Geometric calibration of the circle-plus-arc trajectory.

Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere

Adiabatic perturbation is shown to be singular from the exact solution of a spin-1/2 particle in a uniformly rotating magnetic field. Due to a non-adiabatic effect, its quantum trajectory on a Bloch sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum tra...

Arc changes in arid area rivers (Case study: Qomrood river in Iran)

Qomrood river is one of the rivers that located in arid and semiarid area which has a seasonal fluvial. The river is faced many changes, because of floods or natural- human factors. This study, as a geomorphologic study, tries to survey and identify geometric changes between Kocherey dam and 15-Khordad dam. The study method is a mix of library research and field studies. In library method all p...

On binocular vision: The geometric horopter and Cyclopean eye

We study geometric properties of horopters defined by the criterion of equality of angle. Our primary goal is to derive the precise geometry for anatomically correct horopters. When eyes fixate on points along a curve in the horizontal visual plane for which the vergence remains constant, this curve is the larger arc of a circle connecting the eyes' rotation centers. This isovergence circle is ...

Geometric constraints on quadratic Bézier curves using minimal length and energy

This paper derives expressions for the arc length and the bending energy of quadratic Bézier curves. The formulae are in terms of the control point coordinates. For fixed start and end points of the Bézier curve, the locus of the middle control point is analyzed for curves of fixed arc length or bending energy. In the case of arc length this locus is convex. For bending energy it is not. Given ...

Image Reconstruction for a General Circle-Plus Trajectory