Duc Nguyen CSE 420 Computer Graphics 10/10/2018 Homework 1

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1 Duc Nguyen CSE 420 Computer Graphics 10/10/2018 Homework 1 1. The endpoints of a given line are (0, 0) and (18, 6). Compute the first 4 values of y manually using Bresenham's Line Algorithm as x steps from 0 to 18 and plot the results. Show your steps. (10 Points) Steps 1. Points (x0, y0) = (0, 0) (x1, y1) = (18, 6) 2. Calculate Deltas dy = y1 - y0 = 6-0 = 6 dx = x1 - x0 = 18-0 = Calculate 2 * Deltas 2dy = 2 * 6 = 12 2dx = 2 * 18 = Deltas give P 0 P 0 = 2dy - dx 5. Use Upper or Lower formula depending if P < 0; P k < 0 (x k + 1, y k ) is next plot point P k + 1 = P k + 2dy P k > 0 (x k + 1, y k + 1) is next plot point P k +1 = P k +2dy - 2dx

2 6. Values x0 x1 dx 2dx y0 y1 dy 2dy Plotting k P Upper or Lower Eq. Plug Numbers P x y 0 P0 P 0 = 2dy - dx P1 P1 = P0 + 2dy P2 P2 = P1 + 2dy - 2dx P3 P3 = P2 + 2dy

3 2. Use OpenGL to draw a dot plot of the function f(x) = e - x sin ( 2πx ), whx ), where it is known that as x varies from x low to x high, f(x) takes on values between from y low to y high. Find the appropriate scaling and translation factors so that the dots will lie properly in a screen window with width W pixels and height H pixels. (10 Points) To see the Graph, I changed the values of gluortho2d(-5, 5, -5, 5);

4 3. Use turtle graphics or/and other means to reproduce any 3 of the following images (10 points).

5

6

7 Problem 2 #include <GL/glut.h> #include <math.h> void init(void) glclearcolor(1, 1, 1, 0); glcolor3f(1.0f, 0.0f, 0.0f); glpointsize(4.0); glmatrixmode(gl_projection); glloadidentity(); gluortho2d(-5, 5, -5, 5); float f(float x) return exp(-fabs(x)) * sin(2 * 3.14*x); void display(void) glclear(gl_color_buffer_bit); glviewport(0, 0, 500, 500); for (float x = -6.28; x <= 6.28; x += 0.1) glvertex2f(x, f(x)); glcolor3f(0.0, 0.0, 0.0); glbegin(gl_lines); glvertex2f(-50, 0); glvertex2f(50, 0); glvertex2f(0, -50); glvertex2f(0, 50); glflush();

8 int main(int argc, char** argv) glutinit(&argc, argv); glutinitwindowsize(500, 500); glutinitwindowposition(100, 150); glutcreatewindow("cse-420: Homework 1, Graph"); init(); glutdisplayfunc(display); glutmainloop(); return 0;

9 Problem 3: Turtle #include <GL/glut.h> #include <math.h> #include <stdio.h> //initialization void init(void) glclearcolor(1, 1, 1, 0); glpointsize(4.0); //a dot is 4x4 glmatrixmode(gl_projection); glloadidentity(); //replace current matrix with identity matrix gluortho2d(0, 800, -100, 700); //gluortho2d(left, RIGHT, BOTTOM, TOP); void display(void) glclear(gl_color_buffer_bit); //clear screen // Shell glcolor3f(0.333, 0.420, 0.184); glvertex2i(80, 250); glvertex2i(100, 230); glvertex2i(160, 195); glvertex2i(205, 170); glvertex2i(270, 160); glvertex2i(510, 160); glvertex2i(590, 205); glvertex2i(590, 295); glvertex2i(570, 315); glvertex2i(540, 360); glvertex2i(450, 415); glvertex2i(400, 430); glvertex2i(325, 430); glvertex2i(235, 410);

10 glvertex2i(180, 355); glvertex2i(155, 320); glvertex2i(125, 300); glvertex2i(80, 250); // BackFoot glcolor3f(0.604, 0.804, 0.196); glvertex2i(205, 170); glvertex2i(220, 130); glvertex2i(280, 135); glvertex2i(270, 160); glvertex2i(205, 170); // BackToe glcolor3f(0.333, 0.420, 0.184); glvertex2i(220, 130); glvertex2i(235, 110); glvertex2i(270, 110); glvertex2i(280, 120); glvertex2i(280, 135); glvertex2i(220, 130); // FrontFoot glcolor3f(0.604, 0.804, 0.196); glvertex2i(590, 205); glvertex2i(510, 160); glvertex2i(500, 150); glvertex2i(530, 110); glvertex2i(610, 160); glvertex2i(610, 180); glvertex2i(590, 205); // FrontToe

