peteroznewman
Subscriber
It may be possible to apply a deformation to a set of nodes in the form of a spherical surface, but that seems artificial. Using pressure to press the film down onto a rigid spherical surface seems realistic.
To deform a flat surface into a spherical surface, create a cylindrical coordinate system at the center of the film, where the XY axes are in the plane and the Z axis is normal to the plane. Create a deformation as a function of the X coordinate, which is the radial coordinate, r.
A spherical surface is defined by the Radius of Curvature R and the radius D/2. I would replace D/2 with r in the equation below because if you have the r,theta,z coordinates of a node in the coordinate frame described above, then the value of r is the X coordinate value, and the Z coordinate is calculated by the SAG equation.