The picture plane is the geometrical or representational surface upon which a perspective image is constructed, projected or considered. In conventional linear perspective it is normally imagined as a flat plane positioned between the observer and the spatial scene, rather like a transparent window through which the scene is viewed.
Visual or projection rays extending between points in object space and the station point intersect the picture plane. The positions of these intersections determine the corresponding points in the perspective image. In this sense, the picture plane converts the spatial relationships of three-dimensional object space into a two-dimensional perspective representation.
The picture plane is therefore one of the fundamental elements of graphical and mathematical perspective. It should not be confused with the spatial scene itself, the station point from which that scene is viewed, or the physical retina or image sensor upon which an optical system forms an image.
The Picture Plane in Linear Perspective
Linear perspective can be understood as a geometrical projection in which a spatial object or scene is viewed from a particular station point and represented upon a picture plane. The picture plane provides the two-dimensional surface upon which the spatial projection is organised.
Volume 1 identifies the flat picture or projection plane as one of the principal elements of linear perspective, together with the fixed eye or camera point, the visual cone or pyramid, spatial recession and the spatial object or scene extending into depth.
A linear-perspective image is consequently not simply a flattened copy of a three-dimensional scene. Its geometry is produced by the relationships between object space, station point, projection rays and picture plane. Different geometrical relationships between these elements can produce different perspective views of the same spatial reality.
Picture Plane and Perspective Window
The traditional perspective window provides one of the clearest ways of understanding the picture plane. Imagine a transparent sheet of glass placed between the observer and a spatial scene. If the observer maintains a fixed eye position and traces onto the glass the apparent outlines of the objects beyond it, the glass functions simultaneously as a perspective window and picture plane.
The picture is determined by the points at which the visual rays connecting the observer’s eye with the spatial objects intersect this transparent plane. The resulting image is therefore a section through the visual pyramid or cone associated with the particular view.
The window need not actually exist. In graphical perspective it may be wholly imaginary. A drawing surface, canvas or other representational surface can be treated geometrically as though it occupied the position of such a window.
The terms picture plane and perspective window consequently describe closely related aspects of the same geometrical arrangement: the first emphasises the projection or representational plane, while the second emphasises the idea of viewing the spatial scene through a framed surface.
How the Perspective Image is Formed
Consider a point located upon an object in spatial reality. A straight projection or visual ray can be imagined extending from that object point towards the station point. Where this ray intersects the picture plane establishes the corresponding point in the perspective image.
The same principle applies to all the visible points of the scene. Their collective intersections with the picture plane establish the projected size, shape, position and spatial disposition of the represented objects.
The picture plane therefore does not itself create perspective phenomena independently. The resulting image depends upon the complete geometrical relationship between the station point, viewing direction, spatial object or scene and picture plane. Changing any important part of that relationship may alter the resulting projection.
Position of the Picture Plane
The position of the picture plane is a geometrical choice rather than an absolute feature of physical space. In the familiar perspective-window arrangement it lies between the station point and the object or scene. This is the most intuitive configuration because the observer can be imagined looking through the plane towards the subject.
However, the geometrical plane can be placed elsewhere within the projection system. It may pass through part of the object space, as sometimes occurs in architectural perspective, or it may be considered in another position according to the requirements of the projection method.
It is therefore the relationship of the picture plane to the other elements of the system that matters. Moving the plane along the projection geometry can alter the scale at which the projected image is represented, while changing its orientation relative to the object, station point or viewing direction can alter the geometry of the resulting image.
Orientation of the Picture Plane
In the standard central arrangement, the picture plane is commonly positioned approximately normal to the principal sight direction or optical axis. In many conventional perspective constructions it is also vertical relative to a horizontal ground plane.
This is an important standard arrangement, but it should not be mistaken for a universal definition of the picture plane. A picture plane can be inclined, declined, oblique or otherwise differently oriented relative to the observer, spatial scene or directional system.
Perspective therefore depends upon the relative geometrical arrangement of the elements involved rather than upon an assumption that the picture plane must always possess one particular orientation.
Picture Plane and Station Point
The station point is the eye, camera or viewpoint situated in object space from which the perspective image or view is taken. The picture plane is a different element: it is the surface upon which the perspective projection is represented.
In a conventional arrangement, the station point lies some distance in front of the picture plane. Projection rays connecting spatial points with the station point pass through the plane, and their intersections establish the image.
The distance and angular relationship between station point and picture plane are therefore significant components of the perspective system. They contribute to the field of view and to the geometrical form and scale of the representation.
Picture Plane and Centre of Vision
The picture plane should also be distinguished from the centre of vision or principal point. The station point is situated in object space, whereas the centre of vision or principal point is a defined point upon the picture plane.
In the standard arrangement, a line drawn from the station point perpendicular to the picture plane meets it at the principal point. This point has historically been described by several names, which has sometimes caused it to be confused with the station point itself.
The distinction is fundamental: the station point is a viewpoint in object space; the picture plane is a projection surface; and the principal point or centre of vision is a point located upon that surface.
