The Xara Trompe L'Oeil Room Page 3
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Click the small red magnet icon on the Infobar (Snap to Objects). Zoom in as close as you can get to the lines.

Drag the top end of the light blue segment (as shown) until it snaps onto the end of the red arc.

NOTE: The cursor changes from a 4-way arrow to a magnet to indicate the two sections have snapped.

Continue snapping the segments until you have a spiral. (You were probably wondering what this was leading up to, huh?)

Select all the line segments and from the Arrange menu, select Convert Line to Shape.

(I have added an outline and deleted the fill so you can see that indeed the outline is now a fillable shape. And see how nicely the ends overlap?)

You can leave the lines solid.

Select all the line segments again and this time from the Arrange menu select Combine Shapes > Add Shapes.

This converts the different line segments into one continuous outline.