Traditional Culture Encyclopedia - Photography and portraiture - Definition of projection in mathematics

Definition of projection in mathematics

The projection of a point on a straight line

Definition 1: The vertical foot Q obtained by drawing a vertical line from point P to line A is called the orthogonal projection of point P on line A. Note: There are positive and negative projections.

Projection of a point on a plane

Definition 2: The vertical foot Q obtained by drawing a vertical line from point P to plane α is called the orthogonal projection of point P on plane α.

The projection of a figure on a plane

Definition 3: If all points on a graph F are projected onto a plane to form a graph F', then F' is called the projection of graph F on this plane.

Exercise:

Case 1, the line is parallel to the plane. Take any two points on a straight line and make a plane vertical line to connect two vertical feet on the plane. A straight line is the projection of a straight line on a plane.

In case 2, a straight line intersects a plane. Take a point on the straight line out of the plane, make a plane perpendicular, and connect the vertical foot and (the intersection of the straight line and the plane) to get a straight line, which is the projection of the straight line on the plane.

Vector projection

Let the unit vector E be the direction vector of the straight line M, the vector AB=a, the projection A' of point A on the straight line M, and the projection B' of point B on the straight line M, then the vector A'B' is called the orthogonal projection of AB on the straight line M or in the direction of vector E, which is called projection for short. The modulus of vector A'B' is ∣ A' B' ∣ = ∣.