Difference between revisions of "Stretch"

Revision as of 17:17, 21 December 2010

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When you draw in Inkscape, you are working with a flat, two-dimensional drawing surface. But, when you plot your drawing on an egg or other round object, you subject your drawing to a transformation which will change its appearance. For example, a horizontal line in your Inkscape drawing will have the same physical length when printed on paper regardless of it's vertical height in your drawing. That is not the case when you plot horizontal lines onto a sphere or egg. Horizontal lines in Inkscape becomes lines of latitude on a sphere. The circumference of a line of latitude decreases as you approach the poles. To demonstrate this, draw a horizontal line at the mid-height of your drawing and then make a copy of that line but raise it vertically a quarter of the drawing's height. Now plot this on an egg or sphere. The off equator line will be shorter in length then the equatorial line [1].

This effect of shrinking near the poles can be annoying when, for example, plotting several lines of text. It can cause geometric object to appear bloated near the equator and shrunken near the poles. To combat this, it is possible to horizontally stretch elements of your drawing. The amount of stretch increases the closer the object is to the pole. Such stretching is what this extension does. It will stretch the pattern,

producing the result,

Note how the closer a horizontal line is to either the top or bottom edge of the drawing -- the poles of your egg -- the more the lines are stretched.

The stretching is done such that a vertical line passing through the geometric center is unchanged. Which geometric center? If nothing is selected when the extension is applied, then the geometric center of the drawing page is used. If, however, one or more objects are selected, then the geometric center of the smallest rectangle containing the selected objects is used (i.e., the geometric center of the bounding box containing the objects).

The extension has two parameters. The first value, vertical smoothing, is used to break long line segments into shorter segments before stretching. To illustrate the effect of this setting, consider the following figure,

From left to right, the vertical smoothing values were 200, 100, and 10. The smaller the value, the smoother the result will be. A value between 5 and 10 is generally sufficient. The second value you can set, curve smoothing, is the same value as in the Eggbot Control extension. It effects how smoothly arcs, circles, eliipses, and curves are rendered.

In the following example, text within a box is shown unstretched on the left and stretched on the right,

The box and text were stretched as a whole (i.e., they were not individually stretched). The result of plotting the two on an egg is shown below. The egg on the left is the unstretched box and text. The egg on the right shows the stretched text and box. The picture of the egg on the right does not clearly show the effect of the stretching -- in real life the box looks very rectilinear. The results do not show well in a photograph: the photographic process is, by its very nature, producing yet another transformation as it maps a three-dimensional, spherical picture to a two-dimensional flat image.

Notes

1. What is happening here is that the pixels in your Inkscape drawing are interpreted not as lengths by the Eggbot but rather as stepper motor steps. Regardless of the latitude, each full circle around an egg has the same number of stepper motor steps: 3200 steps. However, the surface distance spanned by each step decreases as you approach the poles. To be more precise, an Inkscape line of length N pixels is interpreted as a line of "length" N stepper motor steps. If a line segment in Inkscape has the endpoints (x1, y1) and (x2 y2) then the plotted result will turn the egg motor x2 - x1 steps and the pen arm motor y2 - y1 steps.

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