11 glcolor3f(0.333, 0.420, 0.184); glvertex2i(500, 150); glvertex2i(465, 100); glvertex2i(515, 100); glvertex2i(530, 110); glvertex2i(500, 150); // Head glcolor3f(0.604, 0.804, 0.196); glvertex2i(590, 205); glvertex2i(680, 250); glvertex2i(705, 220); glvertex2i(705, 230); glvertex2i(680, 280); glvertex2i(590, 295); glvertex2i(590, 205); // Face Triangle glcolor3f(0.333, 0.420, 0.184); glbegin(gl_triangles); glvertex2i(660, 250); glvertex2i(600, 205); glvertex2i(640, 205); glvertex2i(660, 250); // Eye glcolor3f(0.678, 1, 0.184); glvertex2i(680, 250); glvertex2i(660, 250); glvertex2i(650, 270); glvertex2i(680, 270); glvertex2i(680, 250);

12 // Pupil glcolor3f(0.333, 0.420, 0.184); glvertex2i(665, 260); glvertex2i(670, 260); glvertex2i(670, 265); glvertex2i(665, 265); glvertex2i(665, 260); glpointsize(16.0); glcolor3f(0.678, 1, 0.184); glvertex2i(125, 300); glvertex2i(140, 270); glvertex2i(185, 245); glvertex2i(220, 240); glvertex2i(230, 230); glvertex2i(255, 220); glvertex2i(280, 240); glvertex2i(310, 215); glvertex2i(345, 235); glvertex2i(380, 220); glvertex2i(440, 235); glvertex2i(460, 220); glvertex2i(505, 215); glvertex2i(530, 230); glvertex2i(590, 205); glpointsize(32.0); glcolor3f(0.678, 1, 0.184); glvertex2i(180, 355); glvertex2i(240, 340); glvertex2i(290, 350); glvertex2i(350, 345); glvertex2i(435, 345);

13 glvertex2i(490, 345); glvertex2i(550, 260); glvertex2i(590, 240); glvertex2i(180, 355); glvertex2i(140, 270); glvertex2i(100, 230); glvertex2i(325, 430); glvertex2i(300, 400); glvertex2i(290, 350); glvertex2i(235, 410); glvertex2i(300, 400); glvertex2i(400, 430); glvertex2i(435, 345); glvertex2i(440, 235); glvertex2i(540, 360); glvertex2i(490, 345);

14 glvertex2i(570, 315); glvertex2i(550, 260); glvertex2i(530, 230); glvertex2i(590, 205); glvertex2i(350, 345); glvertex2i(345, 235); glvertex2i(240, 340); glvertex2i(220, 240); glvertex2i(160, 195); glvertex2i(180, 245); glvertex2i(230, 230); glvertex2i(205, 170); glvertex2i(255, 220); glvertex2i(270, 160); glvertex2i(310, 215); glvertex2i(325, 160);

15 glvertex2i(380, 220); glvertex2i(380, 160); glvertex2i(460, 220); glvertex2i(440, 160); glvertex2i(505, 215); glvertex2i(510, 155); glflush(); //send all output to screen //initialization void init(void); //does the drawing void display(void); /* Main Loop * Open window with initial window size, title bar, * RGB display mode, depth buffer. */ int main(int argc, char** argv) glutinit(&argc, argv); //initialize toolkit glutinitdisplaymode(glut_single GLUT_RGB); //set display mode: single bufferring, RGBA model glutinitwindowsize(500, 500); //set window size on screen glutinitwindowposition(300, 100); //set window position on screen glutcreatewindow("cse-420: Homework 1, Turtle");

16 //open screen window init(); glutdisplayfunc(display); function glutmainloop(); return 0; //points to display //go into perpetual loop

