Transfer Effects

	http://people.csail.mit.edu/jaffer/Marbling/Transfer-Effects
	Transfer Effects

So far, this investigation has been about the swirling patterns produced by moving tines through simple patterns of paint. It has been computationally convenient to make displacements dependent only on distances perpendicular to those displacements.

Some marbled designs look as though they are images of a marbled fabric which has been rippled or gathered. Regina St. John of Chena River Marblers explained that these three-dimensional effects are achieved by shifting the paper while laying it on the paint bath surface.

The curved fan to the right recapitulates the design from the end of the first chapter.

-50 10 50
{ /idx exch def
-270 idx sub -30 idx 2 mul add [ -270 idx 3 mul sub ] Circle-deformation
} for

Wiggling the paper side-to-side while laying it on surface produces the expected wiggled design; such sinusoidal distortions were used in the production of the bouquet patterns.

-50 10 50
{ /idx exch def
-270 idx sub -30 idx 2 mul add [ -270 idx 3 mul sub ] Circle-deformation
} for
/y exch def /x exch def
y 7 mul sin 6 mul x add y

Wiggling the paper in the direction of laying stretches and squeezes the marbled patterns. Unlike the side-to-side wiggle, the excursions must be limited, lest they overtake themselves and create a fold. A folded pattern would not be capable of being raster-rendered.

/y exch def /x exch def
y 7 mul sin 6 mul y add x exch

Wiggling the paper diagonally, the pattern looks as though it is flowing down stairs or clapboards. Notice that these horizontal jags cannot be produced by tine movements. A tine traversing a paint band bends both sides to the same direction. But here the stretched horizontal displacements are in opposite directions.

/y exch def /x exch def
y 7 mul sin 6 mul dup x add exch y add

Wiggling the virtual paper so violently that it overlaps itself produces edges that seem to hook under.

/y exch def /x exch def
y 7 mul sin 14 mul dup x add exch y add

What if, instead of just wiggling, the paper made a circular motion while being laid on the surface? The result is striking, looking like paints flowing over a series of rollers.

/y exch def /x exch def
y 7 mul dup sin 6 mul x add exch cos 6 mul y add

If both axes drive the perturbations, it gives the diagonal pattern a softer appearance. The pattern looks as though it is flowing over corrugated sheeting.

/y exch def /x exch def
y x sub 5 mul sin 6 mul x add y

If both axes drive circular perturbations, the pattern looks as though it is flowing over rollers or a series of cylindrical troughs.


`y x sub 5 mul dup sin 6 mul x add exch cos 6 mul y add`	`x y sub 5 mul dup sin 6 mul x add exch cos 6 mul y add`

Raster-rendering the diagonal pattern would involve inverting the vector function [x + 6 sin(5 (y - x)), y + 6 sin(5 (y - x))]. But to first order, we can try raster-rendering with [x + 6 sin(5 (x - y)), y + 6 sin(5 (x - y))]. With the squeezing and stretching less crisp than above, the three-dimensional effect is not as strong; but it has a more organic look, which is interesting in its own right.

Some of the three-dimensional effect of physical marbling comes from the stretched regions being lighter in color than the squeezed regions. That would be difficult to produce using contour-rendering in PostScript -- but is simple to add to raster-rendering.

Given that the patterns being stretched and squeezed are not straight to begin with, and given that shading can be very suggestive of non-planarity, just combining an orthogonal wiggle with shading enables practical transfer effects for raster-rendering.

The next chapter investigates paint drop patterns.

I am a guest and not a member of the MIT Computer Science and Artificial Intelligence Laboratory. My actions and comments do not reflect in any way on MIT.
		Topological Computer Graphics
	agj @ alum.mit.edu	Go Figure!