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(Xo,0,0) as shown here and that we want to represent a point P(x1,y1,z1) as a point on the yz-plane. We do this by projecting P1 onto the plane with a ray from E. The point P1 will be portrayed as the point P(0,y,z). The problem for us as graphics designers is to find y and z given E and P1. Write a vector equation that holds between vector EP and vector EP1. Use the equation to express y and z in terms of xo, x1, y1, and z1. What is the correct vector equation? The magnitudes must be the same, EP = EP1 The cross product must be the zero vector, EP×EP1 = 0. The dot product must beone, EP • EP1 = 1. The dot product must bezero, EP • EP1 = 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(Xo,0,0) as shown here and that we want to represent a point P(x1,y1,z1) as a point on the yz-plane. We do this by projecting P1 onto the plane with a ray from E. The point P1 will be portrayed as the point P(0,y,z). The problem for us as graphics designers is to find y and z given E and P1. Write a vector equation that holds between vector EP and vector EP1. Use the equation to express y and z in terms of xo, x1, y1, and z1. What is the correct vector equation? The magnitudes must be the same, EP = EP1 The cross product must be the zero vector, EP×EP1 = 0. The dot product must beone, EP • EP1 = 1. The dot product must bezero, EP • EP1 = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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(Xo,0,0) as shown here and that we want to represent a point P(x1,y1,z1) as a point on the yz-plane.
We do this by projecting P1 onto the plane with a ray from E. The point P1 will be portrayed as the point P(0,y,z). The problem for us as graphics designers is to find y and z given E and P1.
Write a
- The magnitudes must be the same, EP = EP1
- The cross product must be the zero vector, EP×EP1 = 0.
- The dot product must beone, EP • EP1 = 1.
- The dot product must bezero, EP • EP1 = 0
Transcribed Image Text:X
OL
Ex. 0,0)
P₁(x₁. 1. 21)
P(0, y, z)
(₁, 1, 0)
→y
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