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I have this shape that is made from 4 bezier curves and then exstruded. How can I cut of the excess plane so im left with just the shape?

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If you want to do it manually without the Boolean modifier and the existing mesh you already have, you can use the following method - probably not as elegant as Markus' solution, but I think the Split Edges & Faces option deserves more attention in modeling:

  1. In Edit Mode, enable Auto Merge with the option Split Edges & Faces.

    auto merge

  2. Now select all vertices by pressing A, then G 0 to move the vertices by 0 m, left-click or Return to confirm. Afterwards the faces are split along the intersections.

    split faces

  3. If you then select the outer edges on one side and press G twice, you can edge slide them towards the faces until they meet the inner vertices. Left-click or Return to confirm the slide, with the Auto Merge option still enabled they are now merged together.

    edge slide to face

    faces split on edges

  4. Repeat this for the other sides and then you have the desired shape.

    finished shape

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In your case extrusions are axis-aligned, and the beziers are rotated 2D curves, so you can take advantage of 3D beziers interpolating each axis independently, and just copying one axis to the other - remember to make the handles "FREE" otherwise moving one handle will move another and you won't be able to repeat the step on the opposite handle…

Now you can apply a "Screw" modifier with a resolution of 4:

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