An additive manufacturing apparatus, comprising: a material depositing device and a resin handling assembly, wherein the resin handling assembly is a tape casting apparatus and includes a support film or tape and a radiant energy apparatus, the tape casting apparatus includes spaced apart rollers with a transparent flexible polymeric tape or foil extending between the rollers; a resin support that defines a build surface that is configured to support an uncured layer of resin; wherein the resin support comprises the transparent flexible polymeric tape or foil; and wherein the resin support comprises a transparent support plate configured to support portion of the tape or foil from underneath; means configured for driving the roller so as to maintain the tape or foil appropriately tensioned between the rollers and to wind the tape and foil from one of the rollers to another roller; means for applying or depositing resin to the build surface in a general uniform layer; a stage configured to hold a stacked arrangement of one or more cured layers of resin that form a part that defines a surface positioned opposite the stage, wherein the stage defining a planar surface which is capable of being oriented parallel to the build surface of the portion of the tape or foil positioned over the support plate; the radiant energy apparatus positioned opposite to the stage such that it is operable to generate and project radiant energy in a predetermined pattern; an actuator configured to change the relative position of the stage and the resin support; a measuring system that is configured for measuring the position of one or more structures relative to the resin support; wherein the structure is one of the following: the stage, a surface of the uncured layer of resin, a surface of the part, and a combination thereof; and wherein the measuring system is configured to determine a plane of the part by measuring the distance of multiple locations on the structure, wherein, the measuring system is configured to measure a first set of multiple locations after the first cycle and measure a second set of multiple locations after a second cycle and wherein the second set of multiple locations is different than the first set of multiple locations; and a computer that is configured to use a signal generated by the measuring system to implement a closed control loop configured to adjust the height of the stage as determined relative to a reference relative to an expected height. a material depositing device and a resin handling assembly, wherein the resin handling assembly is a tape casting apparatus and includes a support film or tape and a radiant energy apparatus, the tape casting apparatus includes spaced apart rollers with a transparent flexible polymeric tape or foil extending between the rollers; a resin support that defines a build surface that is configured to support an uncured layer of resin; wherein the resin support comprises the transparent flexible polymeric tape or foil; and wherein the resin support comprises a transparent support plate configured to support portion of the tape or foil from underneath; means configured for driving the roller so as to maintain the tape or foil appropriately tensioned between the rollers and to wind the tape and foil from one of the rollers to another roller; means for applying or depositing resin to the build surface in a general uniform layer; a stage configured to hold a stacked arrangement of one or more cured layers of resin that form a part that defines a surface positioned opposite the stage, wherein the stage defining a planar surface which is capable of being oriented parallel to the build surface of the portion of the tape or foil positioned over the support plate; the radiant energy apparatus positioned opposite to the stage such that it is operable to generate and project radiant energy in a predetermined pattern; an actuator configured to change the relative position of the stage and the resin support; a measuring system that is configured for measuring the position of one or more structures relative to the resin support; wherein the structure is one of the following: the stage, a surface of the uncured layer of resin, a surface of the part, and a combination thereof; and wherein the measuring system is configured to determine a plane of the part by measuring the distance of multiple locations on the structure, wherein, the measuring system is configured to measure a first set of multiple locations after the first cycle and measure a second set of multiple locations after a second cycle and wherein the second set of multiple locations is different than the first set of multiple locations; and a computer that is configured to use a signal generated by the measuring system to implement a closed control loop configured to adjust the height of the stage as determined relative to a reference relative to an expected height.