How to project onto a surface a divergent rectangle

[E_Matt_Roberts]

Hi, I would like to perspective-project a rectangle along its normal onto a spherical surface to create a 3D sketch or curve.

The rectangle is within the volume of the sphere

The rectangle is much smaller than the sphere

The rectangle normal may be orientated with any vector

So for parallel projection this can be achieved by creating a 3D sketch and the Project to Surface command.

But I would like to define a divergent angle so the rectangle tapers out towards the spherical surface interior. 

Lofting is difficult or impossible for other factors. the reasons are lengthy to explain here.

Is there a surface or solid modelling trick, or add-in, that allows this?

Thanks

M

[JDMather]

Can you attach the ipt file of what you have attempted so far?  (make up a dummy file if the design is proprietary)

Can you post a picture or url of a similar design to what you are trying to achieve.

[Nicolas.Bourquin]

Dear E_Matt_Roberts,

I hope I have fully understood your request, but maybe the attached ipt file (2014 version) I have prepared for you could help.

The steps I have followed:

0) generation of the sphere

1) generation of a sketch with the rectangle on a plan out of the sphere

2) creation of a 3dsketch line used as a vector passing through a corner of the rectangle.

3) using a"sweep" (generated as a surface) feature based on the vector used as path with a taper value

4) creation of a new 3D sketch => intersection between 2 surfaces (spher and sweep) 

The result is then: projection of a rectangle on the spherical surface following a vector line with a taper value.

I hope that can help

Many thanks

Best Regards