1Perspective in Curved Objects David Salomon（1的角度弯曲的对象大卫·所罗门）.pdfVIP

1 Perspective in Curved Objects This document complements the material in section 3.3 of Transformations and Projec- tions in Computer Graphics (Springer Verlag, 2006, ISBN 1-84628-392-2). It discusses techniques for drawing curved objects in perspective. There are many books, mostly for artists, draftsmen, and architects, that discuss perspective and describe methods for drawing objects in perspective. Unfortunately, these books generally employ cubes, or cubical objects, as examples, and therefore create the wrong impression that only such objects can be drawn in perspective. Experienced artists, illustrators, and other people (such as engineers and architects) who draw both curved and cubical objects, know that even curved objects, even objects that lack any straight lines and flat faces, can be drawn in perspective. This document explains simple techniques and approaches to the perspective drawing of arbitrary objects. For general references on this topic and more examples, see [Hulsey 08] and [Robertson 08]. We start with a general 1-point perspective grid. Figure 1a shows a rectangle bounded by two horizontal lines and the vertical lines a and b. We want to construct an adjacent rectangle of the same width. Two diagonals are drawn (shown in dashed) to locate the center of the rectangle, and a short horizontal line c is drawn to locate point B, the center of line b. Finally, a line is drawn from point A through point B, to determine point C, which becomes the bottom-right corner of the new rectangle. This simple technique is now applied to construct a perspective grid. Figure 1b shows two boundary lines that converge to a vanishing point VP. Two vertical lines a and b are selected arbitrarily (it is useful to assume that the distance between them is one unit) to create a trapezoid. We draw the two diagonals (in dashed) and construct the line from the center of the trapezoid to the vanishing point. In part (c)