In computer graphics and perspective drawing, we need to represent objects seen by the eye in space as images on a two-dimensional plane. Suppose that the eye is at E(xg. 0, 0) as shown here and that we want to represent a point P(x), yi, 21) as a point on the yz-plane. We do this by pro- jecting P, onto the plane with a ray from E. The point P, will be portrayed as the point P(0, y, 2). The problem for us as graphics designers is to find y and z given E and P. a. Write a vector equation that holds between EP and EP. Use the equation to express y and z in terms of xo, X1. Vi, and z1. b. Test the formulas obtained for y and z in part (a) by investi- gating their behavior at x = 0 and x = xo and by seeing what happens as xo →. What do you find? P(0, y. 2) E(xo, 0, 0)
In computer graphics and perspective drawing, we need to represent objects seen by the eye in space as images on a two-dimensional plane. Suppose that the eye is at E(xg. 0, 0) as shown here and that we want to represent a point P(x), yi, 21) as a point on the yz-plane. We do this by pro- jecting P, onto the plane with a ray from E. The point P, will be portrayed as the point P(0, y, 2). The problem for us as graphics designers is to find y and z given E and P. a. Write a vector equation that holds between EP and EP. Use the equation to express y and z in terms of xo, X1. Vi, and z1. b. Test the formulas obtained for y and z in part (a) by investi- gating their behavior at x = 0 and x = xo and by seeing what happens as xo →. What do you find? P(0, y. 2) E(xo, 0, 0)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![In computer graphics and
perspective drawing, we need to represent objects seen by the eye
in space as images on a two-dimensional plane. Suppose that the
eye is at E(xg. 0, 0) as shown here and that we want to represent a
point P(x), yi, 21) as a point on the yz-plane. We do this by pro-
jecting P, onto the plane with a ray from E. The point P, will be
portrayed as the point P(0, y, 2). The problem for us as graphics
designers is to find y and z given E and P.
a. Write a vector equation that holds between EP and EP. Use
the equation to express y and z in terms of xo, X1. Vi , and z1.
b. Test the formulas obtained for y and z in part (a) by investi-
gating their behavior at x = 0 and x = xo and by seeing
what happens as xo →. What do you find?
P(0, y. z)
(X. Y. 0)
E(xo, 0, 0)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79b1f7b5-0cc2-44c5-a683-a0cd83098d86%2Fb23edf37-a5bb-49a3-a276-6b4c91f5f922%2Fz4ne7c_processed.png&w=3840&q=75)
Transcribed Image Text:In computer graphics and
perspective drawing, we need to represent objects seen by the eye
in space as images on a two-dimensional plane. Suppose that the
eye is at E(xg. 0, 0) as shown here and that we want to represent a
point P(x), yi, 21) as a point on the yz-plane. We do this by pro-
jecting P, onto the plane with a ray from E. The point P, will be
portrayed as the point P(0, y, 2). The problem for us as graphics
designers is to find y and z given E and P.
a. Write a vector equation that holds between EP and EP. Use
the equation to express y and z in terms of xo, X1. Vi , and z1.
b. Test the formulas obtained for y and z in part (a) by investi-
gating their behavior at x = 0 and x = xo and by seeing
what happens as xo →. What do you find?
P(0, y. z)
(X. Y. 0)
E(xo, 0, 0)
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