revision as of 17:35, 11 December 2011
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	\end{align}</math>		\end{align}</math>

	Or else the color constraints could be applied using the derivative of the colors over each edge in combination with ''the'' color on the edge (which would be the average of the colors on either side). When blurring an edge the derivative would get smaller (by a factor of <math>1/blurRadius</math> for example).		Or else the color constraints could be applied using the derivative of the colors over each edge in combination with ''the'' color on the edge (which would be the average of the colors on either side). When blurring an edge the derivative would get smaller (by a factor of <math>\frac{1}{blurRadius}</math> for example).

	==Converting to SVG==		==Converting to SVG==

Jaspervdg at 09:09, 14 June 2011

2011-06-14T09:09:56Z

← Older revision		Revision as of 09:09, 14 June 2011
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	*Faster/better solver: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-solver/		*Faster/better solver: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-solver/
	*Application of diffusion curves to texture rendering: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-rendering/		*Application of diffusion curves to texture rendering: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-rendering/
	*Quality issues and using the Analytic Element Method to combat them: http://home.hccnet.nl/th.v.d.gronde/ThesisJvdGFinal2.pdf		*Quality issues and using the Analytic Element Method to combat them: http://irs.ub.rug.nl/dbi/4d10adac9b054 (backup: http://home.hccnet.nl/th.v.d.gronde/ThesisJvdGFinal2.pdf)
	*Some grid-based implementations: https://code.launchpad.net/~jaspervdg/+junk/diffuselib		*Some grid-based implementations: https://code.launchpad.net/~jaspervdg/+junk/diffuselib
	*Implementation based on the Analytic Element Method: https://code.launchpad.net/~jaspervdg/+junk/aem-diffusion-curves		*Implementation based on the Analytic Element Method: https://code.launchpad.net/~jaspervdg/+junk/aem-diffusion-curves
	*More references: http://www.citeulike.org/user/jaspervdg/tag/diffusion_curves		*More references: http://www.citeulike.org/user/jaspervdg/tag/diffusion_curves

Jaspervdg: Updated links

2011-03-08T08:58:15Z

Updated links

← Older revision		Revision as of 08:58, 8 March 2011
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	==Links==		==Links==
	*Original paper: http://artis.imag.fr/Publications/2008/OBWBTS08/		*Original paper (and program to edit/view them): http://artis.imag.fr/Publications/2008/OBWBTS08/
	*PhD thesis (including a method for vectorizing Diffusion Curves): http://artis.imag.fr/Publications/2009/Orz09/		*PhD thesis (including a method for vectorizing Diffusion Curves): http://artis.imag.fr/Publications/2009/Orz09/
	*Diffusion constraints: http://artis.inrialpes.fr/Publications/2010/BEDT10/		*Diffusion constraints: http://artis.inrialpes.fr/Publications/2010/BEDT10/
	*Faster/better solver: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-solver/		*Faster/better solver: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-solver/
	*Application of diffusion curves to texture rendering: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-rendering/		*Application of diffusion curves to texture rendering: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-rendering/
	*~~An initial implementation~~: https://code.launchpad.net/~jaspervdg/+junk/diffuselib		*Quality issues and using the Analytic Element Method to combat them: http://home.hccnet.nl/th.v.d.gronde/ThesisJvdGFinal2.pdf
			*Some grid-based implementations: https://code.launchpad.net/~jaspervdg/+junk/diffuselib
			*Implementation based on the Analytic Element Method: https://code.launchpad.net/~jaspervdg/+junk/aem-diffusion-curves
	*More references: http://www.citeulike.org/user/jaspervdg/tag/diffusion_curves		*More references: http://www.citeulike.org/user/jaspervdg/tag/diffusion_curves

Jaspervdg: /* Questions/Problems */

2011-01-18T08:16:52Z

Questions/Problems

← Older revision		Revision as of 08:16, 18 January 2011
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	*It might be interesting to redefine them in some way that unifies the color diffusion and blurring. E.g. currently colors are either to be met exactly or not at all, is it possible to reformulate the problem in such a way that we can restrict colors to varying degrees?		*It might be interesting to redefine them in some way that unifies the color diffusion and blurring. E.g. currently colors are either to be met exactly or not at all, is it possible to reformulate the problem in such a way that we can restrict colors to varying degrees?
	*Could a diffusion curve have a stop which is not completely opaque? I would find this useful for creating lighting effects over surfaces. --[[User:Pajarico\|Pajarico]] 23:11, 15 January 2011 (UTC)		*Could a diffusion curve have a stop which is not completely opaque? I would find this useful for creating lighting effects over surfaces. --[[User:Pajarico\|Pajarico]] 23:11, 15 January 2011 (UTC)
			** Yes, it could. In fact, it's quite trivial to do so, as diffusion curves are handled per channel anyway. And it's not too difficult to show that this yields sensible results if you use (premultiplied) alpha. How this behaves in practice remains to be seen, however, but I would expect this to more or less just work. --[[User:Jaspervdg\|Jaspervdg]] 08:16, 18 January 2011 (UTC)

