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  2. Euler angles - Wikipedia

    en.wikipedia.org/wiki/Euler_angles

    The Euler angles are three angles introduced by Swiss mathematician Leonhard Euler (1707 – 1783) to describe the orientation of a rigid body with respect to a fixed coordinate system. [ 1] Left: A gimbal set, showing a z - x - z rotation sequence. External frame shown in the base.

  3. Conversion between quaternions and Euler angles - Wikipedia

    en.wikipedia.org/wiki/Conversion_between...

    Quaternion to Euler angles (in 3-2-1 sequence) conversion. A direct formula for the conversion from a quaternion to Euler angles in any of the 12 possible sequences exists. [2] For the rest of this section, the formula for the sequence Body 3-2-1 will be shown. If the quaternion is properly normalized, the Euler angles can be obtained from the ...

  4. Solid angle - Wikipedia

    en.wikipedia.org/wiki/Solid_angle

    Dimension. 1 {\displaystyle 1} In geometry, a solid angle (symbol: Ω) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The point from which the object is viewed is called the apex of the solid ...

  5. Gradian - Wikipedia

    en.wikipedia.org/wiki/Gradian

    In trigonometry, the gradian – also known as the gon (from Ancient Greek γωνία (gōnía) 'angle'), grad, or grade[ 1] – is a unit of measurement of an angle, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees. [ 2][ 3][ 4] It is equivalent to ⁠ 1 400 ⁠ of a turn, [ 5] ⁠ 9 10 ⁠ of a ...

  6. Azimuth - Wikipedia

    en.wikipedia.org/wiki/Azimuth

    The azimuth is the angle formed between a reference direction (in this example north) and a line from the observer to a point of interest projected on the same plane as the reference direction orthogonal to the zenith. An azimuth ( / ˈæzəməθ / ⓘ; from Arabic: اَلسُّمُوت, romanized : as-sumūt, lit. 'the directions') [ 1] is the ...

  7. Grade (slope) - Wikipedia

    en.wikipedia.org/wiki/Grade_(slope)

    The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt".

  8. Sine and cosine - Wikipedia

    en.wikipedia.org/wiki/Sine_and_cosine

    The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse ), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse.

  9. Angle of repose - Wikipedia

    en.wikipedia.org/wiki/Angle_of_repose

    The angle of repose, or critical angle of repose, [ 1] of a granular material is the steepest angle of descent or dip relative to the horizontal plane on which the material can be piled without slumping. At this angle, the material on the slope face is on the verge of sliding. The angle of repose can range from 0° to 90°.

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