Autumn TCSS458A 2008
Computer Graphics
First Name:____________
Last Name:____________________________ID: Midterm
Part I (20%, each question is worth 1 points) Check the letter of the choice that best completes the statement or answers the question.
1. Color is created by our visual systems in reaction to electromagnetic waves. Which color is
produced by the longest wavelengths we can see (check only one): a. green. b. blue. c. red. d. black. Answer: c. 2. Luminance of an image means (check only one): a. color. b. perceived brightness. c. heat. d. shade. Answer: b. 3. Additive color refers to (check only one): a. forming a color by filtering light with cyan, magenta, and yellow. b. color processing used in negative films. c. forming color by adding amounts of three primary colors red, white, and blue. d. forming color by adding amounts of three primary colors red, green, and blue. Answer: d. 4. The synthetic camera model is based on (check only one): a. Separating and modeling objects, viewers, and cameras. b. Separating and modeling light sources, viewers, and cameras. c. Separating and modeling objects, light sources, and viewers. d. Separating and modeling objects, light sources, and cameras. Answer: c. 5. OpenGL is an API with the following characteristics(check only one): a. it is dependent on the window system. b. it is dependent on the operating system. c. it implements algorithms closely to the hardware. d. it implements algorithms independently from the hardware. Answer: c. 6. Cathode Ray Tubes (CRT) have the following characteristics (check only one): a. they were invented in 1990. b. they do not need electricity to work. c. their tube is filled with vacuum. d. they were invented by Edison. Answer: c.
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TCSS458A Autumn 2008
Computer Graphics
7. In CRT's, phosphor emits photons of light characterized by (check only one): a. the light emitted has varied persistences that require varied refresh rates. b. the light emitted has long persistence that does not require to be refreshed. c. the light emitted is always of the same color. d. the light emitted has short persistence that requires very fast refresh rates.
Answer: a. 8. A raster is (check only one): a. a matrix of pixels covering the screen area. b. composed of raster columns. c. rarely used in CRT monitors. d. used in random-scan displays. Answer: a. 9. A color CRT monitor produces color by (check only one): a. using the same kind of phosphor but with different intensity. b. always using beam penetration. c. using different phosphors, each producing a specific color red, green, or blue. d. always using a shadow mask with three electron guns. Answer: c. 10. Important types of displays are all of the following, except one (check only one): a. flat panel displays b. CRT displays c. 3D viewing devices d. virtual motion capture gloves
Answer: d. 11. Input devices examples are all of the following except one (check only one):
a. joysticks b. printers c. light pens d. touch panels Answer: b.
12. Coordinate representation systems include all of the following, except one (check only
one): a. cartesian coordinates. b. world coordinates. c. camera coordinates. d. viewing coordinates. Answer: c.
13. OpenGL geometric primitives include all of the following, except (check only one):
a. circle b. triangle c. rectangle d. line Answer: a.
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TCSS458A Autumn 2008
Computer Graphics
14. What is the frame buffer size, in bytes, of a raster system with resolution 1280 by 1024 storing 12 bits per pixel (check only one):
a. 1000 KB b. 19 KB c. 1900 KB d. 100 KB Answer: c.
15. How many distinct color choices are available in a full-color system using 24 bits per pixel (check only one): a. about 16 million. b. 512. c. about 1 million. d. About 10,000.
Answer: a.
16. An affine transformation has for main property that (check only one): a. it transforms a line into a line. b. it transforms a line into a point. c. it transforms a point into a point. d. none of the above.
Answer: a.
17. A translation glTranslate in OpenGL is a function that takes as arguments 3 scalars representing (check only one): a. a point coordinate. b. the translation vector coordinates. c. the x-axis, y-axis, and z-axis translation values. d. the object coordinates.
Answer: c.
18. The OpenGL rotation function glRotate takes in 3D (check only one): a. 2 parameters. b. 3 parameters. c. 4 parameters. d. no parameter.
Answer: c.
19. To enable polygon filling with a pattern, all the following steps need to be performed, except one (check only one): a. define a fill pattern. b. invoke the polygon-fill routine with glPolygonStipple. c. activate the polygon-fill feature with glEnable (GL_POLYGON_STIPPLE). d. load an image from a file to use as a pattern.
Answer: d.
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TCSS458A Autumn 2008
Computer Graphics
20. Which of these OpenGL output primitive functions does not fill the shape it draws
(check only one):
a. GL_LINE_LOOP. b. GL_POLYGON. c. GL_TRIANGLES.
d. GL_QUADS. Answer: a.
