Is there a way to—with matrices—transform something as if opening the image on a Japanese folding fan?

poem on an open fan
Image from Wikimedia Commons.

I'm at a loss of what to call it, so pointers towards avenues of research would be greatly appreciated. If it isn't possible with matrices, alternate methods would also be good.

If that is not possible either, a way to approximate the perspective tool in most graphics manipulation programs would be nice also.

  • 2
    \$\begingroup\$ If you are defining an object in normal x,y,z coordinate space, then you can't do this with matrices since they are explicitly linear transformations (ie scaling, shearing, rotation). If you wish to bend your object, you could transform to spherical coordinates and scale the angles appropriately. The transformations between Cartesian and spherical aren't too bad. mathworld.wolfram.com/SphericalCoordinates.html \$\endgroup\$ – Jemmy Sep 21 '13 at 23:42
  • \$\begingroup\$ Can you elaborate on "Scale the angles"? \$\endgroup\$ – Kirbinator Sep 22 '13 at 3:36
  • \$\begingroup\$ The complexity of doing this depends on if the object is actually shaped like a fan, or you have some other type of shape that you want to have this fan-opening behavior. \$\endgroup\$ – ChrisC Jan 5 '15 at 23:03

Use trig to sample it into a triangle strip.

fan sampling

As for texturing: a rectangular image UV-mapped to the triangle strip might work, with projective interpolation.


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