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Learn how to rotate a Cartesian coordinate system by an angle and transform the coordinates of points and curves. See examples, formulas, and applications of rotation of axes in two dimensions.
A rotation matrix is a matrix that rotates vectors or points in Euclidean space. Learn the definition, properties, formulas, and examples of rotation matrices in two and three dimensions.
Learn about the concept of rotation in geometry and algebra, and how it can be represented in different dimensions and formalisms. Find out the definitions, properties, and examples of rotations, as well as their applications in physics and mechanics.
Learn how to represent linear and non-linear transformations by matrices in linear algebra. Find examples of common transformations in two and three dimensions, such as rotation, scaling, shearing, reflection, and projection.
Learn about the spherical coordinate system for three-dimensional space, where the position of a point is specified by radial distance, polar angle, and azimuthal angle. Compare different conventions and terminologies for these angles, such as colatitude, elevation, and longitude.
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 ...
Learn about local tangent plane coordinates, a spatial reference system based on the tangent plane defined by the local vertical direction and the Earth's axis of rotation. Find out how they differ from ECEF and geodetic coordinates, and how to convert between them.
Learn how to convert between different coordinate systems in 2-dimensional and 3-dimensional spaces, such as Cartesian, polar, spherical, cylindrical, and bipolar coordinates. See formulas, examples, and references for each transformation.