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  2. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    Then rotate the given axis and the point such that the axis is aligned with one of the two coordinate axes for that particular coordinate plane (x, y or z) Use one of the fundamental rotation matrices to rotate the point depending on the coordinate axis with which the rotation axis is aligned.

  3. 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 .

  4. PDFtk - Wikipedia

    en.wikipedia.org/wiki/Pdftk

    PDFtk (short for PDF Toolkit) is a toolkit for manipulating Portable Document Format (PDF) documents. [3] [4] It runs on Linux, Windows and macOS. [5] It comes in three versions: PDFtk Server (open-source command-line tool), PDFtk Free and PDFtk Pro (proprietary paid). [2] It is able to concatenate, shuffle, split and rotate PDF files.

  5. Isometric projection - Wikipedia

    en.wikipedia.org/wiki/Isometric_projection

    Next, the cube is rotated ±45° about the vertical axis, followed by a rotation of approximately 35.264° (precisely arcsin 1 ⁄ √ 3 or arctan 1 ⁄ √ 2, which is related to the Magic angle) about the horizontal axis. Note that with the cube (see image) the perimeter of the resulting 2D drawing is a perfect regular hexagon: all the black ...

  6. PDF Split and Merge - Wikipedia

    en.wikipedia.org/wiki/PDF_Split_and_Merge

    Split PDF files in a number of ways: After every page, even pages or odd pages; After a given set of page numbers; Every n pages; By bookmark level; By size, where the generated files will roughly have the specified size; Rotate PDF files where multiple files can be rotated, either every page or a selected set of pages (i.e. Mb).

  7. Rotations and reflections in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotations_and_reflections...

    An xy-Cartesian coordinate system rotated through an angle to an x′y′-Cartesian coordinate system 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 ...

  8. Rotation (mathematics) - Wikipedia

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

    The rotation has two angles of rotation, one for each plane of rotation, through which points in the planes rotate. If these are ω 1 and ω 2 then all points not in the planes rotate through an angle between ω 1 and ω 2. Rotations in four dimensions about a fixed point have six degrees of freedom.

  9. Waveplate - Wikipedia

    en.wikipedia.org/wiki/Waveplate

    Download as PDF; Printable version; ... Either the filters can be rotated, ... the plate is inserted between the perpendicular polarizers at an angle of 45 degrees ...