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Welzl, E. (1991) Smallest Enclosing Disks (Balls and Ellipsoids). In: Maurer, H., Ed., New Results and New Trends in Computer Science, Lecture Notes in Computer Science, Vol. 555, Springer, New York, 359-370.
http://dx.doi.org/10.1007/bfb0038202

has been cited by the following article:

  • TITLE: What Do We Mean When We Talk about the Linac Isocenter?

    AUTHORS: Mutian Zhang, Su-Min Zhou, Tanxia Qu

    KEYWORDS: Medical Linear Accelerator, Isocenter, Linac Isocenter, Rotation Isocenter, Radiation Isocenter, Axis of Rotation, Definition

    JOURNAL NAME: International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, Vol.4 No.3, August 4, 2015

    ABSTRACT: Purpose: The isocenter of a medical linac system is a frequently used concept in clinical practice. However, so far not all the isocenters are rigorously defined. This work is intended as an attempt of deriving consistent and operable isocenter definitions. Methods: The isocenter definition is based on a fundamental concept, the axis of rotation of a rigid body. The axis of rotation is determined using the trajectory of any point on a plane that intersects the rigid body. A point on the axis of rotation is found through the minimal bounding sphere of the trajectory when the rigid body makes a full rotation. The essential mathematical tool of the isocenter definition system is three-dimensional coordinate transformation. Results: The axes of rotation of the linac collimator, gantry, and couch are established first. The linac mechanical isocenter (linac isocenter) is defined as the center of a circle that best fits the trajectory of a select linac X-ray source position. The axis of rotation and the minimal bounding sphere are cornerstones for the rotation isocenters of the collimator, gantry and couch. The definition of radiation isocenter incorporates a surrogate of the useful beam axis. Conclusions: A framework of isocenter definitions for medical linacs is presented in this manuscript. Consistent meanings of the mechanical and radiation isocenters can be achieved using this approach.