Picture Plane and Vanishing Points
Vanishing points are located in relation to the picture plane. Sets of parallel lines in object space that possess a depth component relative to the projection system can appear to converge towards corresponding vanishing points in image space.
By contrast, object-space lines parallel to the picture plane do not acquire a depth component relative to that plane and therefore remain parallel in the conventional rectilinear perspective image.
This relationship helps explain familiar one-point, two-point and three-point perspective forms. Their differences arise from the relationships between the principal directions present in object space, the viewpoint or directional arrangement and the picture plane. The picture plane is therefore an essential part of the geometry, but it should not be treated in isolation as the sole cause of the number or position of vanishing points.
Picture Plane in One-Point Perspective
In a conventional one-point perspective construction, two principal dimensions of a rectilinear object or grid are parallel to the picture plane, while the principal depth direction extends away from it.
The depth-direction orthogonals converge towards the principal vanishing point, while lines parallel to the picture plane remain parallel in the image. The familiar arrangement therefore represents a particular relationship between the spatial line system, station point, viewing direction and picture plane.
This is why one-point perspective should be understood as a special geometrical configuration rather than as the universal model of perspective projection.
Picture Plane in Two- and Three-Point Perspective
In two-point perspective, two principal horizontal directional systems possess depth components relative to the picture plane. Their parallel lines consequently converge towards separate lateral vanishing points, while vertical lines normally remain parallel when they are parallel to the picture plane.
In a conventional three-point perspective arrangement, a third principal directional system also possesses a depth component within the projection geometry. A corresponding vertical vanishing point may then appear above or below the principal horizontal horizon system.
These examples demonstrate why the picture plane must always be considered as one component of a larger geometrical system. Perspective form results from the relationships between spatial directions, viewpoint, viewing arrangement and projection surface.
Picture Plane and Image Plane
The picture plane of graphical perspective and the image plane or image surface of an optical instrument are closely related geometrically, but they should not automatically be treated as physically identical things.
In the traditional graphical arrangement, the picture plane is normally conceived as lying between the station point and the scene, producing a convenient upright geometrical representation. In a camera, however, light passes through the lens or aperture and forms an image upon a physical sensor or film surface situated behind the effective projection centre. The rays have crossed, and the physical image is inverted.
The camera image plane can therefore perform a geometrically analogous projection function, while occupying a different physical position within the optical system. Likewise, the eye forms its physical image upon the curved retina rather than upon a flat picture plane positioned in front of the eye.
The conventional location of the perspective picture plane should consequently be understood as part of a geometrical system of representation, not as a claim that an eye or camera physically forms its image upon a plane situated in front of its optical centre.
Flat and Curved Picture Surfaces
Classical rectilinear perspective normally employs a flat picture plane. The resulting projection preserves straight object-space lines as straight image-space lines and forms the familiar geometries associated with linear perspective.
Perspective representation is not restricted to flat surfaces. Cylindrical, spherical and other curved picture surfaces can also be employed. These produce different sections or mappings of the visual field and are associated with various forms of cylindrical, curvilinear and spherical perspective.
Strictly speaking, a curved image support is better understood as a picture surface rather than a geometrical plane. The broader principle nevertheless remains the same: spatial information is mapped onto a selected image or projection surface.
Objects and Lines on the Picture Plane
Elements lying directly within or parallel to the picture plane occupy a special position in conventional linear-perspective geometry. Lines contained within the plane can be represented at their established scale without perspectival depth contraction because they possess no depth component relative to that plane.
This principle is important in measured perspective. Measuring lines or scales situated on the picture plane can provide known dimensions from which corresponding measurements are projected into represented depth.
It also explains why lines parallel to the picture plane remain parallel rather than converging towards finite vanishing points in a standard linear-perspective construction.
Viewing a Perspective Picture
A perspective image constructed for a particular station point and picture-plane relationship has a corresponding geometrically correct viewing position.
If the finished picture is viewed monocularly from the original station point and at the corresponding distance from the picture plane, the directions from the viewer’s eye to points in the image reproduce the geometrical directions associated with the original construction.
In practice, perspective pictures are commonly viewed from other positions and still appear convincing. Human perception can tolerate or compensate for considerable differences between the geometrically prescribed viewing position and the position actually occupied by the observer, particularly when the field of view is not extreme.
Why the Picture Plane Matters
The picture plane is not simply the sheet of paper on which a perspective drawing happens to appear. It is a fundamental geometrical element that establishes where spatial projection becomes image space.
Its relationship to the station point, spatial scene, viewing direction and directional systems helps determine the geometry of the resulting perspective image. It provides the surface upon which projection rays become image points, vanishing points and vanishing lines, and upon which the spatial relationships of object space become a visible representation.
Understanding the picture plane therefore provides a foundation for understanding the station point, centre of vision, principal point, perspective window, line of sight, field of view, vanishing points, horizon lines, perspective projection and the different forms of graphical, mathematical and optical perspective.