6. Make use of glviewport() to display two sine curves on the same screen, one on the

Size: px

Start display at page:

Download "6. Make use of glviewport() to display two sine curves on the same screen, one on the"

Vivien Walters
5 years ago
Views:

1 Duc Nguyen CSE-420: Computer Graphics 10/17/18 1. Modify lines.cpp to display lines in the following patterns: a. a long dash and a dot, (.. ) b. two close dots followed by a distant dot ( ) 2. Modify the program by adding a filled green polygon with 6 sides and a filled yellow polygon with 9 sides. 3. Repeat the above step with two different polygon modes. 4. Draw one polygon with vertices ordered in anti-clockwise direction and another in clockwise direction. Enable culling to see its effects. 5. Suppose you use the Bresenham line algorithm to draw a line from (20, 30) to (250, 100). If the current point drawn is (33, 34), what will be the next two points drawn? Show your steps. 6. Make use of glviewport() to display two sine curves on the same screen, one on the

2 upper left region of the screen and one on the lower right. Report: Drawing objects in 3D space requires a lot of mathematical skills and interaction in order to render a simple image on a computer screen. Tools like OpenGL were not made to solve these problems with brute force, but rather were highly optimized and tweaked superfluously in order to efficiently render pixels in milliseconds. These involve simple lines, stippled lines, polygons, and even 3D polygons that contain a front and back face that can be flipped clockwise or counter-clockwise. The methods that were developed to make them required little processing power and memory, but also had to use a lot of thought to solve line by line. By finishing and completing this lab, I believe I have earned full credit, including an extra twenty points for completing problems 5 and 6. Mastering these concepts were not an easy endeavor

3 Problems 1-4 #include <GL/glut.h> #include <math.h> #define drawoneline(x1,y1,x2,y2) glbegin(gl_lines); glvertex2f ((x1),(y1)); glvertex2f ((x2),(y2)); // prototype function void draw_poly(int Starting x, int Starting Y, int sides, int radius, float rotationangle) void draw_poly(int, int, int, int, float); void draw_poly(int x0, int y0, int n, int radius, float rotangle) glbegin(gl_polygon); double angle = rotangle * / 180; //initial angle double angleinc = 2 * / n; // angle increment for (int k = 0; k < n; k++) //repeat n times angle += angleinc; glvertex2i((int)(radius * cos(angle) + x0), (int) (radius * sin(angle) + y0)); // Text Function void text(char* string) char* p; for (p = string; *p; p++) glutbitmapcharacter(glut_bitmap_helvetica_10, *p); void init(void) glclearcolor(1.0, 1.0, 1.0, 1.0); glshademodel(gl_flat);

4 void display(void) // Starting (x,y) points for shapes int x0, y0; // XY Axis and formatting lines glclear(gl_color_buffer_bit); glrasterpos2i(-490, -480); //text("(-500, -500)"); glrasterpos2i(390, 470); //text("(500, 500)"); glrasterpos2i(0, 5); //text("(0, 0)"); glbegin(gl_lines); // x axis glvertex2f(-500, 0); glvertex2f(500, 0); // y axis glvertex2f(0, -500); glvertex2f(0, 500); glvertex2f(-500, 450); glvertex2f(500, 450); glvertex2f(-500, -50); glvertex2f(500, -50); glvertex2f(0, -250); glvertex2f(500, -250); // Problem 1: glrasterpos2i(-490, 460); //text("1: Stipple Lines"); glenable(gl_line_stipple); // 1st row: a long dash and a dot, (.

