In computer graphics and perspective drawing, we need to represent objects seen by the eye in space
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(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?
Step by Step Answer:
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir