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Some theory requires selecting a fixed point on the sphere, calling the pair (sphere, point) a pointed sphere.
For example, the absence of a sphere (point defect) can be used as an optical cavity or a selective site.
The axial PSF observed from fluorescent sphere point source at various distances from the objective are compared to the theoretical PSF to estimate the mean sphere axial position.
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The metal sphere pointed towards the bottom of the levitation nozzle during melting.
In the Minkowski Lorentz space, oriented spheres and oriented planes of R3 are points on the unit sphere, the points of R3 and the point at infinity are vectors laying on the light-cone.
Actually, there are several one-to-one projections to map points on a sphere to points in the plane.
The force between a sphere and point charge is accurately captured with the effective Debye length, as opposed to the electron Debye length solutions that have errors exceeding 50%.
Measured PET activity in the largest sphere (blue points) and in a background region of the phantom (black points).
For some spaces the choice matters, but for a sphere all points are equivalent so the choice is a matter of convenience.
The key result which allows such an extension is the construction of a small number (two for a 10−2 relative error in reaction potentials inside the sphere) of image point charges for source point charges inside or outside the dielectric sphere.
Geometric analysis software, 3D Reshaper (Technodigit, Gleizé, France), was used to deduce the coordinates of the articular head center by fitting a sphere to its point cloud, and the center of the acetabular component by fitting a circle to its point array, in both cases using the method of least squares.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com