When describing physical or biological phenomena in a multidimensional space, referencing is essential and is typically provided by a coordinate system, or frames. Referencing involves determining the position and representing the velocity of moving objects. For Euclidean spaces, such as a plane or a cube, the Cartesian coordinate system has been the most widely adopted choice. Setting up an x- and y-axis for a plane, or equivalently x-, y-, and z-axes for a cube, provides an effective reference system for the space (see Fig. 1.1). Any point in the multidimensional space can be precisely represented using the adopted coordinate system. When an object moves within the domain, its velocity can also be represented in the coordinate system by tracking its positional changes over a given time interval.

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Introduction to Moving Frames for Curved and Anisotropic Domains

  • Sehun Chun

摘要

When describing physical or biological phenomena in a multidimensional space, referencing is essential and is typically provided by a coordinate system, or frames. Referencing involves determining the position and representing the velocity of moving objects. For Euclidean spaces, such as a plane or a cube, the Cartesian coordinate system has been the most widely adopted choice. Setting up an x- and y-axis for a plane, or equivalently x-, y-, and z-axes for a cube, provides an effective reference system for the space (see Fig. 1.1). Any point in the multidimensional space can be precisely represented using the adopted coordinate system. When an object moves within the domain, its velocity can also be represented in the coordinate system by tracking its positional changes over a given time interval.