The Xara Trompe L'Oeil Room  Page 10
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Center the two objects and group them (Ctrl G ).

 

Create a 200 x 90 pixel ellipse and center it top and over the blue and green sphere.

Select both the ellipse and the grouped blue and green sphere.

Combine Shapes > Intersect Shapes (Arrange menu).

Create a small ellipse, apply an orange fill, and apply a Rounded, To Inside, Bevel to create a little button for the top of the cap.

Create a 200 by 60 pixel ellipse. Apply a pale blue fill RGB 153, 204, 255. Make a duplicate and apply a darker blue fill, RGB 102, 102, 255.

Send the darker blue to the back and position it about 2 pixels below the pale blue ellipse.

Align the two ellipses under the top of the cap as shown on the top.

And that is the convoluted way to create a striped ball cap.