def sector(ray1, ray2, **extra_options):
r"""
Plot a sector between ``ray1`` and ``ray2`` centered at the origin.
.. NOTE::
This function was intended for plotting strictly convex cones, so it
plots the smaller sector between ``ray1`` and ``ray2`` and, therefore,
they cannot be opposite. If you do want to use this function for bigger
regions, split them into several parts.
.. NOTE::
As of version 4.6 Sage does not have a graphic primitive for sectors in
3-dimensional space, so this function will actually approximate them
using polygons (the number of vertices used depends on the angle
between rays).
INPUT:
- ``ray1``, ``ray2`` -- rays in 2- or 3-dimensional space of the same
length;
- ``extra_options`` -- a dictionary of options that should be passed to
lower level plotting functions.
OUTPUT:
- a plot.
EXAMPLES::
sage: from sage.geometry.toric_plotter import sector
sage: print sector((1,0), (0,1))
Graphics object consisting of 1 graphics primitive
sage: print sector((3,2,1), (1,2,3))
Graphics3d Object
"""
ray1 = vector(RDF, ray1)
ray2 = vector(RDF, ray2)
r = ray1.norm()
if len(ray1) == 2:
# Plot an honest sector
phi1 = arctan2(ray1[1], ray1[0])
phi2 = arctan2(ray2[1], ray2[0])
if phi1 > phi2:
phi1, phi2 = phi2, phi1
if phi2 - phi1 > pi:
phi1, phi2 = phi2, phi1 + 2 * pi
return disk((0, 0), r, (phi1, phi2), **extra_options)
else:
# Plot a polygon, 30 vertices per radian.
vertices_per_radian = 30
n = ceil(arccos(ray1 * ray2 / r**2) * vertices_per_radian)
dr = (ray2 - ray1) / n
points = (ray1 + i * dr for i in range(n + 1))
points = [r / pt.norm() * pt for pt in points]
points.append(vector(RDF, 3))
return polygon(points, **extra_options)
def sector(ray1, ray2, **extra_options):
r"""
Plot a sector between ``ray1`` and ``ray2`` centered at the origin.
.. NOTE::
This function was intended for plotting strictly convex cones, so it
plots the smaller sector between ``ray1`` and ``ray2`` and, therefore,
they cannot be opposite. If you do want to use this function for bigger
regions, split them into several parts.
.. NOTE::
As of version 4.6 Sage does not have a graphic primitive for sectors in
3-dimensional space, so this function will actually approximate them
using polygons (the number of vertices used depends on the angle
between rays).
INPUT:
- ``ray1``, ``ray2`` -- rays in 2- or 3-dimensional space of the same
length;
- ``extra_options`` -- a dictionary of options that should be passed to
lower level plotting functions.
OUTPUT:
- a plot.
EXAMPLES::
sage: from sage.geometry.toric_plotter import sector
sage: sector((1,0), (0,1))
Graphics object consisting of 1 graphics primitive
sage: sector((3,2,1), (1,2,3))
Graphics3d Object
"""
ray1 = vector(RDF, ray1)
ray2 = vector(RDF, ray2)
r = ray1.norm()
if len(ray1) == 2:
# Plot an honest sector
phi1 = arctan2(ray1[1], ray1[0])
phi2 = arctan2(ray2[1], ray2[0])
if phi1 > phi2:
phi1, phi2 = phi2, phi1
if phi2 - phi1 > pi:
phi1, phi2 = phi2, phi1 + 2 * pi
return disk((0,0), r, (phi1, phi2), **extra_options)
else:
# Plot a polygon, 30 vertices per radian.
vertices_per_radian = 30
n = ceil(arccos(ray1 * ray2 / r**2) * vertices_per_radian)
dr = (ray2 - ray1) / n
points = (ray1 + i * dr for i in range(n + 1))
points = [r / pt.norm() * pt for pt in points]
points.append(vector(RDF, 3))
return polygon(points, **extra_options)