Is it possible to use a vector graphic as a custom form shape in a WPF application so that if the user wants to resize the application, the vector graphic can be recalculated dynamically and redrawn?
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Yes. In fact, the bulk of the “drawing” API in WPF is this way already.
The Shape class and it’s subclasses provide a retained mode, vector graphics based drawing mechanism, which handles scaling and transforms easily. See Shapes and Basic Drawing for details.