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  2. Axis–angle representation - Wikipedia

    en.wikipedia.org/wiki/Axisangle_representation

    The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axisangle 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 ...

  3. Descriptive geometry - Wikipedia

    en.wikipedia.org/wiki/Descriptive_geometry

    To get a true view (length in the projection is equal to length in 3D space) of one of the lines: SU in this example, projection 3 is drawn with hinge line H 2,3 parallel to S 2 U 2. To get an end view of SU, projection 4 is drawn with hinge line H 3,4 perpendicular to S 3 U 3. The perpendicular distance d gives the shortest distance between PR ...

  4. Isometric projection - Wikipedia

    en.wikipedia.org/wiki/Isometric_projection

    Starting with the camera aligned parallel to the floor and aligned to the coordinate axes, it is first rotated horizontally (around the vertical axis) by ±45°, then 35.264° around the horizontal axis. Another way isometric projection can be visualized is by considering a view within a cubical room starting in an upper corner and looking ...

  5. Multiview orthographic projection - Wikipedia

    en.wikipedia.org/wiki/Multiview_orthographic...

    Third-angle projection is most commonly used in America, [6] Japan (in JIS B 0001:2010); [7] and is preferred in Australia, as laid down in AS 1100.101—1992 6.3.3. [ 8 ] In the UK, BS8888 9.7.2.1 allows for three different conventions for arranging views: Labelled Views, Third Angle Projection, and First Angle Projection.

  6. Parallel projection - Wikipedia

    en.wikipedia.org/wiki/Parallel_projection

    Any line not parallel to direction is mapped onto a line; any line parallel to is mapped onto a point. Parallel lines are mapped on parallel lines, or on a pair of points (if they are parallel to ). The ratio of the length of two line segments on a line stays unchanged. As a special case, midpoints are mapped on midpoints. The length of a line ...

  7. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    Every rotation in three dimensions is defined by its axis (a vector along this axis is unchanged by the rotation), and its angle — the amount of rotation about that axis (Euler rotation theorem). There are several methods to compute the axis and angle from a rotation matrix (see also axisangle representation ).

  8. 3D projection - Wikipedia

    en.wikipedia.org/wiki/3D_projection

    If the normal of the viewing plane (the camera direction) is parallel to one of the primary axes (which is the x, y, or z axis), the mathematical transformation is as follows; To project the 3D point , , onto the 2D point , using an orthographic projection parallel to the y axis (where positive y represents forward direction - profile view ...

  9. Shear mapping - Wikipedia

    en.wikipedia.org/wiki/Shear_mapping

    Straight lines parallel to the x-axis remain where they are, while all other lines are turned (by various angles) about the point where they cross the x-axis. Vertical lines, in particular, become oblique lines with slope. Therefore, the shear factor m is the cotangent of the shear angle between the former verticals and the x-axis. (In the ...

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