# Revision history [back]

The key is the add_condition method already mentioned by @FrédericC in his answer. Anyway, since the O.P. deals with parametric surfaces, I provide a complete example:

var("u,v")
S = parametric_plot3d(((2+cos(v))*cos(u), (2+cos(v))*sin(u), sin(v)), (u,0,2*pi), (v,0,2*pi))
S.show(viewer="threejs")
p1 = (-3,-2,-1)
p2 = (3,2,0.5)
def cond(*xyz):
return all([t[0]<=t[1]<=t[2] for t in zip(p1,xyz,p2)])


This code first shows a torus, then the same torus clipped by the box determined by two given points p1 and p2. See this SageMath Cell. Concerning the second argument of add_condition, the docs indicates that it is the number of steps used on the boundary to cut the triangles that are not entirely within the domain; the larger is this argument, the smoother is the boundary.

The key is the add_condition method already mentioned by @FrédericC in his answer. Anyway, since the O.P. deals with parametric surfaces, I provide a complete example:

var("u,v")
S = parametric_plot3d(((2+cos(v))*cos(u), (2+cos(v))*sin(u), sin(v)), (u,0,2*pi), (v,0,2*pi))
S.show(viewer="threejs")
p1 = (-3,-2,-1)
p2 = (3,2,0.5)
def cond(*xyz):
return all([t[0]<=t[1]<=t[2] for t in zip(p1,xyz,p2)])

This code first shows a torus, then the same torus clipped by the box determined by two given points p1 and p2. See this SageMath Cell. Concerning the second argument of add_condition, the docs indicates that it is the number of steps used on the boundary to cut the triangles that are not entirely within the domain; the larger is this argument, argument is, the smoother is the boundary.boundary is.