Shimamura_Chp 4 - Chapter 4 Chapter 4: Making A Scene The...

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Chapter 4 60 Chapter 4: Making A Scene The Ideal City (Figure 4.1) is a testament to mathematical precision in art. This Renais- sance work depicts a cityscape in accurate linear perspective. The rendering of depth is so pre- cise that one could reconstruct the 3-D layout of the buildings. To build such a model, it is ne- cessary to determine 1) the distance from the viewer to the picture plane , which is the imaginary “window” onto which the scene is projected, 2) the elevation of the viewpoint from the ground, and 3) the scale of objects in the painting compared to those in an actual scene. Two computer scientists established these reference points and constructed a computer-generated 3-D model of the painting. With the model, one can take a virtual stroll around the plaza. Shown in Figure 4.2 is a computer-generated view which shows the plaza as if one were walking along the left side of it. Interesting- ly, art historians have described the original painting as portraying an individual’s view of the city. Yet according to measurements of the elevation of the viewpoint, the viewer would have to have been over 10 ft tall! How does the brain construct a realistic scene? In the previous chapter, form perception was identified as an essential accomplishment of brain processing. This chapter describes how the brain places forms into a spatial environment. One aspect of spatial ability is the use of ego- centric space, in which objects in a scene are defined in relation to the viewer. The 3-D comput- er-generated view of the Ideal City (Figure 4.2) presents such a viewpoint. It is often called a first-person view. Another way we use space is by allocentric analysis, in which objects are re- lated to each other, and thus independent of a specific viewer. Allocentric space is often called a third-person or bird’s eye view. City and satellite maps are examples of space viewed from an allocentric perspective. The primary focus of this chapter is egocentric space and how artists and brains create realistic first-person views of the world. The Geometry of Space Painting realistic scenes requires knowledge about the way light rays reflect off objects and enter our eyes. This knowledge was known as early as the 4 th Century B.C when Euclid de- scribed in Optics a set of mathematical rules about light and how it is projected onto the retina.
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Chapter 4 61 His analysis formed the basis for the geometry of linear perspective, which gave Renaissance artists the method for depicting realistic 3-D scenes onto 2-D surfaces. A Florentine Discovery In the 15 th Century, two architects, Filippo Brunelleschi and Leon Battista Alberti, derived the method of linear perspective. It is perhaps not surprising that architects would have develop this method, as their occupation demanded precision in all three spatial dimensions. Brunelleschi is best known for designing the immense dome of the cathedral in Florence. His biographer, An- tonio di Tuccio Manetti, an architect himself, related a story about Brunelleschi’s discovery. Brunelleschi took a 12-inch square panel and painted in precise linear perspective the Baptistery,
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Shimamura_Chp 4 - Chapter 4 Chapter 4: Making A Scene The...

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