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1. ## Vexillomorphic transformations (Flag-Waving) in Photo

This is an extension of my tutorial on Trigonometrical transformations using Filter > Distort > Equations. This one is focused on simulating flags waving in a light wind. Flags have an advantage in that they have a standard shape (width is twice the height). Edit: I have been told that this is not true. I stand corrected. To get the desired waving, I apply a sine transformation to each of the x and y-axes. The equations to apply are: x=(x+20*sin(360*y/h))/c-100*b y=y+a*(h/10)*sin(2*360*x/w)-(x/w)*h/10 I add a sideways sine wave to the x-axis as a function of the y-position. When the flag waves, the visual width is decreased, so I have added a parameter c which scales the width of the flag. The parameter b is an offset, since the left-hand corners of the flag can otherwise move outside the canvas. The y-axis also has a sine wave, depending on the x-position. The parameter a determines the magnitude of this sine wave. The final expression (-(x/w)*h/10) ensures that the fly (RHS in this case) is below the hoist (LHS here). (Definitions: hoist is the part next to the flagpole; fly is the part flying free.) Here is the UK Union Flag, plus a bit of extra space above and below to create room: And waving in the breeze: And here is a macro that implements these transformations: FlagWaving.afmacro And a macro library containing the single macro: FlagWaving.afmacros The parameters should appear when you run the macro. Parameter a controls the vertical wave; parameter b controls the horizontal offset; parameter c controls the overall horizontal scaling. This macro will not simulate a flag in too strong a wind, where the parts overlap! John
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