	==Links==		==Links==

Pajarico: /* Questions/Problems */

2011-01-15T23:11:19Z

Questions/Problems

← Older revision		Revision as of 23:11, 15 January 2011
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	**It might actually be interesting to not only set colors and blur values (heat capacity?) along the sides of edges (1D), but also for surfaces (2D). This shouldn't complicate things much. In fact, it might even be slightly easier to handle the 2D case properly (as it is easier to discretize for example).		**It might actually be interesting to not only set colors and blur values (heat capacity?) along the sides of edges (1D), but also for surfaces (2D). This shouldn't complicate things much. In fact, it might even be slightly easier to handle the 2D case properly (as it is easier to discretize for example).
	*It might be interesting to redefine them in some way that unifies the color diffusion and blurring. E.g. currently colors are either to be met exactly or not at all, is it possible to reformulate the problem in such a way that we can restrict colors to varying degrees?		*It might be interesting to redefine them in some way that unifies the color diffusion and blurring. E.g. currently colors are either to be met exactly or not at all, is it possible to reformulate the problem in such a way that we can restrict colors to varying degrees?
			*Could a diffusion curve have a stop which is not completely opaque? I would find this useful for creating lighting effects over surfaces. --[[User:Pajarico\|Pajarico]] 23:11, 15 January 2011 (UTC)

	==Links==		==Links==

Jaspervdg: /* Links */ Added citeulike link.

2010-12-09T08:40:09Z

Links: Added citeulike link.

← Older revision		Revision as of 08:40, 9 December 2010
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	*Application of diffusion curves to texture rendering: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-rendering/		*Application of diffusion curves to texture rendering: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-rendering/
	*An initial implementation: https://code.launchpad.net/~jaspervdg/+junk/diffuselib		*An initial implementation: https://code.launchpad.net/~jaspervdg/+junk/diffuselib
			*More references: http://www.citeulike.org/user/jaspervdg/tag/diffusion_curves

Jaspervdg: /* Representation */

2010-09-07T14:00:48Z

Representation

← Older revision		Revision as of 14:00, 7 September 2010
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	leftBoundary="#F00 #00F #F70 #7F0" rightBoundary="#00F #F00 #0F7 #07F"		leftBoundary="#F00 #00F #F70 #7F0" rightBoundary="#00F #F00 #0F7 #07F"
	boundaryBlur="5" diffuse="true" />		boundaryBlur="5" diffuse="true" />

			Or (only a single color per point on the path and no blur):

			<diffusionGradient id="gradient">
			<stop ...>
			...
			</diffusionGradient>
			<path d="M 0,0 L 190,190 M 500,500 L 150,0"
			fill="url(#gradient)" />

			This could lead to an on-canvas interface (using an extended gradient tool) that looks a bit like this:

			[[Image:fudgedDiffCurve.png]]

			Here the "gradient stops" are (necessarily) positioned on the path and represented by the circles. The color inside the circles shows the stop color.

	==Mathematical Definition==		==Mathematical Definition==

Jaspervdg at 10:01, 7 September 2010

2010-09-07T10:01:43Z

Jaspervdg: /* Representation */ Another alternative

2010-05-30T08:13:31Z

Representation: Another alternative

← Older revision		Revision as of 08:13, 30 May 2010
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	Normally diffusion curves will have infinite extent, but this can be controlled when needed by surrounding a set of curves with a closed path that has an outside boundary which is fully transparent.		Normally diffusion curves will have infinite extent, but this can be controlled when needed by surrounding a set of curves with a closed path that has an outside boundary which is fully transparent.

			Instead of defining a group that gets diffused it may also make sense to use subpaths and diffuse those:

			<path d="M 0,0 L 190,190 M 500,500 L 150,0"
			leftBoundary="#F00 #00F #F70 #7F0" rightBoundary="#00F #F00 #0F7 #07F"
			boundaryBlur="5" diffuse="true" />

