17 January, 2009

There are two simple rules about representing depth. Size decreases with distance, meaning objects that are further away from the viewer appear to be smaller. Objects also overlap when one is in front of the other, hiding part or all of the farther objects. These two observations are the basis for perspective. The easiest way to understand how perspective works is to imagine standing in the middle of train tracks (not recommended for safety reasons) and looking along the tracks into the distance. Visually follow the tracks to the horizon (where the earth meets the sky) and the tracks appear to meet at a point in the distance. This converging point is called the vanishing point.



Now imagine that as you look at the train tracks converge into the distance, you are holding a piece of rectangular glass directly in front of you. If you traced what you saw onto the glass with a marker, you would be drawing onto the picture plane. Perspective is a method for representing what is seen through the picture plane on another two-dimensional surface.

Quite simply, perspective is the illusion that something far away from us is smaller. This effect can be naturally occurring as in a photo, or a mechanically created illusion in a painting. In 2D artwork perspective is a technique used to recreate that illusion and give the artwork a three-dimensional depth. Perspective uses overlapping objects, horizon lines, and vanishing points to create a feeling of depth. There are several types of perspective used to achieve different effects.

Perspective Projections:

Like parallel projections, perspective projections define a major subclass of planar geometric projections. Divisions within perspective projections are consistent in that the center of projection (PRP) is placed at a finite distance from the viewplane. Because of this finite distance between the camera and the viewplane, projectors are no longer parallel. By placing the camera near the viewplane, as shown for the perspective projection in figure below, projectors from the PRP to the edges of the projection window, located on the u-, v-plane, define a pyramidal view volume. As shown in figure below, the projectors from the center of projection to line AB form a much shorter line A’B’ in the viewplane. The reduction in length of the projected line is attributed to the decreasing distance between the two projectors as the viewing surface becomes nearer to the center of projection.

In comparison to parallel projections, perspective projections often provide a more natural and realistic view of a three-dimensional object. By comparing the viewplane of a perspective projection with the view seen from the lens of a camera, the underlying principals of a perspective projection can be easily understood. Like the view from a camera, lines in a perspective projection not parallel to the viewplane converge to a distant point (called a vanishing point) in the background. When the eye or camera position is close to the object, perspective foreshortening occurs with distant objects appearing smaller in the viewplane than closer objects of the same size. Perspective projections are typically separated into three classes: one-point, two-point, and three-point projections.

In a one-point perspective projection, lines of a three-dimensional object along a major axis converge to a single vanishing point while lines parallel to the other axes remain horizontal or vertical in the viewplane. To create a one-point perspective view, the viewplane is set parallel to one of the principal planes in the world coordinate system. The viewplane normal is set parallel to a major axis and the viewplane normal vector n is initialized such that two of its three components are zero. Figure below shows a one-point perspective view of a cube. In this projection, the viewplane is positioned in front of the cube and parallel to the x- and y-plane.

A two-point perspective projects an object to the viewplane such that lines parallel to two of the major axes converge into two separate vanishing points. To create a two-point perspective, the viewplane is set parallel to a principal axis rather than a plane. In satisfying this condition, the viewplane normal vector n should be set perpendicular to one of the major world coordinate system axes. In this case, two of the components of n = (nx, ny, nz) are nonzero, while the third is zero. Figure below shows a two-point perspective view of a cube. In this figure, lines parallel to the x-axis converge to vanishing point VP1 while lines parallel to the z-axis converge to vanishing point VP2. Two-point perspective views often provide additional realism in comparison to other projection types; therefore, they are commonly used in architectural, engineering, industrial design, and in advertising drawings.

A three-point perspective has three vanishing points. In this case, the viewplane is not parallel to any of the major axes. To position the viewplane, each component of the viewplane normal is set to a non-zero value so that the viewplane intersects the three major axes. Vanishing points are often used by artists for highlighting features or increasing dramatic effects. However, many disagree as to the extent of their utility. In many of the objects we might select to draw and paint, we find there are three types of perspective that we use most. They are:

  1. One-point Perspective.
  2. Two-point Perspective.
  3. Three-point Perspective.

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