I was wondering, how would you, mathematically speaking, generate x points at random positions on a 3D surface, knowing the number of triangle polygons composing the surface (their dimensions, positions, normals, etc.)? In how many steps would you proceed?
I'm trying to create a "scatterer" in Maya (with Python and API), but I don't even know where to start in terms of concept. Should I generate the points first, and then check if they belong to the surface? Should I create the points directly on the surface (and how, in this case)?
Edit: I want to achieve this without using 2D projection or UVs, as far as possible.
You should compute the area of each triangle, and use those as weights to determine the destination of each random point. It is probably easiest to do this as a batch operation:
def sample_areas(triangles, samples):
# compute and sum triangle areas
totalA = 0.0
areas = []
for t in triangles:
a = t.area()
areas.append(a)
totalA += a
# compute and sort random numbers from [0,1)
rands = sorted([random.random() for x in range(samples)])
# sample based on area
area_limit = 0.0
rand_index = 0
rand_value = rands[rand_index]
for i in range(len(areas)):
area_limit += areas[i]
while rand_value * totalA < area_limit:
# sample randomly over current triangle
triangles[i].add_random_sample()
# advance to next sorted random number
rand_index += 1;
if rand_index >= samples:
return
rand_value = rands[rand_index]
Note that ridged or wrinkled regions may appear to have higher point density, simply because they have more surface area in a smaller space.