## Cube Tutorial

## Perspective Basics Tutorial

**Mathematically, perspective is very simple. All aspects can be explained by the fact that any parallel condition shares the same vanishing point. **

**A cube for example, has three sets of parallel conditions. Three sets of two planes, which are parallel and three sets of four edges which are parallel.**

If the viewer’s gaze happens to be **exactly** perpendicular to one set of lines, then that set of lines will appear parallel.

Imagine the viewer looking at the subject matter with a laser beam projecting out of his/her eyeball. The beam is an exact line that defines the direction of view.

If the viewer happens to be gazing **exactly** perpendicular to one set of parallel lines then perspective convergence is not possible for that set of lines. The **two point perspectives** used to show most buildings assume that the viewer’s gaze is locked exactly onto the horizon line. Because our gaze is perfectly horizontal and all vertical lines are exactly vertical, then we have a condition where all vertical lines are simply drawn using vertical (parallel) lines.

Imagine looking down the length of a hallway. If your gaze is parallel to the side walls, and therefore perpendicular to the back and front wall, then there will only be **one** set of lines that vanish at all. This condition produces the **one point perspective.**

Imagine leaning back to look up at a tall building or leaning over to look down into an elevator shaft. In each of these examples you have a **three point perspective,** because the direction of your gaze is not horizontal or perpendicular to any set of lines. In this case you have added an additional vanishing point for the vertical lines, above your head for the zenith, or below your feet for the nadir

**Develop an eye for perspective. Our mind/eye is an incredibly sophisticated judge of the simple rules of perspective.**

For example, sketch a cube in perspective quickly. Now stand back and evaluate it. It is relatively easy to judge if it is too tall, too wide etc. The faces must be in proportion to each other, depending on the rotation of the object. The more one particular face of the cube is toward you the more “square” it will be. The more a face if the cube is away from you the more foreshortened or skinnier it will appear. Practice extensively with the cube until your judgment becomes automatic as you draw. It is helpful to build up the drawing gradually by drawing lightly until you feel the proportion is correct.

Locate the vanishing points far enough apart to eliminate distortion. Generally it works best to have one vanishing point close to the subject, while the other is further away, typically off the page. Use a long straight edge to a reference point, or develop your eye for converging line. A helpful two-dimensional exercise is to draw two straight, non-parallel lines on a sheet of paper. These two lines imply an intersection point. Now add lines that converge to the same point. This intersection point may be on the page or off the page, but the important thing is that any other line added will converge to the same point. This exercise is helpful in recognizing when convergent lines in perpsective share the same vanishing point.

**Always draw transparently.**

Draw all edges of the object including those on the oppsite faces. **It is critical to think three-dimensionally**, not two-dimensionally. The drawing is about space and volume and the more you can suggest the opposite side of the object then the stronger the sense of volume.

**Use section lines to map out or define the surface of an object.**

Most built objects have lines on the surface where materials come together. Drawing these lines is critically important because they define and reinforce the sense of volume and space.