Search results
Results from the WOW.Com Content Network
Orientation (geometry) Changing orientation of a rigid body is the same as rotating the axes of a reference frame attached to it. In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies. [1]
Orientation (vector space) Choice of reference for distinguishing an object and its mirror image. The left-handed orientation is shown on the left, and the right-handed on the right. The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented and which ...
A torus is an orientable surface The Möbius strip is a non-orientable surface. Note how the disk flips with every loop. The Roman surface is non-orientable.. In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise". [1]
Quaternions and spatial rotation. Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis. Rotation and orientation quaternions have ...
Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius. Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized ...
Curve orientation. In mathematics, an orientation of a curve is the choice of one of the two possible directions for travelling on the curve. For example, for Cartesian coordinates, the x -axis is traditionally oriented toward the right, and the y -axis is upward oriented. In the case of a plane simple closed curve (that is, a curve in the ...
Common geometric terms of location are: Radial – along a direction pointing along a radius from the center of an object, or perpendicular to a curved path. Circumferential (or azimuthal) – following around a curve or circumference of an object. For instance: the pattern of cells in Taylor–Couette flow varies along the azimuth of the ...
In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is ...