Unformatted text preview: re therefore called clipping planes.
1. Suppose the screen is represented by a rectangle in the yz-plane with vertices 0, 400, 0
and 0, 400, 600 , and the camera is placed at 1000, 0, 0 . A line L in the scene passes
through the points 230, 285, 102 and 860, 105, 264 . At what points should L be clipped
by the clipping planes? 2. If the clipped line segment is projected on the screen window, identify the resulting line segment.
3. Use parametric equations to plot the edges of the screen window, the clipped line segment, and its projection on the screen window. Then add sight lines connecting the viewpoint to
each end of the clipped segments to verify that the projection is correct.
4. A rectangle with vertices 621, 147, 206 , 563, 31, 242 , 657, 111, 86 , and
599, 67, 122 is added to the scene. The line L intersects this rectangle. To make the rectangle appear opaque, a programmer can use hidden line rendering which removes portions
of objects that are behind other objects. Identify the portion of L that should be removed. |||| 13.6 Cylinders and Quadric Surfaces
We have already looked at two special types of surfaces—planes (in Section 13.5) and
spheres (in Section 13.1). Here we investigate two other types of surfaces—cylinders and
In order to sketch the graph of a surface, it is useful to determine the curves of intersection of the surface with planes parallel to the coordinate planes. These curves are called
traces (or cross-sections) of the surface. Cylinders
A cylinder is a surface that consists of all lines (called rulings) that are parallel to a given
line and pass through a given plane curve.
EXAMPLE 1 Sketch the graph of the surface z x 2. x 2, doesn’t involve y. This means that
any vertical plane with equation y k (parallel to the x z-plane) intersects the graph in a
curve with equation z x 2. So these vertical traces are parabolas. Figure 1 shows how
the graph is formed by taking the parabola z x 2 in the x z-plane and moving it in the SOLUTION Notice that the equation of the graph, z 5E-13(pp 868-877) 1/18/06 11:34 AM Page 869 S ECTION 1...
View Full Document