Problem 13
Each collection that follows represents the vertices (using the traditional rectangular coordinate system) of a patch in a polygonal mesh. Describe the shape of the mesh. Patch 1: \((0,0,0)(0,4,0)(2,4,0)(2,0,0)\) Patch 2: \((0,0,0)(0,4,0)(1,4,1)\) \((1,0,1)\) Patch 3: \((2,0,0)(1,0,1)(1,4,1)\) \((2,4,0)\) Patch 4: \((0,0,0)(1,0,1)(2,0,0)\) Patch 5: \((2,4,0)(1,4,1)(0,4,0)\)
Problem 14
Design a polygonal mesh representing a rectangular solid. Use the traditional rectangular coordinate system to encode the vertices and draw a sketch representing your solution.
Problem 15
Using no more than eight triangular patches, design a polygonal mesh to approximate the shape of a sphere with radius one. (With only eight patches, your mesh will be a very rough approximation of a sphere, but the goal is for you to display an understanding of what a polygonal mesh is rather than to produce a precise representation of a sphere.) Represent the vertices of your patches using the traditional rectangular coordinate system and draw a sketch of your mesh.
Problem 16
Why would the following four points not be the vertices of a planar patch? \((0,0,0)(1,0,0)(0,1,0)(0,0,1)\)
Problem 17
Suppose the points \((1,0,0),(1,1,1)\), and \((1,0,2)\) are the vertices of a planar patch. Which of the following line segments is/ are normal to the surface of the patch? a. The line segment from \((1,0,0)\) to \((1,1,0)\) b. The line segment from \((1,1,1)\) to \((2,1,1)\) c. The line segment from \((1,0,2)\) to \((0,0,2)\) d. The line segment from \((1,0,0)\) to \((1,1,1)\)
Problem 18
What is meant by flat shading?
Problem 21
Explain the terms hidden-surface removal, back face elimination, and z-buffer in brief.
Problem 22
What is meant by aliasing? Suggest one of the possible ways to overcome the problem of aliasing.
Problem 23
Suppose the surface of the planar patch with vertices \((0,0,0),(0,2,0),(2,2,0)\), and \((2,0,0)\) is smooth and shiny. If a light ray originates at the point \((0,0,1)\) and strikes the surface at \((1,1,0)\), through which of the following points will the reflected ray pass? a. \((0,0,1)\) b. \((1,1,1)\) c. \((2,2,1)\) d. \((3,3,1)\)
Problem 24
Suppose a buoy supports a light ten feet above the surface of still water. At what point on the water's surface will an observer see the reflection of the light if the observer is fifteen feet from the buoy and five feet above the water's surface?