17 Problem 4: Geometric Cubes #include <GL/glut.h> #include <math.h> #include <stdio.h> //initialization void init(void) glclearcolor(1, 1, 1, 0); glcolor3f(0.0f, 0.0f, 0.0f); //set drawing color glpointsize(4.0); //a dot is 4x4 glmatrixmode(gl_projection); glloadidentity(); //replace current matrix with identity matrix gluortho2d(-100, , 0, ); void display(void) glclear(gl_color_buffer_bit); //clear screen glcolor3f(0.0, 0.0, 1.0); // Points glvertex2i(20, 860); // 1 glvertex2i(20, 500); // 2 glvertex2i(280, 360); // 3 glvertex2i(490, 490); // 4 glvertex2i(490, 690); // 5 glvertex2i(360, 760); // 6 glvertex2i(270, 710); // 7 glvertex2i(270, 650); // 8 glvertex2i(700, 410); // 9 glvertex2i(1090, 630); // 10 glvertex2i(1090, 1030); // 11 glvertex2i(780, 1200); // 12 glvertex2i(530, 1060); // 13 glvertex2i(530, 800); // 14 glvertex2i(700, 710); // 15

18 glvertex2i(830, 780); // 16 glvertex2i(830, 880); // 17 glvertex2i(790, 910); // 18 glvertex2i(360, 670); // 19 glvertex2i(360, 200); // 20 glvertex2i(700, 20); // 21 glvertex2i(1000, 190); // 22 glvertex2i(1000, 490); // 23 glvertex2i(790, 610); // 24 glvertex2i(620, 520); // 25 glvertex2i(620, 350); // 26 glvertex2i(700, 310); // 27 glvertex2i(740, 340); // 28 glvertex2i(740, 840); // 29 glvertex2i(360, 1060); // 30 glvertex2i(20, 860); glflush(); //send all output to screen //initialization void init(void); //does the drawing void display(void); /* Main Loop * Open window with initial window size, title bar, * RGB display mode, depth buffer. */ int main(int argc, char** argv) glutinit(&argc, argv); //initialize toolkit glutinitdisplaymode(glut_single GLUT_RGB); //set display mode: single bufferring, RGBA model glutinitwindowsize(500, 500); //set window size on screen glutinitwindowposition(300, 100); //set window position on screen glutcreatewindow("cse-420: Homework 1, Geometric Cubes");

19 //open screen window init(); glutdisplayfunc(display); function glutmainloop(); return 0; //points to display //go into perpetual loop

20 Problem 3: Hexagons #include <GL/glut.h> #include <math.h> #include <stdio.h> //initialization void init(void) glclearcolor(1, 1, 1, 0); glcolor3f(0.0f, 0.0f, 0.0f); //set drawing color glpointsize(4.0); //a dot is 4x4 glmatrixmode(gl_projection); glloadidentity(); //replace current matrix with identity matrix gluortho2d(-500, 500.0, -500, 500.0); void display(void) glclear(gl_color_buffer_bit); //clear screen float pos[] = -1.0, 1.0, -2.0, 1.0 ; gllightfv(gl_light0, GL_POSITION, pos); gldisable(gl_lighting); //Top Hexagon: Yellow //draw points glcolor3f(1.0, 1.0, 0.0); glvertex2i(0, 450); // Vert 1: Top Vert glvertex2i(100, 400); // Vert 2: x + 100, y - 50 glvertex2i(100, 300); // Vert 3: x, y - 100; glvertex2i(0, 250); // Vert 4: x - 100, y - 50 glvertex2i(-100, 300); // Vert 5: x - 100, y + 50 glvertex2i(-100, 400); // Vert 6: x, y glvertex2i(0, 450); // Vert 7: Back to First Vert //Right-Top Hexagon: Red glcolor3f(1.0, 0.0, 0.0); //draw points

21 glvertex2i(200, 150); glvertex2i(100, 100); glvertex2i(100, 300); glvertex2i(200, 350); glvertex2i(300, 300); glvertex2i(300, 200); glvertex2i(200, 150); // Vert 1: Bottom Vert // Vert 2: Botton Left // Vert 3: Top Left // Vert 4: Top // Vert 5: Top Right // Vert 6: Bottom Right // Vert 7: Bottom Vert //Right-top Hexagon: Red //draw points glcolor3f(1.0, 0.0, 0.0); glvertex2i(-200, 150); // Vert 1: Bottom Vert glvertex2i(-100, 100); // Vert 2: Botton Left glvertex2i(-100, 300); // Vert 3: Top Left glvertex2i(-200, 350); // Vert 4: Top glvertex2i(-300, 300); // Vert 5: Top Right glvertex2i(-300, 200); // Vert 6: Bottom Right glvertex2i(-200, 150); // Vert 7: Bottom Vert //Right-Bottom Hexagon: Yellow //draw points glcolor3f(1.0, 1.0, 0.0); glvertex2i(200, -50); // Vert 1: Bottom Vert glvertex2i(100, 0); // Vert 2: Botton Left glvertex2i(100, 200); // Vert 3: Top Left glvertex2i(200, 150); // Vert 4: Top glvertex2i(300, 100); // Vert 5: Top Right glvertex2i(300, 0); // Vert 6: Bottom Right glvertex2i(200, -50); // Vert 7: Bottom Vert //Left-Bottom Hexagon: Yellow //draw points glcolor3f(1.0, 1.0, 0.0); glvertex2i(-200, -50); // Vert 1: Bottom Vert glvertex2i(-100, 0); // Vert 2: Botton Left glvertex2i(-100, 200); // Vert 3: Top Left glvertex2i(-200, 150); // Vert 4: Top