5 . ) glcolor3f(1.0, 0.0, 0.0); glrasterpos2i(-490, 350); //text("row1: gllinestipple(1, 0xF99F)"); gllinestipple(1, 0xF99F); drawoneline(-490.0, 300.0, 0.0, 300); // drawoneline(-490.0x, 300.0y is starting point of Stipple line // 0.0x, 300y) is the ending point of Stipple line; // 2nd row: Two close dots followed by a distant dot ( ) glcolor3f(0.0, 0.0, 1.0); glrasterpos2i(-490, 250); //text("row2: Factor 1: gllinestipple(1, 0x252525);"); gllinestipple(1, 0x252525); drawoneline(-490.0, 200.0, 0, 200.0); // 3rd row: Two close dots followed by a distant dot ( ) glcolor3f(0.0, 0.0, 1.0); glrasterpos2i(-490, 150); //text("row3: Factor 5: gllinestipple(5, 0x252525);"); gllinestipple(5, 0x252525); drawoneline(-490.0, 100, 0, 100); gldisable(gl_line_stipple); //Problem 2: glrasterpos2i(10, 460); //text("2: Green Hexagon & Yellow Nonagon"); //Hexagon: Green glfrontface(gl_cw); glpolygonmode(gl_front, GL_FILL); glcolor3f(0.0, 1.0, 0.0); glbegin(gl_polygon); x0 = 250;

6 y0 = 440; glvertex2i(x0, y0); glvertex2i(x , y0-50); glvertex2i(x , y0-150); glvertex2i(x0, y0-200); glvertex2i(x0-100, y0-150); glvertex2i(x0-100, y0-50); // 9 Sided Poly: Yellow. glpolygonmode(gl_front, GL_FILL); glcolor3f(1.0, 1.0, 0.0); draw_poly(250, 120, 9, 110, 40); // Problem 3 glrasterpos2i(-490, -35); //text("3: 3 Different Polygon Modes"); glrasterpos2i(-490, -80); //text("1: glpolygonmode(gl_front, GL_POINT);"); glrasterpos2i(-490, -120); //text("2: glpolygonmode(gl_front, GL_LINE);"); glrasterpos2i(-490, -160); //text("3: glpolygonmode(gl_front, GL_FILL);"); // 8 Points/Vertices of a Polygon glpolygonmode(gl_front, GL_POINT); glpointsize(8); draw_poly(-250, -320, 8, 120, 45); // 8 Sided Poly: No Fill

7 glpolygonmode(gl_front, GL_LINE); glcolor3f(0.0, 1.0, 1.0); draw_poly(-250, -320, 8, 80, 45); // 8 Sided Poly: Fill: Red glpolygonmode(gl_front, GL_FILL); glcolor3f(1.0, 0.0, 0.0); draw_poly(-250, -320, 8, 40, 45); //Problem 4: glrasterpos2i(10, -35); //text("4: Polygons: CCW and CW with culling."); glrasterpos2i(10, -80); //text("red Diamond: glfrontface(gl_ccw)"); glpolygonmode(gl_front, GL_LINE); draw_poly(250, -175, 8, 50, 45); // Counter-Clockwise glpolygonmode(gl_front, GL_FILL); glcolor3f(1.0, 0.0, 0.0); draw_poly(250, -175, 4, 50, 90); glrasterpos2i(10, -280); //text("red Diamond: glfrontface(gl_cw)");

8 glpolygonmode(gl_front, GL_LINE); draw_poly(250, -375, 8, 50, 45); // Clockwise glfrontface(gl_cw); glpolygonmode(gl_front, GL_FILL); glcolor3f(1.0, 0.0, 0.0); draw_poly(250, -375, 4, 50, 90); glflush(); void reshape(int w, int h) glviewport(0, 0, (GLsizei)w, (GLsizei)h); glmatrixmode(gl_projection); glloadidentity(); // gluortho2d(-500, (GLdouble)w, 500, (GLdouble)h); // Doesn't work with this. gluortho2d(-500, 500, -500, 500); // gluortho2d(left, RIGHT, BOTTOM, TOP); // gluortho2d(-500x to 500x, -500y to 500y); int main(int argc, char** argv) glutinit(&argc, argv); glutinitdisplaymode(glut_single GLUT_RGB); glutinitwindowsize(500, 500); glutinitwindowposition(50, 50); glutcreatewindow("cse-420: Lab4"); init(); glutdisplayfunc(display); glutreshapefunc(reshape); glutmainloop(); return 0;

