Introduction - An Introduction to Computer Graphics for Artists - page 1

Chapter 1
Introduction

1.1 Linear Perspective and Computer Graphics

In 1435, the Italian scholar Leon Battista Alberti wrote a treatise in Latin titled
De Pictura (on painting). In 1436, it was translated into Italian and distributed. It
is the fi rst known publication on the subject of linear perspective (Field 1985 ;
Heffernan 1996 ). Linear perspective is a subject very closely related to the heart
of modern computer graphics because it establishes a way to artifi cially construct
a realistic representation of 3D objects within a 2D picture space. The process is
called projection (Pottman et al. 2007 ). Alberti's treatise was partly based on
observations made by the prominent Florentine sculptor and architect Filippo
Brunelleschi, though other artists from the same period were also experimenting
with the technique. The Italian Renaissance in painting was to some considerable
extent dependent on this major discovery (White 1949 ).
Linear perspective demonstrated that a realistic representation of a 3D environ-
ment could be calculated based on rules that govern how our eyes see the world around
us. Because these rules could be written down and they worked, artists were able to
replicate the results Alberti described, and linear perspective became a standard tool
for artists to the present day (Fig. 1.1 ).
Linear perspective stems from the observation that parallel lines seem to
converge as they move farther from our eye. The reason isn't that they are actually
coming together, but that the human eye is nearly spherical in shape. The result is
shapes that appear to converge the closer they are to the pupil.
As the point of focus shifts to the right or left of center, the angle formed by the
ray from each eye to the subject becomes more acute (Fig. 1.2 , left). This causes
some distortion and an exaggerated impression of curvature. In a perspective pro-
jection, the cone of vision represents approximately a 30° angle of view, or the
amount one unmoving eye can see (Pottman et al. 2007 ). Projections that include
more than 30° have progressively greater distortion until they become unconvincing
as perspective projections at about 50°.