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(x 0 , 0, 0) as shown here and that we want to represent a point P 1 (x 1 , y 1 , z 1 ) as a point on the yz plane We do this by projecting P 1 onto the plane with a ray from E The point P 1 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 P 1 a Write a vector equation that holds between Use the equation to express y and z in terms of x 0 , x 1 , y 1 , and z 1 b Test the formulas obtained for y and z in part (a) by investigating their behavior at x 1 0 and x 1 x0 and by seeing what happens as x 0 What do you find EP and EP

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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

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(x₀, 0, 0) as shown here and that we want to represent a point P₁(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.

a. Write a vector equation that holds between

Use the equation to express y and z in terms of x₀, x₁, y₁, and z₁.

b. Test the formulas obtained for y and z in part (a) by investigating their behavior at x₁ = 0 and x₁ = x0 and by seeing what happens as x₀ → ∞. What do you find?

EP and EP.

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