Ceci est une ancienne révision du document !
This month and next, I’m going to cover a couple of Inkscape features that have fallen through the gaps in my previous coverage. The first of these, disgracefully, dates back to the 4th instalment of this series, way back in 2012! In FCM#64, when describing the options in the Fill and Stroke dialog, I wrote: “Also being put off for later articles are the Unset Paint button that looks like a question mark, and the two splodges on the right of the Fill tab.”
The Unset Paint button was eventually described in part 30 (FCM issue #90), when I covered its use with clones. But what of the “two splodges on the right of the Fill tab”? For clarity, let’s first take a look at a screenshot of the Fill and Stroke dialog, in which I’ve circled the splodges.
To understand what effect these splodges – which are actually a pair of mutually exclusive radio buttons – have on your objects, we’ll need a path to test with. Not just any path will do, however. These buttons have an effect only on paths that are either self-intersecting, or which contain sub-paths. Let’s deal with the former to start with: what exactly do I mean by ‘self-intersecting’?
Consider the paths below. The one on the left is just a simple U-shaped filled path. Nothing special, no sneaky tricks. Just 10 nodes forming a shape with a couple of arms. The shape on the right is just a duplicate of the first one, with the end of the left arm moved to the right, and the end of the right arm moved to the left, so the arms cross each other. No nodes were added or removed, they were just moved around a little.
The second shape is a self-intersecting path. It’s a closed path that is drawn such that it crosses itself, although the word ‘crosses’ carries a misleading implication in this case. Remember that Inkscape is a 2D drawing program, with no notion of the third dimension. So when making this shape I didn’t really move one arm ‘over’ the other, as you would do when making the same shape with a piece of string. Rather I moved it ‘through’ the other, in the same 2D plane. Neither arm is on top of the other. Neither arm ‘crosses’ the other. Instead the resultant shape simply intersects with itself.
Turning on the stroke and reducing the fill opacity makes this a little clearer:
Notice how the stroke is visible for both arms. If one crossed over the other you might expect the stroke of the arm on the bottom to be obscured by the one that’s on top, but that’s not how things work in the 2D graphics world. You’d also expect the colour of the fill to be a little darker where the two translucent arms cross over, but that’s not the case either.
It’s also important to note that the arms don’t have to completely pass through each other in order to be a self intersecting shape, and that the shape could self-intersect multiple times, as demonstrated in these variations on the theme:
Now we’re all clear on what a self-intersecting path actually is, let’s look at how they’re affected by the splodgy radio buttons. The first thing to note is that the images so far have all been taken with the second button selected – the one that’s completely filled in. Switch to the first button, and we get this:
The basic U-shaped path remains unaffected. It’s not a self-intersecting path, and it doesn’t contain any sub-paths, so the radio buttons have no effect. All the others, however, have no fill rendered in the intersecting parts. The stroke is still drawn, but the fill isn’t.
This behaviour is a little confusing at first. Surely the intersecting parts are inside the shape, so they should still be filled, right? Unfortunately our intuitive idea of in-and-out doesn’t always apply in the world of computer graphics. Instead there are different rules or heuristics for determining whether a point is inside or outside a shape – and the splodgy buttons are used to switch between a couple of those rules. Let’s take a look at paths with sub-paths to try to explain why there’s a need for this choice.
When you look at the self-intersecting shapes above, it’s pretty obvious that the fully-filled option (second button) is the right choice most of the time. Imagine trying to draw a figure-of-eight, only to find that the part where the shape crosses itself is unfilled. Definitely better to use the second option, so we’ll ensure that’s selected. Now we’re going to draw a circle with a hole in it. There are a few ways to achieve this but, to make a point, I’m going to use a very specific method: • Draw a circle for the outside. • Draw a smaller circle for the inside. • Path > Combine to create a complex path, made up of two sub-paths.
