Computer Science 455 Instructor: R. P. Burton Fourth Quiz November 4-5, 2002 Name _________________________________________ Score ____________/27 1.A Bezier curve is contained within a polygon (known as a convex hull) whose vertices are a.all the control points, taken in order b.at least some (and sometimes all) of the control points, taken in order c.all the control points, but not necessarily in order d.at least some (and sometimes all) of the control points, but not necessarily in order (d) 2.Given the Bezier blending functions associated with five control points, how many of them have nonzero value at u = 1? a.one b.two c.three d.four e.all five (a) 3.Suppose the first and last control points for a Bezier curve are coincident, but the second and second-to-last control points are not colinear. What can you say about continuity at the first/last control point? a.The curve does not pass through these points. b.The curve passes through these points with zero order continuity c.The curve passes through these points with first order continuity d.The curve passes through these points with continuity dictated by the number of control points. (b) 4.What is the maximum degree of a Bezier curve polynomial determined by 7 control points? a.more than 7 b.exactly 7 c.less than 7 (c) 5.It is possible to piece Bezier curves together, but it is not possible to control continuity at the joint. a.true b.false (b) 6.The degree of a B-spline polynomial typically is ______ the degree of the Bezier curve polynomial determined for the same 10 control points. a.greater than b.the same as c.less than (c) 7.Bezier curves exhibit _____ control and B-spline curves typically exhibit _____ control. a.local, local b.local, global c.global, local d.global, global (c) 8.A Bezier surface is determined by 5 control points in one direction, and 8 control points in the other direction. How many polygonal patches ultimately represent the curve? (Be careful) a.5 x 5 = 25 b.5 x 8 = 40 c.8 x 8 = 64 d.whatever you choose (d) 9.The convex hull property typically accompanies curve forms which _______ the control points. a.interpolate b.approximate (b) 10.A shape generated by a Bezier curve can be swept along a path described by a B-spline curve while undergoing scaling determined by a Gaussian curve. a.true b.nonsense; sweeps always occur translationally or rotationally about the origin with fixed generators. (a) 11.Which of the following “shop” activities is closest to differencing? a.gluing two blocks of wood together b.drilling a hole in a block of wood c.surrounding a wax model with plaster, melting and removing the wax, and pouring molten bronze into the plaster d.taking a break (b) 12.Quadtrees and octrees are used to a.represent graphical objects b.scan-convert graphical objects c.store the contents of the frame buffer more efficiently d.perform hidden-element elimination (a) 13.A matrix for translating points in 7-dimensional homogeneous space (i.e. 6 coordinates plus a homogeneous coordinate) likely has ____ nonzero elements. (be careful) a.0-5 b.6-10 c.11-15 d.16-20 e.more than 20 (c – 13, namely 7 along the diagonal, an additional 6 in column 7) 14.Suppose you have a coordinate system with x pointing up, y pointing out, and z pointing right. You wish to look down the z axis and rotate clockwise. Where (in the array) does the minus sign on the sine go? a.(1,2) b.(1,3) c.(2,1) d.(2,3) e.(3,1) f.(3,2) (a) 15.Rotation (represented by a 4 x 4 matrix) can occur about all of the following EXCEPT a.a principal axis b.an axis parallel to a principal axis c.an axis parallel to a principal plane d.an axis not parallel to a principal axis or a principal plane, but passing through the origin e.an axis not parallel to a principal axis or a principal plane, and not passing through the origin f.(no exceptions here) (f) 16.The seven matrices which are concatenated to achieve rotation about an arbitrary axis could be determined in parallel, since none is dependent on any other. a.true b.false (a) 17.Suppose objects are defined relative to coordinate system A, but must be transformed relative to coordinate system B. How is this achieved? a.simply transform as if the objects are defined relative to coordinate system B b.find a transformation which superimposes coordinate system A onto coordinate system B, use it before doing the transformation, and reverse it after doing the transformation c.find a transformation which superimposes coordinate system B onto coordinate system A, use it before doing the transformation, and reverse it after doing the transformation d.It can’t be done. (b) 18.The viewing position relative to the object can impact the size/dimensions of the projected elements for a.parallel projections only b.perspective projections only c.both parallel and perspective projections d.neither parallel nor perspective projections (c) 19.Which is the following is a synonym for “parallel” projection? a.perspective projection b.orthographic projection c.oblique projection d.(none are synonyms) (d) 20.There can be ____ orthographic projection(s) of a single object. a.only one b.not more than three c.not more than six d.an unlimited number of (d) 21.It is impossible for an oblique projection to preserve lengths. a.true b.false (b – cavalier projections preserve length) 22.The perspective projection is simply a division by depth. a.true b.false (a) 23.The point from which the viewer is looking (the “look from” point) and a point along his viewing axis (a “look at” point) are sufficient to determine a unique viewing transformation. a.true b.false (b – the viewer’s eye can be rotated about his viewing axis) 24.The viewing transformation is nothing more than the imposition of one coordinate frame onto another coordinate frame. a.true b.false (a) 25.“Telephoto” and “wide angle” effects (without distortion) can be achieved, for perspective projection, by leaving the window fixed in position while moving the viewpoint further from or closer to the window along a axis which passes through the center of the window and is perpendicular to the window. a.true b.false (a) 26.Which of the following most simplifies clipping, and probably hidden surface removal? a.parallel orthographic projection b.parallel oblique projection c.perspective orthographic projection d.perspective oblique projection e.(there is no significant difference; clipping and probably hidden surface removal can be done immediately following any of these projections with roughly equivalent efficiency) (a) 27.Where does the “near” plane sit relative to the window? a.closer to the viewer b.it is coincident with the window c.farther from the viewer d.(any of the above) (d)