Understanding Orthogonal Projection: Formula and Definition Explained

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In summary, Orthogonal Projection refers to the process of decomposing a vector into two components - one parallel to another vector and one perpendicular to it. This can be visualized by drawing the two vectors with their tails together and dropping a perpendicular from the head of the second vector to the line of the first vector. The resulting perpendicular vector is the orthogonal projection.
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graycolor
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Can anyone tell me what Orthagonal Projection means. I know the formula is b - proj b onto a.

What does it mean exactly, I tried searching on google.
 
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Given a vector V and another vector W, the idea is to write V as the sum of a vector parallel to W and a vector perpendicular to W. Draw V and W with their tails together and drop a perpendicular from the head of W to the line of vector W. Put appropriate heads on the legs of the little right triangle that forms and you see the two vectors. The perpendicular one is the orthogonal projection.
 

1. What is Orthogonal Projection?

Orthogonal Projection is a mathematical method used to project a point or object onto a lower-dimensional space. It is commonly used in linear algebra and computer graphics to represent 3D objects in 2D space.

2. How is Orthogonal Projection different from Perspective Projection?

Orthogonal Projection preserves the relative sizes and angles of objects, while Perspective Projection creates an illusion of depth by making objects that are further away appear smaller. Additionally, Orthogonal Projection projects objects onto a flat plane, while Perspective Projection projects them onto a curved surface.

3. What are some applications of Orthogonal Projection?

Orthogonal Projection is used in various fields such as engineering, architecture, and computer graphics to create accurate representations of 3D objects in 2D space. It is also used in data visualization to display high-dimensional data in a lower-dimensional space.

4. What is the difference between Orthogonal Projection and Oblique Projection?

The main difference between Orthogonal Projection and Oblique Projection is the angle at which the objects are projected onto the lower-dimensional space. In Orthogonal Projection, the objects are projected at right angles, while in Oblique Projection, they are projected at arbitrary angles.

5. Can Orthogonal Projection be applied to non-linear transformations?

Yes, Orthogonal Projection can be applied to non-linear transformations, but it may not preserve the relative sizes and angles of objects. In such cases, non-orthogonal projections may be used to accurately represent the transformed objects in 2D space.

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