CPSC 314, Midterm Exam. 8 March 2010

Transcription

1 CPSC, Midterm Eam 8 March 00 Closed book, no electronic devices besides (simple, nongraphing) calculators. Cell phones must be turned off. Place our photo ID face up on our desk. One single-sided sheet of handwritten notes is allowed, keep it so that ou can reuse it for the final if ou want. 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 . (6 pts) The point p can be specified as p A = (, ) T in the coordinate frame W, with orthonormal basis vectors i and j. Specif the coordinates of point p in frames A and B.. (0 pts) Find the homogeneous transformation which transforms a point from Frame B into the Frame W coordinate sstem. That is, give M where p W = Mp B. Verif our solution using one of our answers to question.. ( pts) True/false The onl wa to specif a viewing transformation is b using ee point, lookat point, and up vector. If a surface is transformed b a nonuniform scale, transforming its normal vector b the same transformation will leave it perpendicular to the surface. The homogeneous points (,,,) and (,,,8) map to the same Cartesian point after homogenization. Using displa lists will affect performance differentl depending on the graphics card in the machines. A rotation transformation leaves the w coordinate of a homogeneous point unchanged. The transformation from an orthographic view volume to the displa coordinate sstem depends on the size of the viewport. An object with normalized devices coordinates (,, ) is visible in the final framebuffer image given a viewport of width 00 and height 00. In OpenGL, vertices are alwas specified in the world coordinate sstem. In OpenGL, light positions can be specified in either the world or the viewing coordinate sstem. The transformation from the RGB to the HSV colorspace can be epressed b a matri. The CIE colorspace incorporates measurements of human perceptual response and encodes all luminance information in one of its three channels. Intensit in the HSI colorspace correctl encodes luminance information taking into account human perceptual response.

3 . (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 glrotate(90, 0, 0, ); gltranslate(, 0, 0); drawshape(); // shape glrotate(-90, 0, 0, ); glpushmatri(); gltranslate(, 0, 0); drawshape(); // shape glscale(,, ); gltranslate(, -, 0); drawshape(); // shape gltranslate(-,, 0); glrotate(90, 0, 0, ); gltranslate(-, -, 0); glscale(,., ); glrotate(90, 0, 0, ); glpopmatri(); gltranslate(-,, 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

4 . (8 pts) Scene Graphs. The transformation matrices in the following scene graph define the relative transformations of each bod part with respect to its parent. foo. ( pts) Your cat wants an earring, because all the other kitties have one. You should draw it as an offset with respect to the coordinate sstem of the ear. Give the epression for the composite transformation that should be in the modelview matri to get from viewing to ear coordinates: that is, the transformation to get from the viewing coordinate sstem to the ear coordinate sstem, or equivalentl the matri that takes a point specified in ear coordinates and transforms it to viewing coordinates. ( pts) You want to add a TailCam, a second camera that lets ou see what things would look like from a point of view of the end of our cat s tail. (You will get dizz when our cat sees a mouse and lashes its tail!) Give the epression for the composite transformation that ou should use for B, the viewing matri for the TailCam. (B is the VW matri from the coordinate frame point of view, and the WV matri from the point/object point of view.) 6. ( pts) A point p is at location (0,0) in DCS (displa coordinates), with a viewport of width 00 and height 00. Give its and location in NDCS (normalized device coordinates).

5 7. (0 pts) Viewing. glmatrimode(gl_perspective); glloadidentit(); glfrustum(-,, -,,, 0); glmatrimode(gl_modelview); glloadidentit(); 6 glulookat(0, 0, 0, 0, 0, 0, 0,, 0); 7 drawiguana(); The drawiguana() function draws an iguana in the current coordinate sstem with etent ranging from - to in, - to in, and 0 to in z. When ou run our program, ou are sad that ou cannot see the iguana. ( pts) Fi this problem so that the iguana is visible and nearl fills the image plane, b changing onl the ee point. State which line ou are changing, and give new parameters for the OpenGL command. ( pts) Fi this problem so that the iguana is visible and nearl fills the image plane, b changing onl the near clipping plane. State which line ou are changing, and give new parameters for the OpenGL command. ( pts) Change the view b rotating the image of the iguana 90 degrees clockwise on the image plane, b changing onl the up vector. State which line ou are changing, and give new parameters for the OpenGL command. ( pts) Give the viewing matri produced b the original code above. That is, the VW matri considered from the coordinate frame point of view, or the WV matri considered from the transforming object point of view. ( pts) Give the perspective matri produced b the original code above. That is, the NV matri considered from the coordinate frame point of view, or the VN matri considered from the transforming object point of view.

6 8. ( 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 = CBD L d) L = ABAB L 0 0 b) L = CABC L e) L = BBBB L 0 0 c) L = BDC L f) L = CCAA L 0 0 6