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  2. Orientation (geometry) - Wikipedia

    en.wikipedia.org/wiki/Orientation_(geometry)

    For example, the orientation in space of a line, line segment, or vector can be specified with only two values, for example two direction cosines. Another example is the position of a point on the Earth, often described using the orientation of a line joining it with the Earth's center, measured using the two angles of longitude and latitude.

  3. Orientability - Wikipedia

    en.wikipedia.org/wiki/Orientability

    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]

  4. Curve orientation - Wikipedia

    en.wikipedia.org/wiki/Curve_orientation

    Selecting reference points. In two dimensions, given an ordered set of three or more connected vertices (points) (such as in connect-the-dots) which forms a simple polygon, the orientation of the resulting polygon is directly related to the sign of the angle at any vertex of the convex hull of the polygon, for example, of the angle ABC in the picture.

  5. Category:Orientation (geometry) - Wikipedia

    en.wikipedia.org/.../Category:Orientation_(geometry)

    Pages in category "Orientation (geometry)" The following 95 pages are in this category, out of 95 total. This list may not reflect recent changes. ...

  6. Geometrical-optical illusions - Wikipedia

    en.wikipedia.org/wiki/Geometrical-optical_illusions

    For example, these can be in brightness or color, called intensive properties of targets, e.g. Mach bands. Or they can be in their location, size, orientation or depth, called extensive . When an illusion involves properties that fall within the purview of geometry it is geometrical–optical , a term given to it in the first scientific paper ...

  7. Orientation (vector space) - Wikipedia

    en.wikipedia.org/wiki/Orientation_(vector_space)

    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 are "negatively" oriented. In the three-dimensional Euclidean space , right-handed bases are typically declared to be positively oriented, but the choice is arbitrary, as they may also ...

  8. Quaternions and spatial rotation - Wikipedia

    en.wikipedia.org/wiki/Quaternions_and_spatial...

    3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]

  9. Rotation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Rotation_(mathematics)

    Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point.

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