Graphics Programming. August 31, Programming of the Sierpinski gasket. Programming with OpenGL and C/C++
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1 Computer Graphics Graphics Programming August 31, 2005 Contents Our Goal in This Chapter Programming of the Sierpinski gasket How To? Programming with OpenGL and C/C++ OpenGL API (Application Programmer s Interface) Primitives Attributes Color Viewing Control Functions
2 The Sierpinski Gasket What is? Interesting shape in area such as fractal geometry Object that can be defined recursively and randomly How to? Start with three vertices in the plane 1. Pick an initial point at random inside the triangle 2. Select one of the three vertices at random 3. Find the point halfway between the initial point and the randomly selected vertex 4. Display this new point by putting some sort of marker, such as a small circle, at its location 5. Replace the initial point with this new point 6. Return to step 2 Generation of the Sierpinski Gasket v 2 p 0 p 1 p 2 v 1 v 3
3 Algorithm of the Sierpinski Gasket main( main( ) { initialize_the_system( ); ); for( for( some_number_of_points ) { pt pt = generate_a_point( ); ); display_the_point(pt); } } cleanup( ); ); The Sierpinski Gasket
4 The Pen-Plotter Model (1/3) Conceptual Model Referencing the Output Device Produce images by moving a pen held by a gantry 2 Drawing Functions moveto(x, y); lineto(x, y); Example : moveto(0, 0); lineto(1, 0); lineto(1, 1); lineto(0, 1); lineto(0, 0); (0, 1) < Pen plotter > (1, 1) (0, 0) (1, 0) The Pen-Plotter Model (2/3) Vertex Location in space (2D, 3D, 4D) Define the atomic geometric objects 1 : point 2 : line segment 3 : triangle, circle 4 : quadrilateral OpenGL : glvertex*( ) glvertex2i(glint xi, GLint yi); glvertex3f(glfloat x, GLfloat y, GLfloat z); glvertex3fv(vertex); #define GLfloat float GLfloat vertex[3];
5 The Pen-Plotter Model (3/3) OpenGL: glbegin( ), glend( ) Specify the geometric type Line segment glbegin(gl_lines); glvertex2f(x1, y1); glvertex2f(x2, y2); glend( ); ); A pair of points glbegin(gl_points); glvertex2f(x1, y1); glvertex2f(x2, y2); glend( ); ); (x1, y1) (x2, y2) (x1, y1) (x2, y2) Function of display of the Sierpinski Gasket void void display(void){ display(void){ glclear(gl_color_buffer_bit); glcolor3f(1.0, glcolor3f(1.0, 0.0, 0.0, 0.0); 0.0); typedef typedef GLfloat GLfloat point2[2]; point2[2]; /* /* arbitrary arbitrary triangle triangle */ */ point2 point2 vertices[3] vertices[3] = { {0.0,0.0}, {0.0,0.0}, {250.0,500.0}, {250.0,500.0}, {500.0,0.0} {500.0,0.0} }; }; /* /* any any desired desired initial initial point point */ */ point2 point2 p = { 75.0, ,75.0 }; }; glbegin(gl_points); for(int for(int i=0; i=0; i<5000; i<5000; i++) i++) { /* /* pick pick a random random vertex vertex from from 0,1,2 0,1,2 */ */ int int j=rand()%3; j=rand()%3; /* /* compute compute new new point point */ */ p[0] p[0] = (p[0]+vertices[j][0])/2.0; p[1] p[1] = (p[1]+vertices[j][1])/2.0; /* /* display display new new point point */ */ glvertex2fv(p); glvertex2fv(p); } glflush(); glflush(); }
6 The Sierpinski Gasket Generated with 5000 Points OpenGL API (1/3) API (Application Programmer s Interface) Interface between an application program and a graphics system Application Graphics Library Program Library Hardware (API) (API) OpenGL API Easy to learn, compared with other APIs Nevertheless powerful Graphics Functions : Black Box Described by only its inputs and outputs Nothing known about its internal working Input Device Output Device User User Program Function Calls Data Graphics System System Output Input Input/Output Devices
7 OpenGL API (2/3) 6 Groups of Graphics Functions Primitive functions what of an API - that object that can be displayed Attributes functions how of an API : color, filling pattern Viewing functions describe camera - position, orientation Transformation functions rotation, translation,scaling Input functions interactive application : keyboard, mice, data tablet Control functions multiprocessing multiwindow environment - communicate the window system OpenGL API (3/3) OpenGL Interface GLU GLU OpenGL Application Program GL GL GLUT Xlib, Xlib, Xtk Xtk Frame Buffer GLX GLX OpenGL functions(names : gl~) : GL Graphics utility library : GLU Use only GL functions Contain code for common objects such as spheres Graphics utility toolkit : GLUT interface with the window system
