Search results
Results from the WOW.Com Content Network
Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
The spherical coordinates of a point P then are defined as follows: The radius or radial distance is the Euclidean distance from the origin O to P. The inclination (or polar angle) is the signed angle from the zenith reference direction to the line segment OP. (Elevation may be used as the polar angle instead of inclination; see below.)
rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates v = (x, y), it should be written as a column vector, and multiplied by the matrix R:
The AOL.com video experience serves up the best video content from AOL and around the web, curating informative and entertaining snackable videos.
μ – scale factor, which is unitless; if it is given in ppm, it must be divided by 1,000,000 and added to 1. R – rotation matrix. Consists of three axes (small [clarification needed] rotations around each of the three coordinate axes) r x, r y, r z. The rotation matrix is an orthogonal matrix. The angles are given in either degrees or radians.
The solid angle of a sphere measured from any point in its interior is 4 π sr. The solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2 π /3 sr. The solid angle subtended at the corner of a cube (an octant) or spanned by a spherical octant is π /2 sr, one-eight of the solid angle of a sphere. [1]
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
Horizontal shear of a square into parallelograms with factors and =. In the plane =, a horizontal shear (or shear parallel to the x-axis) is a function that takes a generic point with coordinates (,) to the point (+,); where m is a fixed parameter, called the shear factor.