In this work, motivated by the effectiveness of the local representation for shaped reflectors, we explore the use of axis-displaced confocal quadrics into the numerical solution of the MA equation.
The shaped reflector surface is defined by a set of grid points and confocal quadrics that are employed to locally interpolate the surface.
Here, alternatively, the numerical solution employs axis-displaced confocal quadrics to locally describe the reflector's surface, which allows an analytical representation of the derivatives and the simplification of (3).
It explores the local interpolating properties of confocal quadrics to represent shaped reflector surfaces, which allows the partial derivatives involved in the formulation to be analytically expressed and provides a significant simplification of the MA equation.