# How to orthogonaly project a 3d plot to coordinate planes?

Hi, I created a 3d plot with

parametric_plot3d( (cos(t)^3, sin(t)^3, cos(2*t)), (t, 0, 2*pi))


I looked over at google for some projection() functions but I didn't find much.

Basically what I need to do is orthogonally project that plot onto coordinate planes (x, y, z).

If anyone has any idea or an approximate algorithm, that would be nice.

Edit: is it possible that this is an orthogonal projection to coordinate planes? I'm showing 3 plots, first has z = 0, second has x = 0 and third has y = 0.

show( parametric_plot3d((cos(t)^3, sin(t)^3, 0), (t, 0, 2*pi)) + parametric_plot3d( (0, sin(t)^3, cos(2*t)), (t, 0, 2*pi)) + parametric_plot3d( (cos(t)^3, 0, cos(2*t)), (t, 0, 2*pi)));

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Is this what you mean? We can just "slice" the vector here to get the coordinate pieces.

sage: var('t')
t
sage: V = vector((cos(t)^3, sin(t)^3, cos(2*t)))
sage: parametric_plot3d(V,(t,0,2*pi))
sage: parametric_plot(V[:2],(t,0,2*pi))
sage: parametric_plot(V[1:],(t,0,2*pi))
sage: parametric_plot(vector((V,V)),(t,0,2*pi))


Naturally, orthogonal projection to some random plane would be more involved (though basically you could use the vector projection, I guess), but maybe you don't need that much firepower.

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