Geometric Entities
Points
A point represents a location in space or on a drawing, and has no width, height or depth. We can locate a point (X,Y) in the Cartesian coordinate system by starting at the origin, moving X units along the positive X direction and then moving Y units in the positive Y direction.

Lines
Lines are one dimensional geometric entities (entities that have length without breadth) that are drawn by connecting two points located in space.

Planes
The Cartesian coordinate axes represents a planar surface or area, the XY plane. In a 3D coordinate system, any two of the three mutually coordinate axes forms a planar surface, the XY, XZ and YZ planes.

Surfaces
A bounded plane forms a surface. A surface can be bounded by lines or curves, or a combination of the two. A surface can be generated when a planar figure is revolved or rotated about a coordinate axis or some other line in 3D space. Each face of a 3D object represents a surface.

Objects
An object has width, height and depth. When a number of bounded planes or surfaces combine such that they define a closed space (volume), an object is created.

Form
The shape or profile of an object.

Color
The three visual attributes required for the complete specification of any color are:

• Hue
• Saturation
• Brightness

Hue
That attribute of a color by which it is recognized as a "red" a "blue", a "green", etc., and which approximately corresponds to its dominant wavelength.
Saturation
The degree of color from "white" to "full color intensity", i.e. from "white" to "blue" or "red." The more white light is added the more desaturated the color becomes.
Brightness
The quality of being illuminated, shining, and emitting light.

Shadows and Shading
Most objects in the world do not let much light pass through so that these objects cast shadows. The exact shape and description of the shadows changes depending on the direction of the light, e.g. when outside shadows are long and go to the west in early morning, short and northerly at noon, and then long but to the east in the late afternoon.

There are certain general rules about shadows:

• With only one source of light (e.g. outside), the shadows from all the objects in the area all go in the same direction.
• In the case of natural light and for most artificial lights, the light comes primarily from above the object.
• For a solid object, the side of the object in shadow is the side away from the light. But for a hole in the ground, the shadow is on the side near the light.

Shadows can play a very powerful role in defining form by giving the object a three-dimensional appearance. Shadows can also be used to highlight different portions of an object at different depths. The object closer to the light will cast a shadow on the more distant object.

Figure-Ground
Our visual system simplifies a scene into a figure that we look at and a ground that is everything else and forms the background. This tendency is exploited in the reversible figure-ground figure of the Rubin Vase as shown below. The drawing appears as either a central vase, or two faces that are looking at each other. Generally when we see one of the perceptions, the other region forms a background and is not seen.

Depth Cues
3D objects must be represented on flat surfaces. To help us visualize and represent the depth of an object, we need to utilize depth perception cues in our drawings.

Some of the perceptual cues that give rise to the impression of depth include:
 

• Interposition
• Relative Height
• Relative Size
• Texture Gradient

Interposition
Interposition is the partial blocking of a more distant object by a nearer object. In the figure below, the two triangles appear at different depths because one is partially obscured by the other. Actually both triangles are at the same distance (the distance of the screen from your eyes). Interposition (overlap, occlusion or superposition) causes the sense of depth to arise.

Relative Height
Another pictorial cue to depth is the relative height of objects in the drawing. An object close to the viewer will be at the bottom of the drawing, an object off in the distance will be near the middle of the drawing, and objects will be ever higher as they are more distant. This cue can lead to a powerful sense of depth.

Relative Size
Another pictorial cue to depth is the relative size of objects in the drawing. Objects are drawn smaller as they move further away from the viewer.

Texture Gradient
Most surfaces, such as walls and roads, and fields, like a field of flowers in bloom, have a texture. As the surface gets farther away from us this texture gets finer and appears smoother (Gibson, 1950). The figure below attempts to illustrate texture gradient using circles. At each level, as the circles get smaller, we get the impression that the circles are getting farther away.

In perspective projection, the visual rays converge at a point. The representation on the transparent plane may be considered the view that would be seen by a single eye at a known point in space. The picture is formed on the transparent plane by the intersecting points of the projecting lines from the eye to the object.

The size of the view will vary as the relative positions of the eye, the projection plane, and the object are altered. Although perspective projection produces a realistic pictorial view of the object, its distortion of angles and distances prevents its meeting the exacting requirements demanded of a technical drawing. Perspective projection is used primarily by architects and commercial artists to describe the external appearance of an object.

One-point perspective occurs when the projection plane is parallel to two principal axes. Conversely, when the projection plane is perpendicular to one of the principal axis, one point perspective occurs. Receding lines along one of the principal axis converge to a vanishing point. A one-point perspective is used almost exclusively for interior-room views. It gives the observer the illusion of looking into the room.

Multiview orthographic projection forms the basis for the most drawings used in technical communication. The main purpose is to obtain views of an object on which true measurements can be made. Therefore, the front face is oriented parallel to the projection plane so that the established view shows the true width and height of the object. Since a single orthographic view in itself cannot fully describe an object, an additional view on a projection plane perpendicular to the first is needed to show the depth of the object.

A conventional means of showing several views on a single plane has been developed. The figure below shows three orthogonal picture planes. The picture planes are customarily called the principal or coordinate planes of projection. There are three principal coordinate planes of projection : the frontal plane, the horizontal plane, and the profile plane. All three planes are mutually perpendicular.

Isometric Drawings are the quickest and easiest of all pictorials to draw and are therefore the most commonly used. In an isometric drawing the three normal surfaces of a rectangular solid will have equal angles between them (120 degrees). However there is a distinct difference between isometric drawings and isometric projections. This is particularly important because most computer generated pictorials are actually projections.

The biggest visual difference between isometric drawings and isometric projections is the size of the two images. The isometric drawing is drawn using 100% true length measurements on the height, width, and depth axes. However, in isometric projections the height, width and depth are displayed at 82% of their true length.

In isometric projections the object is first rotated about the Y axis by -45 degrees. Then the object is rotated about the X axis by 35 degrees. Because the normal surfaces of the object are no longer parallel or perpendicular to the picture plane, the image edges will appear foreshortened on each axis by 18%. The foreshortened view is called an isometric projection.

When you draw a pictorial on a computer, the image that appears on the screen is a projection, and therefore it is foreshortened. The big advantage of drawing these pictorials on the screen is that the object may be easily rotated about the axes in a countless number of positions once the data for the object's features have been entered.

There are many types of pictorial drawings. Although pictorial drawings are simply rough sketches, they still use the basic principles of projection. Some of the major types of pictorials are isometric drawings, oblique drawings, multiview drawings and perspectives.

Isometric Drawings