Love our work? Support Us
Score to pass: 70%
1. Parallel projection involves projecting an object onto a plane along parallel lines. In other words, all the projection lines are parallel to each other. It is commonly used in engineering and technical drawing to represent three-dimensional objects on a two-dimensional surface, like a sheet of paper. Nevertheless, parallel projections do not preserve angles or lengths accurately, which can lead to distorted representations.
We can found many different types of parallel projections, such as orthographic projection and oblique projection, each with its own properties and uses.
2. Orthogonal projection is a specific type of parallel projection where the projection lines are perpendicular (orthogonal) to the projection plane. It preserves lengths and angles, which makes it useful in various mathematical and geometrical contexts.
In Mathematics, usually in linear algebra, orthogonal projection is commonly used to project a vector onto a subspace. That is, given a vector space, if you want to find the closest vector in a subspace to a given vector, you use orthogonal projection. Therefore, the resulting projected vector will be orthogonal (perpendicular) to the subspace.
Simply, orthogonal projection can be thought of as "dropping a perpendicular" from a point onto a line, plane, or subspace, resulting in a new point that represents the projection.
As a summary, parallel projection involves projecting objects along parallel lines onto a plane, often used for simplified representations in technical drawings. That is, orthogonal projection is a specific type of parallel projection where the projection lines are perpendicular to the projection plane, preserving lengths and angles, and is used in various mathematical and geometrical applications.