Generate random locations within a triangular domain

Question

I want to generate x and y having a uniform distribution and limited by [xmin,xmax] and [ymin,ymax]

The points (x

Answer 1

Uniform on the triangle?

import numpy as np

N = 10 # number of points to create in one go

rvs = np.random.random((N, 2)) # uniform on the unit square
# Now use the fact that the unit square is tiled by the two triangles
# 0 <= y <= x <= 1 and 0 <= x < y <= 1
# which are mapped onto each other (except for the diagonal which has
# probability 0) by swapping x and y.
# We use this map to send all points of the square to the same of the
# two triangles. Because the map preserves areas this will yield 
# uniformly distributed points.
rvs = np.where(rvs[:, 0, None]>rvs[:, 1, None], rvs, rvs[:, ::-1])

Finally, transform the coordinates
xmin, ymin, xmax, ymax = -0.1, 1.1, 2.0, 3.3
rvs = np.array((ymin, xmin)) + rvs*(ymax-ymin, xmax-xmin)

Uniform marginals? The simplest solution would be to uniformly concentrate the mass on the line (ymin, xmin) - (ymax, xmax)

rvs = np.random.random((N,))
rvs = np.c_[ymin + (ymax-ymin)*rvs, xmin + (xmax-xmin)*rvs]

but that is not very interesting, is it?