projecting

Projecting refers to the act of casting, extending, or forecasting an image, impression, or value outward from a source. In different domains, it denotes distinct processes that share a common idea of transferring or forecasting from one domain to another.

In psychology, projection is a defense mechanism where a person attributes their own unacceptable thoughts, impulses, or emotions to others rather than facing them. It can be conscious or unconscious and is often discussed in the context of interpersonal conflict or personality pathology. Identifying projection can help in psychotherapy by distinguishing one's own feelings from perceived ones in others.

In mathematics and computer graphics, projection describes a mapping that transfers points from a space into a subspace or onto a plane. Orthogonal projection minimizes distance to a subspace, while perspective projection models how a 3D scene is projected onto a 2D image plane, as in camera or computer graphics pipelines. Projection matrices and homogeneous coordinates are common tools to perform these transformations.

In statistics and planning, projection means forecasting future values based on models and current data, such as population or revenue projections. Projections rely on assumptions about trends and uncertainty and are used for decision making and policy analysis.

In cinema and education, projecting refers to the display of images or films on a screen using a projector, and to the act of presenting material to an audience.