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The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as proj b a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .
ρ is the length of the vector projected onto the xy-plane, φ is the angle between the projection of the vector onto the xy-plane (i.e. ρ) and the positive x-axis (0 ≤ φ < 2π), z is the regular z-coordinate. (ρ, φ, z) is given in Cartesian coordinates by:
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 ...
FreeCAD is a free and open-source application that can work with the DWG files by using the proprietary ODA File Converter for .dwg and .dxf files from the Open Design Alliance (ODA). [55] The ODA also provides a freeware stand-alone viewer for .dwg and .dgn files, ODA Drawings Explorer, which runs on Windows, Linux, and Mac OS X.
The projected area onto a plane is given by the dot product of the vector area S and the target plane unit normal m̂: = ^ For example, the projected area onto the xy-plane is equivalent to the z-component of the vector area, and is also equal to = | | where θ is the angle between the plane normal n̂ and the z-axis.
The origin and vector direction of the projectors (also called projection lines) differs, as explained below. In first-angle projection, the parallel projectors originate as if radiated from behind the viewer and pass through the 3D object to project a 2D image onto the orthogonal plane behind it.
Orthographic projection (also orthogonal projection and analemma) [a] is a means of representing three-dimensional objects in two dimensions.Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, [2] resulting in every plane of the scene appearing in affine transformation on the viewing surface.
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