22 glvertex2i(-300, 100); glvertex2i(-300, 0); glvertex2i(-200, -50); // Vert 5: Top Right // Vert 6: Bottom Right // Vert 7: Bottom Vert //Middle Hexagon: Blue //draw points glcolor3f(0.0, 0.0, 1.0); glvertex2i(0, 250); // Vert 1: Top Vert glvertex2i(100, 200); // Vert 2: x + 100, y - 50 glvertex2i(100, 100); // Vert 3: x, y - 100; glvertex2i(0, 50); // Vert 4: x - 100, y - 50 glvertex2i(-100, 100); // Vert 5: x - 100, y + 50 glvertex2i(-100, 200); // Vert 6: x, y glvertex2i(0, 250); // Vert 7: Back to First Vert //Bottom Hexagon: Red //draw points glcolor3f(1.0, 0.0, 0.0); glvertex2i(0, 50); // Vert 1: Top Vert glvertex2i(100, 0); // Vert 2: x + 100, y - 50 glvertex2i(100, -100); // Vert 3: x, y - 100; glvertex2i(0, -150); // Vert 4: x - 100, y - 50 glvertex2i(-100, -100); // Vert 5: x - 100, y + 50 glvertex2i(-100, 0); // Vert 6: x, y glvertex2i(0, 50); // Vert 7: Back to First Vert // TRIANGLES///////////////////////////// // Top-right Triangle: Green glbegin(gl_triangles); //draw points glcolor3f(0.0, 1.0, 0.0); glvertex2i(100, 300); glvertex2i(100, 200); glvertex2i(0, 250); glvertex2i(100, 300);

23 // Top-left Triangle: Green glbegin(gl_triangles); glcolor3f(0.0, 1.0, 0.0); glvertex2i(100, 300); glvertex2i(100, 200); glvertex2i(0, 250); glvertex2i(100, 300); // Top-left Triangle: Green glbegin(gl_triangles); glcolor3f(0.0, 1.0, 0.0); glvertex2i(-100, 300); glvertex2i(-100, 200); glvertex2i(0, 250); glvertex2i(-100, 300); //draw points //draw points // Botton-right Triangle: Green glbegin(gl_triangles); //draw points glcolor3f(0.0, 1.0, 0.0); glvertex2i(100, 100); glvertex2i(100, 0); glvertex2i(0, 50); glvertex2i(100, 100); // Botton-left Triangle: Green glbegin(gl_triangles); //draw points glcolor3f(0.0, 1.0, 0.0); glvertex2i(-100, 100); glvertex2i(-100, 0); glvertex2i(0, 50); glvertex2i(-100, 100); // Triangle Right glbegin(gl_triangles); glcolor3f(0.0, 1.0, 0.0); glvertex2i(100, 200); //draw points

24 glvertex2i(100, 100); glvertex2i(200, 150); glvertex2i(100, 200); // Triangle Left glbegin(gl_triangles); glcolor3f(0.0, 1.0, 0.0); glvertex2i(-100, 100); glvertex2i(-100, 200); glvertex2i(-200, 150); glvertex2i(-100, 200); glflush(); //send all output to screen //initialization void init(void); //does the drawing void display(void); /* Main Loop * Open window with initial window size, title bar, * RGB display mode, depth buffer. */ int main(int argc, char** argv) glutinit(&argc, argv); //initialize toolkit glutinitdisplaymode(glut_single GLUT_RGB); //set display mode: single bufferring, RGBA model glutinitwindowsize(500, 500); //set window size on screen glutinitwindowposition(300, 100); //set window position on screen glutcreatewindow("cse-420: Homework 1, Hexagons"); //open screen window init(); glutdisplayfunc(display); //points to display function

25 glutmainloop(); return 0; //go into perpetual loop

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