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DX11 Creating New Control Points In Hull Shader

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I'm experimenting with terrain hardware tessellation in DirectX 11. What I want to do is to take a single control point as input in the hull shader, and produce a patch with 4 control points as output. And then the patch constant function will apply the tessellation factors to these 4 edges and send it to the tessellator. But in every tutorial and example I can find, they're using the same amount of control points for both the hull shader and the patch constant function.

So I wonder if anyone could please help me a bit on how to do this?

I do find it a bit weird if this would not be possible, because for example, the geometry shader can do this, and that's what I've been using so far. But the geometry shader doesn't provide any tessellation, so that's why I'm experimenting with this change. If the hull shader actually doesn't support this, are there any efficient workarounds?

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