# Plotting planes

Hi, how can I plot these planes? http://oi59.tinypic.com/11se51t.jpg

I'd especially like to know how to plot the second plane. Thanks.

Plotting planes

Hi, how can I plot these planes? http://oi59.tinypic.com/11se51t.jpg

I'd especially like to know how to plot the second plane. Thanks.

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0

Hi,

For the first example, you can use **parametric_plot3d**

```
sage: v0 = vector([1,0,1])
sage: v1 = vector([-2,1,3])
sage: v2 = vector([0,-1,1])
sage: s,t = var('s,t')
sage: parametric_plot3d(v0 + s*v1 + t*v2, (s,-2,2), (t,-2,2))
```

And for the second one you can use **implicit_plot3d**

```
sage: x,y,z = var('x,y,z')
sage: v = vector([-1,2,1])
sage: X = vector([x,y,z])
sage: implicit_plot3d(X.dot_product(v) == 1, (x,-2,2), (y,-2,2), (z,-2,2))
```

Vincent

1

Yet another solution is to define the planes as (non-compact) polyhedra:

```
sage: P_prime = Polyhedron(eqns=[(1, -1,2,1)])
sage: P_prime.Hrepresentation()
(An equation (1, -2, -1) x - 1 == 0,)
sage: P_prime.Vrepresentation()
(A line in the direction (0, 1, -2),
A line in the direction (1, 0, 1),
A vertex at (0, 0, -1))
sage: P_prime.plot()
```

0

This is possible using hyperplane arrangements, for example:

```
sage: H.<x,y,z> = HyperplaneArrangements(QQ)
sage: ha = H(x, y, x - 1, y - 1, x + y - z)
sage: ha.plot()
```

Note that you will have to work out the equations of your hyperplanes.

Asked: **
2014-11-09 06:26:00 -0500
**

Seen: **135 times**

Last updated: **Nov 11 '14**

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