<p>If instead of stereographic projection you can use other conformal projection. I would recommend you the "Least Squares Conformal Maps" algorithm. There are several implementations out there, including the prominent CGAL (<a href="https://doc.cgal.org/latest/Surface_mesh_parameterization/index.html" rel="nofollow noreferrer">https://doc.cgal.org/latest/Surface_mesh_parameterization/index.html</a>).</p>

CC BY-SA 3.0
2018-03-08T01:29:58.833Z
2018-03-08T01:29:58.833Z
Mauricio Cele Lopez Belon
<p>Using blender, you can position the camera at the north pole of the sphere you are stereographically projecting, and then set a really wide <a href="https://docs.blender.org/manual/en/dev/render/cycles/camera.html#perspective" rel="nofollow noreferrer">field of view</a>. For example, I had to set my focal length to around 5 mm to get a hemisphere in the stereographic projection, but it will depend on the model, of course. Then simply render and you're done!</p>

CC BY-SA 3.0
2018-03-07T15:38:18.230Z
2018-03-07T15:38:18.230Z
Christopher King
<p>Given a 3D model, is there a way to <a href="https://en.wikipedia.org/wiki/Stereographic_projection" rel="nofollow noreferrer">stereographically project</a> it to a 2D image? In particular, I would only need a little more than half the model (the lower half) to be mapped to the plane (mapping the whole 3D model would be impossible, since the stereographic projection is infinite).</p>

<p>I am using Linux, if that makes any difference. Also, I would prefer to use free software.</p>

<p>(Note: If I could increase the viewing angle, I could do this with most any 3D viewing software, since the stereographic projection is just the view from a certain point with a wide viewing angle. In particular, I was able to get a small portion of the stereographic projection from meshlab.)</p>

CC BY-SA 3.0
2018-03-06T10:53:43.707Z
Stereographic projection implies projecting the surface of a sphere onto a plane. So unless your model is also spherical you're gonna get self-intersections on the plane. Is this what you want?
russ
CC BY-SA 3.0
2018-03-06T16:53:36.207Z
@russ It is nearly spherical (a polyhedron).
Christopher King
CC BY-SA 3.0
2018-03-08T01:17:29.530Z
Do you need an actual stereographic projection? Or just any conformal one-to-one projection to the plane would also work. There are better approaches to map surfaces (or any topological disk) to a plane. You acn even map a topological sphere (closed surface) to the plane without seams decomposing it in two charts. Closed surface of high genus can be also mapped but would require more charts.
Mauricio Cele Lopez Belon
CC BY-SA 3.0
2018-03-08T01:18:27.273Z
@MauricioCeleLopezBelon I wanted sterographic, but that works too.
Christopher King
<image-processing><projections><raster-image>
How to generate the stereographic projection of a 3D model
Christopher King
# How to generate the stereographic projection of a 3D model

(Asked by: username_0 on 2018-03-06)

Given a 3D model, is there a way to [stereographically project](https://en.wikipedia.org/wiki/Stereographic_projection) it to a 2D image? In particular, I would only need a little more than half the model (the lower half) to be mapped to the plane (mapping the whole 3D model would be impossible, since the stereographic projection is infinite).

I am using Linux, if that makes any difference. Also, I would prefer to use free software.

(Note: If I could increase the viewing angle, I could do this with most any 3D viewing software, since the stereographic projection is just the view from a certain point with a wide viewing angle. In particular, I was able to get a small portion of the stereographic projection from meshlab.)

**Tags:** image-processing, projections, raster-image

> **Comments:**
> **username_1**: Stereographic projection implies projecting the surface of a sphere onto a plane. So unless your model is also spherical you're gonna get self-intersections on the plane. Is this what you want?  
> **username_0**: @username_1 It is nearly spherical (a polyhedron).  
> **username_2**: Do you need an actual stereographic projection? Or just any conformal one-to-one projection to the plane would also work. There are better approaches to map surfaces (or any topological disk) to a plane. You acn even map a topological sphere (closed surface) to the plane without seams decomposing it in two charts. Closed surface of high genus can be also mapped but would require more charts.  
> **username_0**: @username_2 I wanted sterographic, but that works too.  

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## 2 answers

### Answer by username_2 on 2018-03-08. Score: 1

If instead of stereographic projection you can use other conformal projection. I would recommend you the "Least Squares Conformal Maps" algorithm. There are several implementations out there, including the prominent CGAL (<https://doc.cgal.org/latest/Surface_mesh_parameterization/index.html>).


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### Answer by username_0 on 2018-03-07. Score: 0

Using blender, you can position the camera at the north pole of the sphere you are stereographically projecting, and then set a really wide [field of view](https://docs.blender.org/manual/en/dev/render/cycles/camera.html#perspective). For example, I had to set my focal length to around 5 mm to get a hemisphere in the stereographic projection, but it will depend on the model, of course. Then simply render and you're done!


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