Perspective

DEFINITIONS

Picture Plane - An imaginary, transparent flat-surface on which a drawing is made. It exists between the subject being drawn and the observer. Synonymous with drawing surface (paper)

Technical Perspective - A geometric/mathematical system is used for converting sizes and distances of known objects into a unified spatial order, consistent in scale, and assuming a view from a single, fixed position at a particular moment in time.

Applied Perspective - Perspective drawing which applies the rules of technical perspective in a representational drawing.

Convergence - Lines/edges that in reality are parallel to each other appear, in perspective, to come together (converge)or meet as they recede from the observer toward the horizon line. A classic example is railroad tracks appearing to converge at a single vanishing point on the distant horizon line.

Foreshortening - The apparent diminishing of the length of lines or edges or planes to create the illusion of depth. Lines/edges/planes appear progressively shorter as their angle to the picture plane increases. Therefore only lines, edges or planes that are parallel to the picture plane show their true/actual length.

One-Point Perspective – When one “face” or plane or side of a form is parallel to the picture plane, facing the observer directly. The left and right sides, and the top and bottom of the form all converge on a single vanishing point located on the horizon line (eye level).

One - Point Perspective

One - Point Perspective Cube Multiplication

Two-Point Perspective – When no “face” or plane or side of a form is parallel to the picture place, but rather all places are at an oblique angle to the picture plane. The front or leading edge of a cube is closest to the observer. All vertical edges are represented as vertical lines with no evidence of converging. All other lines, and all planes converge on two different vanishing points located on the horizon line (eye level).

Two- Point Perspective

Two-Point Perspective Cube Multiplication

Eye-Level (EL) – The line on which point of convergence exist. Represents the height of the station point (or observer) in a perspective line. Synonymous with “Horizon Line” which is the place in reality where the sky and earth seem to meet.

Horizon Line (HL) - In perspective drawing, it is synonymous with the eye level.

Scale – The actual size of the subject in a drawing in relation to the actual size of the subject in reality.

Picture Plane (PP) – An imaginary, transparent, flat surface, infinite in size, on which the drawing is made. Located between the subject being drawn and the observer.

Ground Plane (GP) – The surface upon which objects rest. The most obvious example being the surface of the earth, or the actual ground of an exterior space, or the floor of an interior space.

Ground Line (GL) – Represents the intersection of the picture plane and the ground plane. It is always parallel to the horizon line (or eye level)

Cone of Vision (COV) – Represent the limited area that can be clearly seen at any one time by the observer and remain in focus. Trying to draw objects beyond or outside of the cone of vision results in pronounced distortion.

Vanishing Point (VP) – Where two or more parallel receding edges or lines appear to converge. These exist on the horizon line (or eye level) for all horizontal parallel edges or receding lines.

Central Vanishing Point (CVP) – The point of convergence (meeting point) for all lines or edges perpendicular to the picture plane. It is used in one-point perspective and is located directly in front of the observer’s station point, at the 90 degree intersection of the observer’s line of vision and the eye level.

Special Vanishing Point (SVP) – Vanishing points that are established for measuring foreshortened lines or edges or planes. These points exist where one or more diagonal measuring line(s) intersect the horizonal line (or eye level).

Vertical Trace (VT) - A vertical extension of a vanishing point located on the eye-level.

Auxillary Vanishing Point (AVP) - Vanishing points that are for parallel lines or edges on receding diagonal or inclined planes, such as angled box flaps or rooftops or stairways. These vanishing points are never located on the eye-level, but rather are located at the appropriate position along a vertical trace.

Examples of Vertical Trace & Auxillary Vanishing Points

Measuring Line (ML) - Used for direct scale measurements in a drawing. These lines must be parallel to the edges of the picture plane.

Diagonal Measuring Line (DML) - Used in one-point perspective to determine the actual depth of a true, equal sided cube and in one- and two-point perspective to determine consistent scale for cubes in relation to the key cube. These measuring lines always converge at a special vanishing point (SVP) located on the eye level/horizon line.

Vanishing Point Three (VP3) - This is the vanishing point for receding vertical lines or edges or planes. This occurs only in three-point perspective when the observer is positioned at a very low eye level, looking up (worm’s eye view), or at a very high eye level, looking down (a bird’s eye view), which causes the picture plane to tilt.

Geometric Solids - The cube, the cylinder, the cone and the sphere provide the basic forms from which all other forms are composed. All forms, to varying degrees can be ultimately reduced to one of the geometric solids

ellipses

Ellipse - A circle seen in perspective, a foreshortened circle

Foreshortening - The apparent diminishing of the length of lines or edges or planes to create the illusion of depth.

8 Tangent Points: The relationship of a circle to a square can be found by identifying the 8 tangent points necessary for guiding ellipse construction as seen in perspective.

A circle fits precisely within a square, touching the exact midpoint of each side of a square and intersecting the square's diagonals in the same two places on each diagonal. With an awareness of how to construct squares and cubes in perspective and with the knowledge that a cube consists of six equal sides, we are able to construct accurate ellipses using the foreshortened square as a guide.

The changing appearance of ellipses based on their proximity to the eye level and the CVP is shown here. Ellipses widen as they travel farther horizontally from the horizon line and vertically from the CVP, and become shallower as they travel closer to those points. Note that ellipses appear as straight lines with no visible depth when they are horizontally at eye level or vertically at the CVP.

Ellipses formation within Cube Multiplication: Note the behavior of ellipses receding in space is different depending on whether they are in parallel planes or in the same plane. In parallel planes, ellipses open as they recede, while in the same plane ellipses close as they recede.

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