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In a wider sense, an improper rotation may be defined as any indirect isometry; i.e., an element of E(3)\E + (3): thus it can also be a pure reflection in a plane, or have a glide plane. An indirect isometry is an affine transformation with an orthogonal matrix that has a determinant of −1.
In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric. In conclusion, a line of symmetry splits the shape in half and those halves should be identical.
This familiar equation for a plane is called the general form of the equation of the plane or just the plane equation. [6] Thus for example a regression equation of the form y = d + ax + cz (with b = −1) establishes a best-fit plane in three-dimensional space when there are two explanatory variables.
Along a vertical axis (often the y-axis): The top and bottom views, which are known as plans (because they show the arrangement of features on a horizontal plane, such as a floor in a building). Along a horizontal axis (often the z -axis): The front and back views, which are known as elevations (because they show the heights of features of an ...
The Earth showing its axis and plane of rotation, both inclined relative to the plane and perpendicular of Earth's orbit. Another example is the Earth's rotation. The axis of rotation is the line joining the North Pole and South Pole and the plane of rotation is the plane through the equator between the Northern and Southern Hemispheres.
This article summarizes the classes of discrete symmetry groups of the Euclidean plane. The symmetry groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane: 2 families of rosette groups – 2D point groups; 7 frieze groups – 2D line ...
The stereographic projection of a trace is an arc. The Wulff net is arcs corresponding to planes that share a common axis in the (x,y) plane. If the pole and the trace of a plane are represented on the same diagram, then we turn the Wulff net so the trace corresponds to an arc of the net;
A sphere rotating (spinning) about an axis. Rotation or rotational 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 or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation.
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