Drawing

Mathematics

Perspective is a mathematical system for projecting the three-dimensional world onto a two-dimensional surface. It allows a flat image to convey a three-dimensional state.

The linear perpective relies on lines of sight converging on either one or two vanishing points. Our position in relation to the base (on which an object sits) affects how much of the objects we see, and what view we have of the space around them.

As a Subjective View

Perspective is an individual's "point of view". It can subjectively color his or her interpretation of events and policies, because he sees how they affect his particular area or group.

Putting art aside for a moment, according to one dictionary, the word perspective originally comes from the Latin words per meaning "through" and specere which means "to look." These are combined to mean "to look through" or "to look at."

However, the meaning of a word can change and usually even splits into several meanings over time. The conventional "art definition" of perspective specifically describes creating the appearance of distance into our art. This emphasis on distance stems from it being a difficult and impressive effect to achieve, especially on paper that is completely flat. Here we are attempting to convey a sense of reality with space and depth on something which has none. As such, the most typical "art definition" of perspective has evolved into:

"The technique of representing a three-dimensional image on a two-dimensional surface."

But being three-dimensional means that an object has height and width, not just depth alone. Despite this, perspective became less about three-dimensional form than obsessing almost exclusively on that third dimension of depth. This is so much the case that it is commonly referred to as depth perspective.

Furthermore, perspective already exists while seeing in reality where no kind of flat surface is involved. There are also perspective art forms that make no use of flat surfaces in their final states such as interior design, landscape design, stage set design, sculpture, architecture or in any kind of display or exhibit.

With that said, "the technique of representing a three-dimensional image on a two-dimensional surface" does not actually explain what perspective is at all, despite any true importance that depth may have.

First understand that our viewpoint is simply that position we are seeing things from. With that in mind, perspective basically means the same as "viewpoint" and "position." For example, "It looks good from my viewpoint," "It looks good from my position" and "It looks good from my perspective."

Oddly, this meaning of perspective is primarily used outside of art.

So the most general definition of perspective is "a position in relation to different positions." For example, this includes the position of our eye in relation to the positions of objects in a scene.

Applying this to art, we do not necessarily mean the viewpoint of the artist in relation to the subject. More specific, what matters is the best perspective for the audience. A more universal "art definition" of perspective, therefore, is "Creating viewpoints that best communicate a subject to an audience."

Perspective is really about establishing "an eye" in your art through which your audience sees. So although it has been considered the most difficult subject in all of art, its concept is quite simple.

1. Draw the image of the object. Use the principle that the object distance is equal to the image distance to determine the exact location of the object. Pick one extreme on the object and carefully measure the distance from this extreme pointto the mirror. Mark off the same distance on the opposite side of the mirror and mark the image of this extreme point. Repeat this process for all extremes on the object until you have determined the complete location and shape of the image. Note that all distance measurements should be made by measuring along a segment that is perpendicular to the mirror.

2. Pick one extreme on the image of the object and draw the reflected ray that will travel to the eye as it sights at this point. Use the line of sight principle: the eye must sight along a line at the image of the object in order to see the image of the object. It is customary to draw a bold line for the reflected ray (from the mirror to the eye) and a dashed line as an extension of this reflected ray; the dashed line extends behind the mirror to the location of the image point. The reflected ray should have an arrowhead upon it to indicate the direction that the light is traveling. The arrowhead should be pointing towards the eye since the light is traveling from the mirror to the eye, thus enabling the eye to see the image.

3. Draw the incident ray for light traveling from the corresponding extreme on the object to the mirror.The incident ray reflects at the mirror's surface according to the law of reflection. But rather than measuring angles, you can merely draw the incident ray from the extreme of the object to the point of incidence on the mirror's surface. Since you drew the reflected ray in step 2, the point of incidence has already been determined; the point of incidence is merely the point where the line of sight intersects the mirror's surface. Thus draw the incident ray from the extreme point to the point of incidence. Once more, be sure to draw an arrowhead upon the ray to indicate its direction of travel. The arrowhead should be pointing towards the mirror since light travels from the object to the mirror.

4. Repeat steps 2 and 3 for all other extremities on the object. After completing steps 2 and 3, you have only shown how light travels from a single extreme on the object to the mirror and finally to the eye. You will also have to show how light travels from the other extremes on the object to the eye. This is merely a matter of repeating steps 2 and 3 for each individual extreme. Once repeated for each extreme, your ray diagram is complete.

Really, though, the best way to learn to draw ray diagrams involves trying it yourself. It's easy. Merely duplicate the two setups below onto a blank sheet of paper, grab a ruler/straightedge, and begin. If necessary, refer to the four-step procedure listed above.