# Perspective and the Cube

In linear perspective it is necessary to understand the concept of the picture plane, which is the actual two-dimensional surface of your paper (or canvas). The image on the paper is the depiction of what would be seen behind the paper's surface. If you were to trace the view out a window onto the glass, the glass would represent the picture plane.

The other concept to understand is the horizon line, which is, of course, the horizon; it is also called the eye level. Imagine a piece of cardboard with a rectangle cut out of it-a viewfinder. If you hold the viewfinder at the level of your eye, the horizon will be in the middle of the opening. If you lower the viewfinder, the horizon appears to move to the top of the opening. If you raise the viewfinder, the horizon appears to move to the bottom of the opening. Thus, in a drawing, when the horizon is high on the page, our focus is on things below our eye level (we are looking down). When the horizon is low on the page, our focus is on things above our eye level-over our head (we are looking up).

Imagine you are looking at a level box. If you can see the top of the box, it is below your eye level, so the horizon is above the box. If you can see the underside of the box, it is above your eye level, so the horizon is below the box.

The picture plane is the actual surface upon which an image is created. The image appears to be behind the surface.

To give the impression of looking down, the horizon is placed high on the page.

To give the impression of looking up, the horizon is placed Iow on the page.

To give the impression of looking down, the horizon is placed high on the page. To give the impression of looking up, the horizon is placed low on the page.

One-Point Perspective and the Cube
The two most common and useful types of perspective are one-point and two-point perspective. The simplest demonstration of one- point perspective is to look down a straight road. We know the road to be the same width throughout its length, and yet as we look toward the horizon the road appears to get increasingly narrow, until it diminishes to a point on the horizon. This is called the vanishing point because it is where the road appears to vanish. On level ground, the vanishing point is always on the horizon. Place a cube in this road with the sides of the cube parallel to the sides of the road. The lines that describe the receding edges of the cube will converge at the same vanishing point that the road does. All receding parallel lines will share the same vanishing point.

These three boxes are drawn in one-point perspective. The dotted lines indicate receding lines. All the receding lines meet at one point on the horizon line, indicating that they are parallel to one another.

In one-point perspective, a straight flat road seems to get narrower in the distance, although we know that it doesn't. Imagine a box whose receding edges are parallel to those of the road. All of these edges "vanish" at the same point on the horizon.

One-point perspective is also used when you are depicting boxes or interiors that have races or walls parallel to the picture plane. The horizontal and vertical lines on the faces parallel to the picture plane are drawn perpendicular to each other. All other receding edges or an object will converge at a point on the horizon line. In one-point perspective, the front and back of a cube are parallel to the picture plane. They are drawn as squares with perpendicular corners. The top, bottom, and sides of a cube in one-point perspective recede into space. The lines defining their receding edges will converge at a point somewhere behind the cube.

Remember: In one-point perspective, verticals and horizontals are perpendicular to each other on surfaces parallel to the picture plane.

When drawing a cube or box in one-point perspective, start with a perfect square or rectangle (all corners are 90° angles). This represents the side that is parallel to the picture plane. (The vanishing point is denoted as VP.)

To establish the top of the cube, draw lines from the top corners of the square to a point behind the cube on the horizon line.

The back of the cube is established (arbitrarily for now) by making a line parallel to the top of the front of the cube; the width of this line is defined by the perspective lines you drew from the cube's top front corners.

The receding lines of the top are now drawn in, connecting the back of the cube to the front.

We have now established a closed cube in one-point perspective.

To open the front of the cube, draw the receding lines of the bottom of the cube from the bottom front corners to the vanishing point. The bottom edges are parallel to the top ones, so they will share the same vanishing point.

Vertical lines are now drawn from the back corners of the cube to the receding lines of the bottom of the cube.

Where the vertical lines of the back of the cube meet the receding lines of the bottom, draw a line parallel to the front bottom line.

The back vertical fines are now drawn to where they meet the receding lines of the bottom of the cube. Note: We can't see through the top of the cube, so we won't see these lines meet the top back corners.

This is an open cube in one-point perspective.

Two-point perspective and the Cube
Two-point perspective is used when only the vertical edges of the cube are parallel to the picture plane. This is unlike one-point perspective, in which whole sides of the cube are parallel to the picture plane.

With a cube in two-point perspective, only the verticals are truly parallel to each other. All other lines will appear to point to one of two vanishing points. If the cube is level, the vanishing points will be on the horizon. All lines parallel to each other will share the same vanishing point. The farther apart the two vanishing points are placed, the farther away from the object your viewpoint appears to be.

In one-point perspective, whole sides of the cube are parallel to the picture plane, as the example at near right shows. In two-point perspective, only the cube's vertical edges are parallel to the picture plane, as in the example at for right.

To draw a cube in two-point perspective, we start with the vertical edge nearest the picture plane. Vanishing points are placed (arbitrarily for now) on the left and right sides of the horizon line.

Lines from the top and bottom of the near edge are drawn to the vanishing point at right. This will establish the top and bottom edges of the right side of the cube.

Similar lines are drawn for the left side of the cube.

Vertical lines are now chosen (arbitrarily for now) for the back corners of the cube. These lines fit between the receding dotted lines.

The top and bottom edges of the two sides are now drawn.

To find the back edges of the top of the cube, draw a line from the left bock corner to the vanishing point at right. Draw another line from the right back corner to the vanishing point at left.

The back top edges are now drawn in.

This is a closed cube in two-point perspective.

To depict an open cube in two-point perspective, draw a line from the vanishing point at left to the right front bottom corner.

To establish the depth of the cube, draw a line from the vanishing point at right to the back left bottom corner. Then draw a vertical line from the top back corner to where the lines from the vanishing points cross.

Draw the lines where we would see them if only the right side of the box were open.

This is an open cube in two-point perspective.