计算机图形学（第三版）DonaldHearn蔡士杰译课后习题答案6 - CSDN文库

计算机图形学（第三版）Donald

课后习题答案

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Chapter 6

Two-Dimensional Viewing

Exercises for this chapter deal with the two-dimensional viewing pipeline. This includes prob-

lems relating to display windows and viewports, transformations from world to viewing coordi-

nates, clipping procedures, and applications of the OpenGL two-dimension viewing functions.

Exercises

6-1. Matrix 6-1 is formed by ﬁrst translating P

0

to the world coordinate origin, then rotating

the viewing-coordinate axes to align them with the world-coordinate axes. The elements

of the rotation matrix can be obtained from axis vector V using the methods described

in Section 6-2.

6-2. First set up the matrix for scaling the coordinates of the clipping window vertices, relative

to the window center position, so that the window is the same size as the viewport. Next,

premultiply the scaling matrix by a matrix that translates the coordinates of the window

center point to the viewport center point. Then express the elements of the composite

matrix in terms of the scaling and translation parameters in Eqs. 6-4 and 6-5.

6-3. Input to this procedure is the set of coordinates for the clipping-window vertices. The

elements of the transformation matrix are then calculated from a sequence of scale-rotate

operations, as in the preceding exercise. Any position on either the clipping window or

the normalized square can be used as the ﬁxed point for the transformation sequence.

6-4. A circle and a few polygons, such as a triangle, rectangle, and hexagon, can each be deﬁned

relative to the coordinate origin. For example, each polygon could be deﬁned with its

centroid coordinates as (0, 0). Then a scene is constructed by positioning the objects

within a world-coordinate space. Viewing coordinates and a clipping window are deﬁned

using the methods described in Section 6-2, and the normalized-square transformation is

given in Section 6-3.

A viewing table can be set up as a list of values for viewing-coordinate parameters P

0

and V (Section 5-8), along with the coordinate limits for the clipping window. Each set

of values can be referenced with a numerical index, such as the list position, and an input

37

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DayThinking

2012-07-19

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