8 Primitives in OpenGL Points Lines Line segments Polylines Polygons Polygons Triangles and quadrilaterals Strips and fans Text Curved objects Points in OpenGL glbegin(gl_points); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv();
9 Lines in OpenGL (1/3) Line Segments glbegin(gl_lines); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); Lines in OpenGL (2/3) Polylines Line Strip glbegin(gl_line_strip); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv();
10 Lines in OpenGL (3/3) Polylines Line Loop glbegin(gl_line_loop); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); Polygons (1/2) Definition Object that is closed as a line loop, but that has an interior Simple Polygon No pair of edges of a polygon cross each other Simple Nonsimple
11 Polygons (2/2) Convexity If all points on the line segment between any two points inside the object, or on its boundary, are inside the object Convex Objects Polygons in OpenGL (1/6) Polygon glbegin(gl_polygon); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv();
12 Polygons in OpenGL (2/6) Quadrilaterals glbegin(gl_quads); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); Polygons in OpenGL (3/6) Quadstrip glbegin(gl_quad_strip); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv();
13 Polygons in OpenGL (4/6) Triangles glbegin(gl_triangles); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); Polygons in OpenGL (5/6) Triangle Strip glbegin(gl_triangle_strip); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv();
14 Polygons in OpenGL (6/6) Triangle Fan glbegin(gl_triangle_fan); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); glvertex2fv(); Attributes Properties that Determines How to Render a Geometric Primitive Color, thickness, pattern of filling, etc. Color Three color theory Red Blue M C Y Green Yellow G R Cyan B Magenta Additive Color Subtractive Color Color Solid
15 Color in OpenGL Set the Clear Color glclearcolor(1.0, 1.0, 1.0, 1.0) Opaque: opacity is 1.0 Window is cleared by white color Set the Color State Variable glcolor3f(1.0, 0.0, 0.0); RGB color red color Set the Size of Points glpointsize(2.0); 2 pixel wide Viewing Viewing Volume glortho(gldouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far); glortho2d(gldouble left, GLdouble right, GLdouble bottom, GLdouble top); Matrix Mode 2 types: model-view, projection glmatrixmode(gl_projection); glloadidentity( ); ); gluortho2d(0.0, 500.0, 0.0, 0.0, 500.0); glmatrixmode(gl_modelview);
16 Control (1/2) Interaction with Window Systems glutinit(int *argc, char *argv); glutinitdisplaymode(glut_rgb GLUT_DEPTH GLUT_DOUBLE); glutinitwindowsize(480, 640); glutintiwindowposition(0, 0); Aspect Ratio and Viewport glviewprot(glint x, GLint y,glsizei w, GLsizei h); <Aspect-Ratio Mismatch> <Mapping to the Viewpot> Control (2/2) Example main, display, and myinit Functions #include #include <windows.h> <windows.h> #include #include <GL/gl.h> <GL/gl.h> #include #include <GL/glu.h> <GL/glu.h> #include #include <GL/glut.h> <GL/glut.h> void void main(int main(int argc, argc, char char **argv){ **argv){ glutinitdisplaymode(glut_single GLUT_RGB); glutinitwindowsize(500, 500); 500); glutinitwindowposition(0, 0); 0); glutcreatewindow("simple OpenGL OpenGL example"); example"); glutdisplayfunc(display); myinit(); myinit(); glutmainloop(); glutmainloop(); } void void myinit(void){ myinit(void){ /* /* attributes attributes */ */ glclearcolor(1.0, 1.0, 1.0, 1.0, 1.0, 1.0); 1.0); /* /* set set up up viewing viewing */ */ glmatrixmode(gl_projection); glloadidentity(); gluortho2d(0.0, gluortho2d(0.0, 500.0, 500.0, 0.0, 0.0, 500.0); 500.0); glmatrixmode(gl_modelview); }
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