	==Mathematical Definition==		==Mathematical Definition==

Jaspervdg at 14:23, 29 May 2010

2010-05-29T14:23:17Z

← Older revision		Revision as of 14:23, 29 May 2010
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	**+ High quality at a specific resolution.		**+ High quality at a specific resolution.
	**- Low quality on zooming in.		**- Low quality on zooming in.
	**- Also large for simple images.		**- Also large for simple images (although it's not too bad, the gradients compress ''very'' well).
	*Using filters (for example, it should be possible to [[Spatially Varying Blur\|simulate spatially varying blur]] by doing multiple blurs and combining the results using weights).		*Using filters (for example, it should be possible to [[Spatially Varying Blur\|simulate spatially varying blur]] by doing multiple blurs and combining the results using weights).
	**+ Very low (almost fixed) storage requirements.		**+ Very low (almost fixed) storage requirements.
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	**+ Storage scales directly with the complexity of the image.		**+ Storage scales directly with the complexity of the image.
	**- Needs "add" (and "in") compositing, which is only available in filters in SVG 1.1 (it is also available in [http://www.w3.org/TR/SVGCompositing/ SVG Compositing]).		**- Needs "add" (and "in") compositing, which is only available in filters in SVG 1.1 (it is also available in [http://www.w3.org/TR/SVGCompositing/ SVG Compositing]).
			**- A mesh is apparently hard to render in a high quality manner on existing renderers (at least Batik has problems with rendering the triangles precisely).
	**Note that other interpolation/approximation schemes can give higher quality result but are also harder to use in the solver (as well as in the resulting SVG).		**Note that other interpolation/approximation schemes can give higher quality result but are also harder to use in the solver (as well as in the resulting SVG).

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	*Faster/better solver: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-solver/		*Faster/better solver: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-solver/
	*Application of diffusion curves to texture rendering: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-rendering/		*Application of diffusion curves to texture rendering: http://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-rendering/
			*An initial implementation: https://code.launchpad.net/~jaspervdg/+junk/diffuselib

← Older revision		Revision as of 10:01, 7 September 2010
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	Note that with diffusion curves the blur itself can also vary along the path, which could be used in the above image to let the edge be sharper in some areas. This is useful for depth of field effects for example.		Note that with diffusion curves the blur itself can also vary along the path, which could be used in the above image to let the edge be sharper in some areas. This is useful for depth of field effects for example.

	Normally diffusion curves will have infinite extent, but this can be controlled when needed by surrounding a set of curves with a closed path that has an outside boundary which is fully transparent.		Normally diffusion curves will have infinite extent, but this can be controlled when needed by surrounding a set of curves with a closed path that has an outside boundary which is fully transparent. Or by simply treating diffusion curves as yet another paint server.

	Instead of defining a group that gets diffused it may also make sense to use subpaths and diffuse those:		Instead of defining a group that gets diffused it may also make sense to use subpaths and diffuse those:
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	*Using filters (for example, it should be possible to [[Spatially Varying Blur\|simulate spatially varying blur]] by doing multiple blurs and combining the results using weights).		*Using filters (for example, it should be possible to [[Spatially Varying Blur\|simulate spatially varying blur]] by doing multiple blurs and combining the results using weights).
	**+ Very low (almost fixed) storage requirements.		**+ Very low (almost fixed) storage requirements.
	**- Diffusion difficult to implement efficiently (fast solvers ~~either~~ use multigrid methods or kernels of spatially varying size).		**- Diffusion difficult to implement efficiently (fast solvers on grids generally use multigrid methods or kernels of spatially varying size).
	**- Spatially varying blur is difficult to implement with good quality.		**- Spatially varying blur is difficult to implement with good quality.
	*By solving the Laplace equations on a (Delaunay) triangulation, using barycentric interpolation between the vertices.		*By solving the Laplace equations on a (Delaunay) triangulation, using barycentric interpolation between the vertices.
	**+ Good quality at any resolution.		**+ Good quality at any resolution.
	**+ Storage scales directly with the complexity of the image.		**+ Storage scales directly with the complexity of the image.
			**- Storage can be quite bad for curved geometries (because of the number of triangles needed to approximate the curve).
	**- Needs "add" (and "in") compositing, which is only available in filters in SVG 1.1 (it is also available in [http://www.w3.org/TR/SVGCompositing/ SVG Compositing]).		**- Needs "add" (and "in") compositing, which is only available in filters in SVG 1.1 (it is also available in [http://www.w3.org/TR/SVGCompositing/ SVG Compositing]).
	**- A mesh is apparently hard to render in a high quality manner on existing renderers (at least Batik has problems with rendering the triangles precisely).		**- A mesh is apparently hard to render in a high quality manner on existing renderers (at least Batik has problems with rendering the triangles precisely).
	**Note that other interpolation/approximation schemes can give higher quality result but are also harder to use in the solver (as well as in the resulting SVG).		**Note that other interpolation/approximation schemes can give a higher quality result but are also harder to use in the solver (as well as in the resulting SVG).
			*It might be possible to use the result of a boundary element computation directly and just combine basis functions.

	==Questions/Problems==		==Questions/Problems==