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9

You are looking for TransformedRegion. GeometricTransformation is for transforming graphics primitives, but you are looking at region functionality. This is a case where the difference is important. Simply, t = TransformedRegion[p, AffineTransform@A] (* Parallelogram[{0, 0}, {{-1, 2}, {3, 0}}] *) where the AffineTransform was needed as TransformedRegion ...


2

The only way I could find to add the ellipse you are asking for to your graphic was to compute a set of points along the ellipse and make line segments from them. Here is how I did it. The following generates the graphic you show int the question. origin = Point[{0, 0, 0}]; cone1 = Cone[{{0, 0, 1}, {0, 0, 0}}]; transform = {{0.3, 0, 0.15}, {0, 0.35, 0}, {0....



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