List Plots

sage.plot.plot3d.list_plot3d.list_plot3d(v, interpolation_type='default', texture='automatic', point_list=None, **kwds)

A 3-dimensional plot of a surface defined by the list of points in 3-dimensional space.

INPUT:

• v - something that defines a set of points in 3 space, for example:
  • a matrix
  • a list of 3-tuples
  • a list of lists (all of the same length) - this is treated the same as a matrix.
• texture - (default: “automatic”), solid light blue

OPTIONAL KEYWORDS:

• interpolation_type - ‘linear’, ‘nn’ (nearest neighbor), ‘spline’

  ‘linear’ will perform linear interpolation

  The option ‘nn’ will interpolate by averaging the value of the nearest neighbors, this produces an interpolating function that is smoother than a linear interpolation, it has one derivative everywhere except at the sample points.

  The option ‘spline’ interpolates using a bivariate B-spline.

  When v is a matrix the default is to use linear interpolation, when v is a list of points the default is nearest neighbor.

• degree - an integer between 1 and 5, controls the degree of spline used for spline interpolation. For data that is highly oscillatory use higher values

• point_list - If point_list=True is passed, then if the array is a list of lists of length three, it will be treated as an array of points rather than a 3xn array.

• num_points - Number of points to sample interpolating function in each direction. By default for an nxn array this is n.

• **kwds - all other arguments are passed to the surface function

OUTPUT: a 3d plot

EXAMPLES:

We plot a matrix that illustrates summation modulo .

sage: n = 5; list_plot3d(matrix(RDF,n,[(i+j)%n for i in [1..n] for j in [1..n]]))

We plot a matrix of values of sin.

sage: pi = float(pi)
sage: m = matrix(RDF, 6, [sin(i^2 + j^2) for i in [0,pi/5,..,pi] for j in [0,pi/5,..,pi]])
sage: list_plot3d(m, texture='yellow', frame_aspect_ratio=[1,1,1/3])

Though it doesn’t change the shape of the graph, increasing num_points can increase the clarity of the graph.

sage: list_plot3d(m, texture='yellow', frame_aspect_ratio=[1,1,1/3],num_points=40)

We can change the interpolation type.

sage: list_plot3d(m, texture='yellow', interpolation_type='nn',frame_aspect_ratio=[1,1,1/3])

We can make this look better by increasing the number of samples.

sage: list_plot3d(m, texture='yellow', interpolation_type='nn',frame_aspect_ratio=[1,1,1/3],num_points=40)

Let’s try a spline.

sage: list_plot3d(m, texture='yellow', interpolation_type='spline',frame_aspect_ratio=[1,1,1/3])

That spline doesn’t capture the oscillation very well; let’s try a higher degree spline.

sage: list_plot3d(m, texture='yellow', interpolation_type='spline', degree=5, frame_aspect_ratio=[1,1,1/3])

We plot a list of lists:

sage: show(list_plot3d([[1, 1, 1, 1], [1, 2, 1, 2], [1, 1, 3, 1], [1, 2, 1, 4]]))

We plot a list of points. As a first example we can extract the (x,y,z) coordinates from the above example and make a list plot out of it. By default we do linear interpolation.

sage: l=[]
sage: for i in range(6):
...      for j in range(6):
...         l.append((float(i*pi/5),float(j*pi/5),m[i,j]))
sage: list_plot3d(l,texture='yellow')

Note that the points do not have to be regularly sampled. For example:

sage: l=[]
sage: for i in range(-5,5):
...    for j in range(-5,5):
...      l.append((normalvariate(0,1),normalvariate(0,1),normalvariate(0,1)))
sage: list_plot3d(l,interpolation_type='nn',texture='yellow',num_points=100)

TESTS: We plot 0, 1, and 2 points:

sage: list_plot3d([])
sage: list_plot3d([(2,3,4)])
sage: list_plot3d([(0,0,1), (2,3,4)])

However, if two points are given with the same x,y coordinates but different z coordinates, an exception will be raised:

sage: pts =[(-4/5, -2/5, -2/5), (-4/5, -2/5, 2/5), (-4/5, 2/5, -2/5), (-4/5, 2/5, 2/5), (-2/5, -4/5, -2/5), (-2/5, -4/5, 2/5), (-2/5, -2/5, -4/5), (-2/5, -2/5, 4/5), (-2/5, 2/5, -4/5), (-2/5, 2/5, 4/5), (-2/5, 4/5, -2/5), (-2/5, 4/5, 2/5), (2/5, -4/5, -2/5), (2/5, -4/5, 2/5), (2/5, -2/5, -4/5), (2/5, -2/5, 4/5), (2/5, 2/5, -4/5), (2/5, 2/5, 4/5), (2/5, 4/5, -2/5), (2/5, 4/5, 2/5), (4/5, -2/5, -2/5), (4/5, -2/5, 2/5), (4/5, 2/5, -2/5), (4/5, 2/5, 2/5)]
sage: show(list_plot3d(pts, interpolation_type='nn'))
...
ValueError: Two points with same x,y coordinates and different z coordinates were given. Interpolation cannot handle this.

Additionally we need at least 3 points to do the interpolation:

sage: mat = matrix(RDF, 1, 2, [3.2, 1.550])
sage: show(list_plot3d(mat,interpolation_type='nn'))
... 
ValueError: We need at least 3 points to perform the interpolation

sage.plot.plot3d.list_plot3d.list_plot3d_array_of_arrays(v, interpolation_type, texture, **kwds)

sage.plot.plot3d.list_plot3d.list_plot3d_matrix(m, texture, **kwds)

sage.plot.plot3d.list_plot3d.list_plot3d_tuples(v, interpolation_type, texture, **kwds)