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  2. Rotation of axes in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_of_axes_in_two...

    In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .

  3. Clockwise - Wikipedia

    en.wikipedia.org/wiki/Clockwise

    A circle defined parametrically in a positive Cartesian plane by the equations x = cos t and y = sin t is traced counterclockwise as the angle t increases in value, from the right-most point at t = 0. An alternative formulation with sin and cos swapped gives a clockwise trace from the upper-most point, where t can be considered akin to a ...

  4. Curve orientation - Wikipedia

    en.wikipedia.org/wiki/Curve_orientation

    If the determinant is negative, then the polygon is oriented clockwise. If the determinant is positive, the polygon is oriented counterclockwise. The determinant is non-zero if points A, B, and C are non-collinear. In the above example, with points ordered A, B, C, etc., the determinant is negative, and therefore the polygon is clockwise.

  5. Rotation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Rotation_(mathematics)

    Rotation can have a sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude. A rotation is different from other types of motions: translations , which have no fixed points, and (hyperplane) reflections , each of them having an entire ( n − 1) -dimensional flat of ...

  6. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    The examples in this article apply to active rotations of vectors counterclockwise in a right-handed coordinate system (y counterclockwise from x) by pre-multiplication (R on the left). If any one of these is changed (such as rotating axes instead of vectors, a passive transformation ), then the inverse of the example matrix should be used ...

  7. Rotation - Wikipedia

    en.wikipedia.org/wiki/Rotation

    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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