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,xisoyisozXYZxyzXYZ, , XYZXYZwhere θc and θg are the collimator and gantry angles, respectively. The senses of rotation of the collimator and gantry followed the IEC61217 scale convention, and the directions of the X′, Y′, and Z′ axes are presented in Figure 3. (3) A point in the BCS was projected onto the BEV plane at the 001ICS), was performed.where (xiso, yiso, ziso) are the coordinates of the isocenter in the DCS. (2) The coordinate transfor-mation from the ICS to a coordinate system (X′, Y′, Z′) fixed at the gantry with the isocenter as the origin (beam coordinate system [BCS]) was performed.Figure 3　Definition of the beam coordinate system (BCS) and beam’s eye view (BEV) plane, which are fixed to the collimator and rotate with the collimator and gantry. When both the collimator and gantry angles are 0°, the X′ axis is in the cross-plane direction, Y′ axis is in the vertical direction, Z′ axis is in the in-plane direction, rotation of the collimator is around the Y′ axis (θc), and rotation of the gantry is around the Z′ axis (θg). Point A is the isocenter. By projecting onto the BEV plane, the point B′ (X′, Y′, Z′) is moved to BBEV (XBEV, 0, ZBEV).isocenter (Y′ = 0 in the BCS) as follows:where SAD is the source-to-isocenter distance of 100 cm. With the projection, point B′ was moved to point BBEV, as shown in Figure 3. By projecting all hotspots in the 3D dose distribution, the projec-tion of the hotspot region on the BEV was obtained as a binary image (Figure 4). The MLC leaves in the sub-beams were moved to cover the hotspot region in the BEV as in Figure 4. An MLC leave which is on the side of a hotspot was used to block the hotspot if the hotspot did not cross the vertical center line of a field. If a hotspot region crossed the vertical center line of a field, the horizontal distances from the center of the field to the outer edges of the hotspot were measured, as SAD+Y(SAD)0Y(SAD+SAD)cos0sin0sin100cos378iso=+=ccggggccXZ=000000sincos0cossin0BEV0BEV