# Orthogonal Projection

## Orthogonal Projection

Parallel projection in which the projection direction is perpendicular to the projection target (or screen).

The target figure can be a line, a plane, a sphere, etc.

• Orthogonal projection on a line in a plane
Transformation in a plane determined by two perpendicular lines d (line on which the figures are projected) and d1 which determines the projection direction that applies all points P on the plane on a point P‘ so that P‘ is the point of intersection of d with the parallel to d1 that passes through P.

• Orthogonal projections on a line in a plane preserve the order of the points on the segments. If p is a parallel projection of the plane on a line d according to a direction d1, then no matter what the points A and B of the plane are so that the line AB intersects with d1, if A<B, then p(A) < p(B).In a Cartesian plane, the coordinates of the points of the plane are obtained by orthogonal projection from the point on each of the axes.
• Orthogonal projection on one plane in space
Transformation in the space determined by a plane p (plane on which the figures are projected) and d (line that determines the projection direction) perpendicular to p that applies all points P of the plane on a point P‘ so that P‘ is the point of intersection with p with the parallel to d that passes through P.
• Orthogonal projections on a plane preserve the order of the points and the parallelism of the figures.
• Orthogonal projections are used to represent an object in three-dimensional space on three planes that are perpendicular to one another, called top view, side view, and front view.