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A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number. There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles.
The two most common types of orientation are portrait and landscape. [1] The term "portrait orientation" comes from visual art terminology and describes the dimensions used to capture a person's face and upper body in a picture; in such images, the height of the display area is greater than the width.
Line breaking, also known as word wrapping, is breaking a section of text into lines so that it will fit into the available width of a page, window or other display area. In text display, line wrap is continuing on a new line when a line is full, so that each line fits into the viewable window, allowing text to be read from top to bottom ...
Pagination, also known as paging, is the process of dividing a document into discrete pages, either electronic pages or printed pages.. In reference to books produced without a computer, pagination can mean the consecutive page numbering to indicate the proper order of the pages, which was rarely found in documents pre-dating 1500, and only became common practice c. 1550, when it replaced ...
where q is the versor, q −1 is its inverse, and x is the vector treated as a quaternion with zero scalar part. The quaternion can be related to the rotation vector form of the axis angle rotation by the exponential map over the quaternions, = /, where v is the rotation vector treated as a quaternion.
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]
Thus we can write the trace itself as 2w 2 + 2w 2 − 1; and from the previous version of the matrix we see that the diagonal entries themselves have the same form: 2x 2 + 2w 2 − 1, 2y 2 + 2w 2 − 1, and 2z 2 + 2w 2 − 1. So we can easily compare the magnitudes of all four quaternion components using the matrix diagonal.
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]