9 Problem 5: Bresenham Line 1. Points (x 0, y 0 ) = (20, 30) (x 1, y 1 ) = (250, 100) 2. Calculate Δxx and Δxy Δxx = x 1 - x 0 = = 230 Δxy = y 1 - y 0 = = Calculate 2*Δxx and 2*Δxy. 2Δxx = 2 * 230 = 460 2Δxy = 2 * 70 = Deltas give P 0 P 0 = 2Δxy - Δxx 5. Use upper or lower formula if P < 0; P k < 0 (x k + 1, y k ) is next plot point P k + 1 = P k + 2Δxy P k > 0 (x k + 1, y k + 1) is next plot point P k + 1 = P k +2Δxy - 2Δxx 6. Calculate Slope m. m = Δxy/Δxx = 70/230 = Values m x0 x1 dx 2dx y0 y1 dy 2dy Plotting k P Upper or Lower Eq. Plug Numbers P x y 0 P 0 P 0 = 2dy - dx P 1 P 1 = P 0 + 2dy P 2 P 2 = P 1 + 2dy - 2dx P 3 P 3 = P 2 + 2dy P 4 P 4 = P 3 + 2dy

10 5 P 5 P 5 = P 4 + 2dy P 6 P 6 = P 5 + 2dy -2dx P 7 P 7 = P 6 + 2dy P 8 P 8 = P 7 + 2dy P 9 P 9 = P 8 + 2dy - 2dx P 10 P 10 = P 9 + 2dy P 11 P 11 = P dy P 12 P 12 = P dy P 13 P 13 = P dy P 14 P 14 = P dy - 2dx P 15 P 15 = P dy Result a. Next two points from (33, 34) is i. (34, 34) ii. (35, 34)

11 Problem 6: Viewport #include <GL/glut.h> #include <math.h> void init(void) glclearcolor(1, 1, 1, 0); glmatrixmode(gl_projection); glloadidentity(); // Draw Sine and Negative Sine Function void drawsin(); void drawsin() float x; //First Sine Curve glcolor3f(1.0f, 0.0f, 0.0f); glbegin(gl_line_strip); for (x = -2.0; x <= 2.0; x += 0.01) glvertex2f(x, sin(2 * 3.14*x)); //Second Sine Curve glbegin(gl_line_strip); glcolor3f(0.0f, 1.0f, 0.0f); for (x = -2.0; x <= 2.0; x += 0.01) glvertex2f(x, -sin(2 * 3.14*x)); //XY Axis Lines

12 glbegin(gl_lines); glvertex2f(-2, 0); glvertex2f(2, 0); glvertex2f(0, -2); glvertex2f(0, 2); void display(void) glclear(gl_color_buffer_bit); // 1st Viewport // Scale View to (-2, 2, -2, 2) cause sine -1 < y < 1 gluortho2d(-2, 2, -2, 2); glviewport(0, 250, 250, 250); // (0x, 250y,... is the point of the bottom-left corner of this 1st viewport. // Original window 500px wide by 500px high. glutinitwindowsize(500, 500); drawsin(); glloadidentity(); // Reset Identity //2nd Viewport gluortho2d(-2, 2, -2, 2); glviewport(250, 0, 250, 250); // (250x, 0y,... is the point of the bottom-left corner of this 2nd viewport. drawsin(); glloadidentity(); // Reset Back to original Size; glviewport(0, 0, 500, 500); // XY axis lines: Blue glcolor3f(0.0, 0.0, 1.0); glbegin(gl_lines); glvertex2f(-2, 0); glvertex2f(2, 0); glvertex2f(0, -2);

13 glvertex2f(0, 2); glflush(); int main(int argc, char** argv) glutinit(&argc, argv); glutinitwindowsize(500, 500); glutinitwindowposition(200, 20); glutcreatewindow("cse-420: Lab4, Viewports"); init(); glutdisplayfunc(display); glutmainloop(); return 0;

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