Automatic extraction of the 3D symmetry line of back surface: application on scoliotic adolescents

The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...

Automatic processing refers to the cognitive operations that occur without conscious intent or awareness, playing a fundamental role in shaping social cognition and behavior. These processes enable individuals to navigate complex social environments efficiently by relying on mental shortcuts and pre-existing knowledge structures known as schemas. One of the most influential mechanisms underlying automatic processing is priming, which subtly activates mental representations through exposure to...

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...

During adolescence, individuals experience significant cognitive development that enhances their understanding of others' emotions and thoughts, known as cognitive empathy. This period is marked by an increased ability to adapt to others' perspectives and a more nuanced understanding of others' mental states, a skill that is foundational for social problem-solving and conflict avoidance. The development of cognitive empathy relies heavily on the theory of mind — the...

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...