For the quadrangle one, it appears to be the same as Gimp's perspective (the basic transforms: rotate, scale, shear, perspective, flip, as well as the Unified transform that combines manyl of them are all affine transforms). Then you shouldn't need to set precision, a property of Bézier curves is that for affine transforms, the transform result of the whole curve is the curve produced by the transform of the four control points (this property is what makes Bézier curves so popular despite other shortcomings).
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Path transformations
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