euclidean group वाक्य
उदाहरण वाक्य
मोबाइल
- The Euclidean group of all rigid motions ( conjugate of the original translation ).
- See also subgroups of the Euclidean group.
- The set of Euclidean plane isometries forms a composition : the Euclidean group in two dimensions.
- The Euclidean group SE ( d ) of direct isometries is generated by translations and rotations.
- The set consisting of all point reflections and translations is Lie subgroup of the Euclidean group.
- It is precisely the subgroup of the Euclidean group that fixes the line at infinity pointwise.
- These visualizations show the fundamental domains for 2D and 3D Euclidean groups, and 2D spherical groups.
- A " rigid body motion " is in effect the same as a curve in the Euclidean group.
- Similarly the Euclidean group, which consists of all isometries of Euclidean space, is generated by reflections in affine hyperplanes.
- The Euclidean group for SE ( 3 ) is used for the kinematics of a rigid body, in classical mechanics.
- The set of proper rigid transformation is called special Euclidean group, denoted SE ( " n " ).
- It is generated by reflections in lines, and every element of the Euclidean group is the composite of at most three distinct reflections.
- The smallest subgroup of the Euclidean group containing all translations by a given distance is the set of " all " translations.
- The geometry associated with this pseudo-metric was investigated by translations and plays the same role as Euclidean groups of ordinary Euclidean spaces.
- Is a subgroup of the Euclidean group, the group of-sphere and all objects with spherical symmetry, if the origin is chosen at the center.
- Another classical case occurs when M is the cotangent bundle of \ mathbb { R } ^ 3 and G is the Euclidean group generated by rotations and translations.
- For "'su "'( 2 ) one obtains a quantum group deformation of the Euclidean group E ( 3 ) of motions in 3 dimensions.
- As the group of all isometries,, the Euclidean group is important because it makes Euclidean geometry a case of Klein geometry, a theoretical framework including many alternative geometries.
- In the terms of Felix Klein's Erlangen programme, we read off from this that Euclidean geometry, the geometry of the Euclidean group of symmetries, is therefore a specialisation of affine geometry.
- The even isometries identity, rotation, and translation never do; they correspond to " rigid motions ", and form a normal subgroup of the full Euclidean group of isometries.
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