In this image (above) you can see the two separate shapes on the left, and the result of combining them in the middle. The ‘hole’ in the shape is filled – not really what we were after. Switching to the first button, however, gives the expected result, as shown in the version on the right. Now we’ve got a simple rule-of-thumb: use the left-hand button for paths with sub-paths, and the right-hand button for self-intersecting paths. But what if we have a path that is both self-intersecting and has a sub-path describing a cut-out? Something like this odd piece of jewelry or alien symbol, shown as it appears with each of the two splodgy radio buttons selected:
On the left we have the problem of no fill in the self-intersecting part, but the hole is fine. With the right-hand button we get a fill in the self-intersecting part, but no hole. Is there any way we can have the best of both options?
The answer is obviously ‘yes’, but to get there it helps to understand what the two heuristics are that we’ve been switching between. The first button has a tooltip that reads “any path self-intersections or subpaths create holes in the fill”, and is referred to as the “even-odd” rule. The heuristic for this is pretty simple: • Pick a point in the shape. • Draw an imaginary straight line from that point out of the shape in any direction. • Keep a ‘crossing’ count, which starts at zero. • Add one to the count each time the line crosses a path or sub-path boundary. • If the final count is even, the point was outside the shape. If the count is odd, the point was inside the shape.
By performing this for a point in each region of the shape, Inkscape can determine which areas are inside, and therefore need to be filled, and which are outside. But it does result in self-intersections being counted as outside, and left unfilled.
The second button has a tooltip that reads “fill is solid unless a subpath is counterdirectional”, and is referred to as the “non-zero” or “winding” rule. This heuristic relies on the fact that each sub-path has a direction associated with it, and works like this: • Pick a point in the shape. • Draw an imaginary straight line from that point out of the shape in any direction. • Keep a ‘winding count’ which starts at zero. • Each time the line crosses a path or sub-path, add one to the count if the path is crossing the line from left to right (clockwise from the perspective of the point) or subtract one if the path is crossing from right to left (counter-clockwise). • If the final count is zero the point is outside the shape, otherwise it is inside.
From this algorithm and the mention of “counterdirectional” in the tooltip – you may have already worked out that using the second splodgy button (non-zero) lets us switch sub-paths between filled and unfilled by reversing the direction of the nodes. Fortunately for us, Inkscape makes this fairly easy: • Select the composite path and switch to the node tool (F2). • Select a node in the sub-path. • Use Path > Reverse to reverse the order of the nodes in the sub-path without changing the shape.
You can see the effect of this approach in the following image. In this case I’ve also added arrow markers to the paths, to clarify what’s happening. The first image is our starting path, created by combining an oval with a self-intersecting shape. You can see from the arrows that the sub-path is running counter-clockwise. In the second image I’ve reversed the direction of the sub-path, the arrows point the opposite way, and the shape has a hole for the sub-path but not for the self-intersection. Unfortunately this simple approach doesn’t appear to work in the beta of Inkscape v1.0, where the Path > Reverse operation reverses the entire path rather than the selected sub-path. The only option in this case is to use Path > Break Apart to split the shape down into its constituent parts, then use Path > Reverse on just one of those paths, then finally use Path > Combine to re-combine them back into your original complex path. This is a definite step backwards in the workflow, so I will be filing a bug about this on the Inkscape issue tracker.
This path-reversing approach works for simple shapes where the nesting of sub-paths isn’t very deep. For more complex arrangements you may need to reverse more than one path to get the effect you want. And if there are also intersections between sub-paths, or self-intersections within them, you may never be able to get just the fill you want, no matter what you try. In those cases you may find it easiest to use the first splodge (even-odd) to fill the entire shape, then create your complex hole arrangement by clipping with a suitably constructed path.
It’s worth noting that you might never experience this problem. Punching a hole through a shape is more commonly done using Path > Difference than Path > Combine, and the former usually results in a sub-path going in the right direction. But it’s worth knowing about these splodgy buttons and how to work with them, just in case you ever find yourself presented with a path that contains inexplicable holes or fills where it shouldn’t.