Processing field manipulation in three-dimensional printing

An apparatus for printing a three-dimensional object comprising:

• one or more controllers configured to
• (i) operatively couple (a) to an electrical power source, (b) to an energy beam source, and (c) to one or more guidance systems;
• (ii) select, or direct selection of, a location Aj of the one or more guidance systems from a location set A1, A2, . . . An, wherein n and j are integers;
• and
• (iii) direct the one or more guidance systems to guide an energy beam from the location Aj to a point P on a surface of the three-dimensional object, wherein Vj is a unit vector of a vector from the location Aj to the point P, wherein Uj is a unit vector of a projection of Vj on a plane normal to a global vector, the energy beam being generated by the energy beam source,
• wherein the global vector is (a) directed to a gravitational center of an ambient environment, (b) directed opposite to a direction of layer-wise deposition to print the three-dimensional object, and/or (c) normal to a platform configured to support the three-dimensional object during its printing and directed opposite to a surface of the platform that supports the three-dimensional object,
• wherein a unit vector N normal to an average of the surface of the three-dimensional object at the point P forms an angle alpha with the global vector, wherein the angle alpha is at most about 45 degrees, wherein the unit vector N is directed away from the three-dimensional object, and
• wherein M is a unit vector of a projection of N on a plane normal to the global vector, wherein Sj is a scalar product of Uj·M, and wherein the point P satisfies having a Sj value of from about minus one (−1) to about half (0.5).