<p>I have three points P<sub>0</sub>, P<sub>1</sub>, P<sub>2</sub>, which are located on an arbitrarily oriented ellipse in 3D space. I have a square texture map with a circle on it. I would like to render a textured quad (with the obvious UV mapping) so that the circle in the texture map projects onto the ellipse that P<sub>0</sub>, P<sub>1</sub>, P<sub>2</sub> are on. </p>

<p>How do I calculate the vertices of the quad to project the ellipse correctly?</p>

<p>(Alternately, in addition to P<sub>0</sub>, P<sub>1</sub>, P<sub>2</sub>, I have the <a href="https://en.wikipedia.org/wiki/Orbital_elements#Keplerian_elements" rel="nofollow">Keplerian elements</a> of an elliptical orbit, if that's more straightforward.)</p>

CC BY-SA 3.0
2015-12-01T13:20:31.557Z
Isn't this slightly under-constrained?   If you only have 3  coplanar(?),  non-colinear points, won't that allow you to have a circle? (Or do you also have the centre?)
Simon F
CC BY-SA 3.0
2015-12-01T15:16:01.610Z
Are the three points any particular points on the ellipse? e.g. if one is guaranteed to be one end of the major axis, and another is one end of the minor axis, then the problem is trivial.
Dan Hulme
CC BY-SA 3.0
2015-12-01T16:43:47.290Z
Yeah, someone elsewhere pointed out it's underconstrained, and the Keplerian elements are probably more usable. That said, I can arrange for the points to be the end of the major and minor axes if that trivializes the problem.
Russell Borogove
CC BY-SA 3.0
2015-12-02T01:10:19.490Z
If you have the center and major/minor axis vectors, then the corners of the quad will just be center ± major ± minor.
Nathan Reed
<3d><projections>
Project quad onto ellipse in 3D
Russell Borogove
# Project quad onto ellipse in 3D

(Asked by: username_0 on 2015-12-01)

I have three points P0, P1, P2, which are located on an arbitrarily oriented ellipse in 3D space. I have a square texture map with a circle on it. I would like to render a textured quad (with the obvious UV mapping) so that the circle in the texture map projects onto the ellipse that P0, P1, P2 are on.

How do I calculate the vertices of the quad to project the ellipse correctly?

(Alternately, in addition to P0, P1, P2, I have the [Keplerian elements](https://en.wikipedia.org/wiki/Orbital_elements#Keplerian_elements) of an elliptical orbit, if that's more straightforward.)

**Tags:** 3d, projections

> **Comments:**
> **username_1**: Isn't this slightly under-constrained?   If you only have 3  coplanar(?),  non-colinear points, won't that allow you to have a circle? (Or do you also have the centre?)  
> **username_2**: Are the three points any particular points on the ellipse? e.g. if one is guaranteed to be one end of the major axis, and another is one end of the minor axis, then the problem is trivial.  
> **username_0**: Yeah, someone elsewhere pointed out it's underconstrained, and the Keplerian elements are probably more usable. That said, I can arrange for the points to be the end of the major and minor axes if that trivializes the problem.  
> **username_3**: If you have the center and major/minor axis vectors, then the corners of the quad will just be center ± major ± minor.  

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## 0 answers

