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Student Support Forum: 'project ellipsoid on 2D' topicStudent Support Forum > General > "project ellipsoid on 2D"

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phd student
04/29/13 01:55am

I am a phd student, I work on quadric surfaces. I have an ellipsoid such that:

a = 20.;
b = 60.;
c = 20.;
x0 = 0.;
y0 = 0.;
z0 = 0.;
eq = (x + x0)^2/a^2 + (y - y0)^2/b^2 + (z - z0)^2/c^2 - 1;
QH = {{1/a^2, 0, 0, -(x0/a^2)}, {0, 1/b^2, 0, -(y0/b^2)}, {0, 0, 1/
c^2, -(z0/c^2)}, {0, 0, 0, -1 + x0^2/a^2 + y0^2/b^2 + z0^2/c^2}};

I need to project it by the camera

Matcam = {{39.1596, -203.069, 526.526, 196977.}, {-75.0686, -410.767,
75.0686, 147733.}, {-0.609208, -0.507673, 0.609208, 492.443}};

The result is a conic, it is an ellipse. I project Qs by applying this formula:

m = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}};
H = PseudoInverse[Matcam].m;
m // MatrixForm
H // MatrixForm
conic = Transpose[H].QH.H;
conic // MatrixForm
coniq = conic[[{1, 2, 4}, {1, 2, 4}]];
coniq // MatrixForm

my conic result is conic, I plot it using contour plot like this:

ContourPlot[{x, y, 1}.coniq.{x, y, 1} == 0, {x, -20, 20}, {y, -20,
20}]

but it does not give any graphics.

Please help me? may the formula of projection is false?

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Subject (listing for 'project ellipsoid on 2D')
Author Date Posted
project ellipsoid on 2D phd student 04/29/13 01:55am
Re: project ellipsoid on 2D Bill Simpson 04/30/13 00:42am
Re: Re: project ellipsoid on 2D phd student 04/30/13 11:01am
Re: Re: Re: project ellipsoid on 2D Bill Simpson 05/02/13 08:30am
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