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TCSS458A Autumn 2008
Computer Graphics
Part II (80%, each question is worth 20 points)
1.
Explain the main principles of the Bresenham's line drawing algorithm. State the hypotheses you make when applying this algorithm to the following problem. Trace the different steps run by the Bresenham's line drawing algorithm with their corresponding pk, xk, and yk values: line with endpoints (0, 15) and (10, 20).
Answer The Bresenham's line drawing algorithm proposes an efficient algorithm using only integers to incrementally calculate the closest pixel positions to the line.
Bresenham's line drawing algorithm (positive slope less than 1
1. 2. 3. 4. Input the two line endpoints and store the left endpoint in (x0, y0). Set the color for the frame-buffer position (x0, y0) i.e. plot the first point. Calculate the constant 2y x, and set the starting value for the decision parameter as p0 = 2y x. At each xk along the line, from k=0, perform the following test:
if next pk<0, point to plot is (xk + 1, yk) and pk+1 = pk + 2y otherwise, next point to plot is (xk + 1, yk + 1 ) and pk+1 = pk + 2y- 2x Repeat step 4 x - 1 times.
5.
The hypothesis is that the slope is positive and less than 1: m = y / x = . x = 10, y = 5, p0 = 2y x = 2 * 5 10 = 0 (x0 , y0 ) = (0, 15) k 0 1 2 3 4 5 6 7 8 9 pk 0 -10 0 -10 0 -10 0 -10 0 -10 (xk+1, yk+1) ( 1, 16) (2, 16) (3, 17) (4, 17 ) ( 5, 18 ) (6, 18) (7, 19) (8, 19) (9, 20) (10, 20)
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TCSS458A Autumn 2008 2.
Computer Graphics
Explain the main principles of the marching squares drawing algorithm. Providing the detail of your calculations, apply it to drawing the curve of level 1 passing through the following square:
-1 -2
2
-2
Answer The marching squares algorithm divides the space in which to draw a curve in squares and approximates the curve by a line inside each square. In general, each square will have same width and height. The line approximating a curve inside each square is calculated by interpolation between the values of the function at each corner of a square. Here: a = 2, b = -2, c = 1, d = -1 Because the function has a positive value in a, and negative values at each other corner of the square, the function passes through this square. x = 0 + (a-c) * delta(x) / (a-b) = (2-1) / 2+2) = 1/4 y = 0 + (a-c) * delta(y) / (a-d) = (2-1) / (2+1) = 1/3
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TCSS458A Autumn 2008 1.
Computer Graphics
Using exclusively the OpenGL primitives, write the OpenGL code to display the following shape:
Answer gl.glClear(GL.GL_COLOR_BUFFER_BIT ); // clear color buffer gl.glColor3f(0.0f, 0.0f, 1.0f); // set color to blue parallelepepides (130, 100, 100, 100, 50, 60); gl.glFlush(); void parallelepepides (int xOrigin, int yOrigin, int w, int h, int d, int angle) { double x, y; double a; gl.glBegin (GL.GL_LINE_LOOP); gl.glVertex2i (xOrigin, yOrigin); gl.glVertex2i (xOrigin + w, yOrigin); gl.glVertex2i (xOrigin + w, yOrigin + h); gl.glVertex2i (xOrigin, yOrigin + h); gl.glEnd ( ); a = angle * Math.PI * 2 / 360; x = d * Math.cos(a); y = d * Math.sin(a); gl.glBegin (GL.GL_LINE_STRIP); gl.glVertex2i (xOrigin + w, yOrigin); // display cube
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TCSS458A Autumn 2008
Computer Graphics
gl.glVertex2d (xOrigin + w + x, yOrigin + y); gl.glVertex2d (xOrigin + w + x, yOrigin + h + y); gl.glVertex2d (xOrigin + w, yOrigin + h); gl.glEnd ( ); gl.glBegin (GL.GL_LINE_STRIP); gl.glVertex2i (xOrigin + w, yOrigin + h); gl.glVertex2d (xOrigin + w + x, yOrigin + h + y); gl.glVertex2d (xOrigin + x, yOrigin + h + y); gl.glVertex2d (xOrigin, yOrigin + h); gl.glEnd ( ); }
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TCSS458A Autumn 2008
Computer Graphics
2.
