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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.
The z-axis is vertical and the x-axis is highlighted in green. Thus, the red plane shows the points with x = 1, the blue plane shows the points with z = 1, and the yellow plane shows the points with y = −1. The three surfaces intersect at the point P (shown as a black sphere) with the Cartesian coordinates (1, −1, 1).
Using the x-convention, the 3-1-3 extrinsic Euler angles φ, θ and ψ (around the z-axis, x-axis and again the -axis) can be obtained as follows: = (,) = = (,) Note that atan2( a , b ) is equivalent to arctan a / b where it also takes into account the quadrant that the point ( b , a ) is in; see atan2 .
Customarily, two rays of sight are chosen for each of the three axes of the object's coordinate system; that is, parallel to each axis, the object may be viewed in one of 2 opposite directions, making for a total of 6 orthographic projections (or "views") of the object: [1] Along a vertical axis (often the y-axis): The top and bottom views ...
The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. [9] Such a drawing is called a plane graph or planar embedding of the graph.
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