WAWERU HANNAH NYAKIO B02/53847/2012

PERSPECTIVE DRAWING  Perspective drawing is a drawing technique used to illustrate dimension through a flat surface. It is an approximate representation of a three- dimensional object on a flat surface as it is seen by the eye.  The two most characteristic features of perspective are that objects are drawn: I. Smaller as their distance from the observer increases II. Foreshortened: the size of an object's dimensions along the line of sight are relatively shorter than dimensions across the line of sight.  There are many forms used under perspective drawing such as, one perspective, two-point perspective, three-point perspective, four-point perspective, five-point perspective, bird’s eye view, worm’s eye view and others.

FORESHORTENING  Foreshortening is the visual effect or optical illusion that causes an object or distance to appear shorter than it actually is because it is angled toward the viewer.  Additionally, an object is often not scaled evenly: a circle often appears as an ellipse and a square can appear as a trapezoid.  Although foreshortening is an important element in art where visual perspective is being depicted, foreshortening occurs in other types of two- dimensional representations of three-dimensional scenes.  Some other types where foreshortening can occur include: I. Oblique parallel projection drawings. Two different projections of a stack of two cubes, illustrating oblique parallel projection foreshortening ("A") and perspective foreshortening ("B") II. Epimetheus (lower left) and Janus (right). The two moons appear close because of foreshortening; in reality, Janus is about 40,000 km farther from the observer than Epimetheus. EpimetheusJanus (i) (ii)

ONE POINT A linear perspective in which all parallel lines meet at a single point on the horizon. Therefore one establishes the flat side of the object, then makes all the receding lines to meet at a single vanishing point.

TWO POINT A graphical technique in which a three- dimensional object is represented in two- dimensions and in which parallel lines in two of its dimensions are shown to converge towards two vanishing points.

THREE-POINT Linear perspective in which parallel lines along the width of an object meet at two separate points on the horizon and vertical lines on the object meet at a point on the perpendicular bisector of the horizon line.

FOUR POINT  Four-point perspective, also called infinite-point perspective, is the curvilinear variant of two-point perspective.  As the result when made into an infinite point version), a four point perspective image becomes a panorama that can go to a 360 degree view and beyond – when going beyond the 360 degree view the artist might depict an "impossible" room as the artist might depict something new when it's supposed to show part of what already exists within those 360 degrees.  This elongated frame can be used both horizontally and vertically and when used vertically can be described as an image that depicts both a worm's- and bird's-eye view of a scene at the same time. bird's-eye view  Like all other foreshortened variants of perspective (respectively one- to six- point perspective), it starts off with a horizon line, followed by four equally spaced vanishing points to delineate four vertical lines.  The vanishing points made to create the curvilinear orthogonals are thus made ad hoc on the four vertical lines placed on the opposite side of the horizon line. The only dimension not foreshortened in this type of perspective is the rectilinear and parallel lines perpendicular to the horizon line – similar to the vertical lines used in two-point perspective.

FIVE-POINT A curvilinear perspective with its vanishing points are mapped into a circle such that four vanishing points are at the cardinal headings i.e. n, w, s, e and one at the circle origin.

ZERO POINT  Since vanishing points exist only when parallel lines are present in the scene, a perspective with no vanishing points ("zero-point" perspective) occurs if the viewer is observing a non-linear scene.  The most common example of a nonlinear scene is a natural scene (e.g., a mountain range) which frequently does not contain any parallel lines.  A perspective without vanishing points can still create a sense of depth.

METHODS OF CONSTRUCTION  Several methods of constructing perspectives exist, including:  Freehand sketching (common in art)  Graphically constructing (once common in architecture)  Using a perspective grid  Computing a perspective transform (common in 3D computer applications)perspective transform  Mimicry using tools such as a proportional divider (sometimes called a (variscaler)

LIMITATIONS i. Only three sides of a component are shown. ii. No feature is a true proportion. They are not drawn to a constant scale. iii. Sectioned perspective drawings are often confusing. iv. Sometimes a hidden outline is shown which can be confusing. v. Dimensions are often difficult to show. It is due to these disadvantages that engineering drawings are rarely drawn in perspective projection.