In geometry, an axis-aligned object (axis-parallel, axis-oriented) is an object in n-dimensional space whose shape is aligned with the coordinate axes...

coordinate for the points in S. Axis-aligned minimal bounding boxes are used as an approximate location of an object in question and as a very simple...

iso-oriented, axis-aligned, and axis-oriented polygons. These adjectives are less confusing when the polygons of this type are rectangles, and the term axis-aligned...

trans-Neptunian object (ETNO) orbits are suspected to be aligned with the hypothetical Planet Nine while the blue-colored ETNO orbits are anti-aligned. The highly...

rotation of an object around its first and third principal axes is stable, whereas rotation around its second principal axis (or intermediate axis) is not....

\end{aligned}}} Here I x x {\displaystyle I_{xx}} denotes the moment of inertia around the x {\displaystyle x} -axis when the objects are rotated...

alignment also switched, from more aligned to anti-aligned with increasing semi-major axis, and from anti-aligned to aligned with increasing perihelion distance...

kinetic energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than for general rotational...

of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular...

rotational/rotary motion is the circular movement of an object around a central line, known as an axis of rotation. A plane figure can rotate in either a clockwise...

v 2 r = F c {\displaystyle {\begin{aligned}F_{\text{net}}&=ma\\&=ma_{r}\\&={\frac {mv^{2}}{r}}\\&=F_{c}\end{aligned}}} Radial acceleration is used when...

{\displaystyle {\begin{aligned}b&=a{\sqrt {1-e^{2}}},\\\ell &=a(1-e^{2}),\\a\ell &=b^{2}.\end{aligned}}} The semi-major axis of a hyperbola is, depending...

{\displaystyle J} (for an axis perpendicular to the plane). In both cases, it is calculated with a multiple integral over the object in question. Its dimension...

vary with semi-major axis of the object and if the object is in resonance. At smaller semi-major axes the aligned and anti-aligned regions shrink and eventually...

{\displaystyle {\begin{aligned}(+x,+y,+z)&&(-x,+y,+z)&&(+x,-y,+z)&&(+x,+y,-z)\\(+x,-y,-z)&&(-x,+y,-z)&&(-x,-y,+z)&&(-x,-y,-z)\end{aligned}}} The coordinates...

The Axis powers, originally called the Rome–Berlin Axis and also Rome–Berlin–Tokyo Axis, was the military coalition which initiated World War II and fought...

instrument attached to it to stay fixed on any celestial object with diurnal motion by driving one axis at a constant speed. Such an arrangement is called a...

horizontal axis and time on the vertical axis. Additionally, the time and space units of measurement are chosen in such a way that an object moving at...

+ X η = y + Y ζ = z + Z {\displaystyle {\begin{aligned}\xi &=x+X\\\eta &=y+Y\\\zeta &=z+Z\end{aligned}}} Celestial coordinate system Planetary coordinate...

accommodate rotation about one axis, leaving the suspended object effectively locked (i.e. unable to rotate) around that axis. The problem can be generalized...

{\displaystyle {\begin{aligned}\mathbf {b} _{x}&=\mathbf {f} _{x}/\mathbf {f} _{w}\\\mathbf {b} _{y}&=\mathbf {f} _{y}/\mathbf {f} _{w}\end{aligned}}} The distance...

in the object axis is a line, while the trajectory of any point in the object rim is a cycloid. The velocity of any point in the rolling object is given...

object. In most applications the axis of the cylinder is aligned with the vertical direction of the scene. Cylinders are appropriate for 3-D objects that...

quadrics. Geometric objects are coaxial if they share the same axis (line of symmetry). Geometric objects with a well-defined axis include circles (any...

{\begin{aligned}\mathbf {r} _{i}&=\mathbf {v} _{i}=\mathbf {0} ,\\\mathbf {r} &=\mathbf {R} ,\\\mathbf {v} &=\mathbf {V} ,\\m&=M,\end{aligned}}} ∑ i r...

{\begin{aligned}e&\approx nr_{2}\\&=n(i-r_{1})\\&\approx n(i-{\frac {i}{n}})\end{aligned}}} If the incoming ray is parallel to the optical axis and distance...

with the camera aligned parallel to the floor and aligned to the coordinate axes, it is first rotated horizontally (around the vertical axis) by ±45°, then...

d r 1 n , {\displaystyle {\begin{aligned}H&=-{\frac {f(n-1)d}{r_{2}n}}\\H'&=-{\frac {f(n-1)d}{r_{1}n}},\end{aligned}}} where f is the focal length of...

material), u {\textstyle u} is the on-axis (on the optical axis) object distance from the line perpendicular to the axis toward the refraction point on the...

lowercase Greek nu, and also n), is the frequency of rotation of an object around an axis. Its SI unit is the reciprocal seconds (s−1); other common units...