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Projection using Formula or increase triangulation.

Projection using Formula or increase triangulation.

Projection using Formula or increase triangulation.

(OP)
Hi everyone,
I have to project all the faces of a body on a plane in such a way that the all coordinates (x,y,z) of the body become (x,0,sqrt(y^2+z^2))on the plane.
Is it possible to do this using a law formula? I had a look at this potential possibility but it turns out that I have no idea how to do it so I looked for other options. So far I have tried the following:


1- Create a journal to revolve all the FACES of the body around the Z axis, then cutting this with a plane to get a slice that contains all these points. Problem -> Some faces cannot be revolved (e.g. cylinders, caps etc).


2- Create a journal to project all the EDGES of the body on the plane following (x,y,z) -> (x,0,sqrt(y^2+z^2)). Problem -> Some edges cannot be projected(e.g. cylinders, caps etc).


3- Create a journal to project all the POINTS of the body on the plane following (x,y,z) -> (x,0,sqrt(y^2+z^2))and then trying to fit a surface that pass through those points. Problem -> It is hard to fit a surface in complicated shapes.


4- Save the initial body as VRML in order to get tessellated geometry (triangle coordinates), then create a code to parse the file changing directly the(x,y,z) coordinates of each triangle for (x,0,sqrt(y^2+z^2). It works OK but for some bodies I would need to increase the number of triangles if I want to get a good result (e.g a rectangular face will have only 2 triangles but I would need more triangle for my purpose in some cases).

Do you have any ideas regarding the law formula or how to increase the number of triangles in a face or any other suggestions to help me accomplishing this task?

Please see a picture illustrating the end purpose of this.

Many thanks!
J

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