CPSC 314, Midterm Exam 1. 9 Feb 2007

Transcription

1 CPSC, Midterm Eam 9 Feb 007 Closed book, no calculators or other electronic devices. Cell phones must be turned off. Place our photo ID face up on our desk. One single-sided sheet of handwritten notes is allowed. At the end of the eam, turn in the note sheet with the eam. Do not open the eam until told to do so. Answer the questions in the space provided. If ou run out of room for an answer, continue on the back. There are 00 points, ou have 0 minutes. Good luck! Name: Student Number: Question Points Earned Points Possible Total 00

2 . ( pts) For each equation below, sketch the new location L of the L shape on the grid and provide the OpenGL sequence needed to carr out those operations. Use the function drawl(), which draws an L shape with the lower left corner at the current origin as shown below. You ma assume the matri mode is GL MODELVIEW and that the stack has been initialized with glloadidentit(). For reference, the OpenGL command snta is glrotatef(angle,,,z), gltranslatef(,,z), glscalef(,,z). 0 drawl(); A = , B = , C = , D = a) L = ABC L b) L = CAD L 0 0 c) L = CBD L d) L = DCCAD L 0 0

3 . (8 pts) The point p can be specified as p A = (, ) T in the coordinate frame A, with orthonormal basis vectors i and j. Specif the coordinates of point p in frames B and C. Ci p Cj Aj Ai Bi Bj. (0 pts) Find the homogeneous transformation which transforms a point from Frame C into the Frame A coordinate sstem. That is, give M where p A = Mp C. Verif our solution using one of our answers to question.. ( pts) True/false Specifing the ee point, lookat point, and up vector completel determines a projective camera transformation. If a surface is transformed b a rotation, transforming its normal vector b the same rotation will leave it perpendicular to the surface. The homogeneous points (,,,) and (,,0,) map to the same Cartesian point after homogenization. Including an affine transformation in a displa list will cause the object to shear with respect to the image plane. After undergoing an orthographic projection, a unit cube will appear to have either or vanishing points, but cannot have. A nonuniform scaling transformation leaves the w coordinate of a homogeneous point unchanged. Both oblique and orthographic projections have projectors perpendicular to the projection plane. The transformation from an orthographic view volume to the normalized device coordinate sstem depends on the size of the viewport. After transforming from a perspective view volume to the normalized device coordinate sstem, the coordinate of a visible point has a range of. Affine transformations can change the origin of the local coordinate frame. BAp = ABp when A = and B =

4 . (6 pts) Draw shapes,,, and transformed b the appropriate OpenGL commands in the left column below. The drawshape() code is shown in the middle column, and the result of the first call is shown in the right column. glidentit(); drawshape(); // shape gltranslate(,-,0); drawshape(); // shape glrotate(90, 0, 0, ); drawshape(); // shape glpushmatri(); gltranslate(, 0, 0); drawshape(); // shape gltranslate(0,, 0); glscale(,,); glrotate(90, 0, 0, ); gltranslate(-, 0, 0); glpopmatri(); glscale(,., ); gltranslate(0, -, 0); drawshape(); // shape drawshape() { glbegin(gl_polygon); glverte(0,0,0,); glverte(,0,0,); glverte(,,0,); glverte(,,0,); glverte(,,0,); glverte(0,,0,); glend(gl_polygon); } 0 a) shape b) shape 0 0 c) shape d) shape 0 0

5 6. ( pts) A square is drawn in world coordinates, with vertices (,, 0, ) T, (,, 0, ) T, (,, 0, ) T, (,, 0, ) T. (That is, vertices are column vectors.) The camera has an ee point of (6,, 0, ) T, a lookat point of (,, 0, ) T, and an up vector of (0, 0,, ) T. The view frustum has a near plane of and a far plane of 6, with an aspect ratio of : and field of view of 90. a) Provide a new value for the near plane location so that the object is entirel contained within the view frustum and within one unit of the near plane. b) If the ee point is then changed to (0, 0, 0, ), will the entire object be within the view frustum? All other parameters sta the same, including the near clipping plane value ou provided above.

6 7. (6 pts) Construct a matri M = ABC that transforms points from normalized device coordinates (NDCS) to displa coordinates (DCS) given a viewport of width 000 and height 000 with the origin in the upper left. Show our intermediate work. 6

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