How does a central projection create an image on a picture plane?
The sight lines drawn from the image in the reality plane (RP) to the artist's eye intersect the picture plane (PP) to form a projective, or perspective, drawing. The horizontal line drawn parallel to PP corresponds to the horizon. Early perspective experimenters sometimes used translucent paper or glass for the picture plane, which they drew on while looking through a small hole to keep their focus steady.
In projective geometry, a central projection creates an image on a picture plane by establishing a correspondence between points on an original figure (often called the reality plane) and a second surface.12
The process functions as follows:
* Focal Point: A specific point, known as the origin or center of projection, is chosen as the focal point.12
* Sight Lines: Linesâoften referred to as sight linesâare constructed from this focal point to each point on the original figure.12
* Intersection: The image is generated by the intersection of these sight lines with the picture plane.12
This method, which originated from perspective drawing techniques developed during the Italian Renaissance, allows for the mapping of complex shapes onto a flat surface. While this projection does not preserve distances or angles, it maintains certain invariant properties, such as collinearity, meaning that points lying on a single line in the original figure will also lie on a single line in the projected image.2