Using exclusively the OpenGL primitives, and suppose that you have available a filledCircle function, write the OpenGL code to display the following scene with color filled primitives. The display is 400 x 300 pixels. Colors used are provided: Pink (1.0f, 193 / 255, 1.0f) Yellow (1.0f, 1.0f, 193 / 255) Green (0.5f, 1.0f, 0.5f) Blue (254 / 255, 1.0f, 1.0f, 0.0f)
Answer gl.glClearColor(254 / 255, 1.0f, 1.0f, 0.0f); // set display window color to blue gl.glClear(GL.GL_COLOR_BUFFER_BIT ); gl.glColor3f(0.5f, 1.0f, 0.5f); filledCircle(20, 20, 10); gl.glColor3f(1.0f, 193 / 255, 1.0f); filledCircle(60, 140, 10); gl.glColor3f(1.0f, 1.0f, 193 / 255); filledCircle(20, 250, 10); gl.glColor3f(1.0f, 193 / 255, 1.0f); filledCircle(180, 20, 10); gl.glColor3f(1.0f, 1.0f, 193 / 255); filledCircle(350, 20, 10); gl.glColor3f(1.0f, 193 / 255, 1.0f); filledCircle(310, 140, 10); gl.glColor3f(0.5f, 1.0f, 0.5f); // display green dot // display pink dot // display yellow dot // display pink dot // display yellow dot // display pink dot
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TCSS458A Autumn 2008
Computer Graphics
filledCircle(350, 250, 10);
// display green dot
parallelepepides (130, 100, 100, 100, 50, 60, 1.0f, 254/255, 1.0f); // display cube text(); gl.glFlush(); // process all OpenGL routines as quickly as possible
void parallelepepides (int xOrigin, int yOrigin, int w, int h, int d, int angle, float r, float g, float b) { double x, y; double a; gl.glColor3f(r, g, b); gl.glBegin (GL.GL_POLYGON); gl.glVertex2i (xOrigin, yOrigin); gl.glVertex2i (xOrigin + w, yOrigin); gl.glVertex2i (xOrigin + w, yOrigin + h); gl.glVertex2i (xOrigin, yOrigin + h); gl.glEnd ( ); a = angle * Math.PI * 2 / 360; x = d * Math.cos(a); y = d * Math.sin(a); gl.glBegin (GL.GL_POLYGON); gl.glVertex2i (xOrigin + w, yOrigin); gl.glVertex2d (xOrigin + w + x, yOrigin + y); gl.glVertex2d (xOrigin + w + x, yOrigin + h + y); gl.glVertex2d (xOrigin + w, yOrigin + h); gl.glEnd ( ); gl.glBegin (GL.GL_POLYGON); gl.glVertex2i (xOrigin + w, yOrigin + h); gl.glVertex2d (xOrigin + w + x, yOrigin + h + y); gl.glVertex2d (xOrigin + x, yOrigin + h + y); gl.glVertex2d (xOrigin, yOrigin + h); gl.glEnd ( ); gl.glColor3f(0.0f, 0.0f, 0.0f); gl.glBegin (GL.GL_LINE_LOOP); gl.glVertex2i (xOrigin, yOrigin); gl.glVertex2i (xOrigin + w, yOrigin); gl.glVertex2i (xOrigin + w, yOrigin + h); gl.glVertex2i (xOrigin, yOrigin + h); gl.glEnd ( );
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TCSS458A Autumn 2008
Computer Graphics
a = angle * Math.PI * 2 / 360; x = d * Math.cos(a); y = d * Math.sin(a); gl.glBegin (GL.GL_LINE_LOOP); gl.glVertex2i (xOrigin + w, yOrigin); gl.glVertex2d (xOrigin + w + x, yOrigin + y); gl.glVertex2d (xOrigin + w + x, yOrigin + h + y); gl.glVertex2d (xOrigin + w, yOrigin + h); gl.glEnd ( ); gl.glBegin (GL.GL_LINE_LOOP); gl.glVertex2i (xOrigin + w, yOrigin + h); gl.glVertex2d (xOrigin + w + x, yOrigin + h + y); gl.glVertex2d (xOrigin + x, yOrigin + h + y); gl.glVertex2d (xOrigin, yOrigin + h); gl.glEnd ( ); } private void text() { glut = new GLUT(); int font = GLUT.BITMAP_HELVETICA_12; //Set font color gl.glColor3f (1.0f, 1.0f, 193 / 255); //Go to the bottom left position of the text gl.glRasterPos2i(160, 160); //Draw the text glut.glutBitmapString(gl, font, "HAPPY"); //Go to the bottom left position of the text gl.glRasterPos2i(150, 140); //Draw the text glut.glutBitmapString(gl, font, "BIRTHDAY"); }
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