Module: sage.plot.plot3d.list_plot3d
List Plots
Module-level Functions
v, [interpolation_type=default], [texture=automatic], [point_list=None]) |
A 3-dimensional plot of a surface defined by the list
of
points in 3-dimensional space.
Input:
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.
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 shap 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)
Lets 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, lets 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)
v, interpolation_type, texture) |
m, texture) |
v, interpolation_type, texture) |