1、CAP 4703 Computer Graphic Methods,Prof. Roy Levow Lecture 2,2-Dimensional Drawing with OpenGL,Two-dimensional objects are a special case of three-dimensional figures The drawing is limited (by the programmer) to a plane Viewing is normally an orthogonal view, perpendicular to the drawing plane,Sierp
2、inski Gasket,A simple but interesting example Start with any triangle Pick an internal point at random Pick a vertex at random Find the midpoint between 1 and 2 Display this point Replace initial point with this one Repeat from step 2,Sierpinski Gasket Construction,OpenGL Program for Sierpinski Gask
3、et,main() initialize_the_system();for (some_number_of_points)pt = generate_a_point();display_the_point(pt);cleanup();return 0; ,Points or Vertices,Points are represented by vectors with an entry for each coordinatep = (x, y, z) in 3 dimensionsp = (x, y, 0) gives 2 dimensions by always setting z to 0
4、 OpenGL allows up to 4 dimensions Internal representation is always the same,OpenGL Vertices,Vertex creating functions have general nameglVertex*The suffix is 2 or 3 characters Number of dimensions: 2, 3, or 4 Data type: i = integer, f = float, d = double Optional v if pointer,Underlying Representat
5、ion,OpenGL data types are defined in header file#define GLfloat float so a header might look likeglVertex2i(GLint xi, GLint yi) orglVertex3f(GLfloat xf, GLfloat yf,GLfloat zf),Representation (cont.),For the vector formGLfloat vertex3; and then useglVertex3fv(vertex);,Defining Geometric Objects,Objec
6、ts are defined by collections of point constructors bounded by calls to glBegin and glEnd A line is defined byglBegin(GL_LINES);glVertex2f(x1, y1);glVertex2f(x2, y2);glEnd();,OpenGL Code for Sierpinski Gasket,See p. 41 of textCode leaves many open questions by using default values colors image posit
7、ion size clipping? persistence,A Resulting Image,Coordinate System,Early systems depended on specific device mapping Device-independent graphics broke link Use application or problem coordinate system to define image Use device coordinates, raster coordinates, screen coordinates for device,Coordinat
8、es,Application coordinates can be integer or real and multi-dimensional Screen or raster coordinates are always integer and essentially 2-dimensional Graphics program maps application coordinates onto device coordinates,App to Device Mapping,Classes for OpenGL Functions,Primitives draw points, line
9、segments, polygons, text, curves, surfaces Attributes specify display characteristics of objects: color, fill, line width, font Viewing determine aspects of view: position and angle of camera, view port size, ,Function Classes (cont),Transformations change appearance or characteristics of objects: r
10、otate, scale, translate Input handle keyboard, mouse, etc. Control communicate with window system Inquiry get display information: size, raster value, ,OpenGL Interface,Graphics Utility Interface (GLU) Creates common objects like spheres GL Utility Toolkit (GLUT) Provides generic interface to window
11、 system GLX for Unix/Linux and wgl for Microsoft Windows provide low-level glue to window system,Library Organization,Using Libraries,Header files #include #include #include On some systems the GL/ is not used,Primitives,OpenGL supports both geometric primitives and raster primitives,Geometric Primi
12、tives,Points = GL_POINTS vertex displayed with size = 1 pixel Line segments = GL_LINES defined by pairs of vertices as endpoints of segments Polygons = GL_LINE_STRIPE or GL_LINE_LOOP Loop is closed, stripe is not,Primitive Examples,Properties of Polygons,Defined by line loop border Simple if no edge
13、s cross Convex if every line segment connecting pair of points on boundary or inside lies completely inside,Polygon Types in OpenGL,Polygons are either filled regions (default) or boundaries Set with glPolygonMode To get polygon with boundary must draw twice, once as filled and once as boundary or l
14、ine loop,Special Polygons,GL_TRIANGLES, GL_QUADS Groups of 3 or 4 points are grouped as triangles or quadrilaterals,Special Polygons,GL_TRIANGLE_STRIPE, GL_QUAD_STRIPE, GL_TRIANGEL_FAN Contiguous stripe or fan of triangles or quadrilaterals,Drawing a Sphere,Draw great circles Fill between latitudes
15、with quad strips Fill caps with triangle fans Code on p.52,Text,May be raster from bit map Fast Does not scale well Poor in rotation other than 90o Vector from drawn curves Slow to draw Scales, rotates, etc. well,Raster text,Color,The physiology of vision leads to 3-color theory Any color can be pro
16、duced by a combination of red, green, and blue at intensities that produce the same response in the cones as the true color,Colors in OpenGL,Colors are stored using 4 attributes, RGBA A = Alpha channel Controls opacity or transparency Color values can be integers in range from 0 to max component val
17、ue 0 255 for 24-bit color Real numbers between 0.0 and 1.0,Colors in OpenGL (cont),Colors are set with glColor* functions * is two characters, nt n = 3 or 4 color values t = date type: i, f, etc.,Clearing Frame Buffer,To get predictable results a program must first clear the frame bufferglClearColor
18、(1.0, 1.0, 1.0, 1.0) sets color to white,Indexed Color,OpenGL also supports indexed color Saves space when only a limited number of distince colors are used,Indexed Color (cont),Set color in table withglutSetColor(int color, GLfloat red,GLfloat blue, GLfloat green) Access color in table withglIndexi
19、(element),Viewing,Based on synthetic camera model If nothing is specified, there are default viewing parameters Rarely used Would force us to fit model world to camera Prefer flexibility of setting viewing parameters,Two-Dimensional Viewing,Selected rectangle from 2-dimensional world is displayed Ca
20、lled viewing rectangle or clipping rectangle,Viewing Volume,2-dimensional viewing is special case of 3-dimensional viewing viewing volume Default is 2 x 2 x 2 cube centered at (0,0,0),Orthographic Projection,Projects point (x,y,z) onto (x,y,0) View is perpendicular to plane x=0 Set viewing rectagle
21、withvoid glOrtho(GLdouble left, GLdouble right, GLdouble bottom,GLdouble top),Matrix Modes,Graphic pipelines perform matrix transformations on images at each stage Most important matrices are model-view projection State includes both,Manipulating Mode Matrices,Matrix mode operations operate on matri
22、x for currently selected mode Model-view is default Mode is set with glMatrixMode(mode) mode = GL_PROJECTION, GL_MODELVIEW, etc. Always return to model-view to insure consistency,Control Functions,Depend on particular window system GLUT provides standard set of basic operations We will consider only
23、 these,Window Control,Operations only on display window for the program Initialization glutInit Creation glutCreateWindow Display mode glutInitDisplayMode RGB or indexed hidden-surface removal singer or double buffering,Example Code,glutInit(,Aspect Ratio and Viewports,Ratio of width to length is as
24、pect ratio If aspect ratio of viewing rectangle and window differ, image will be stretched and distorted Viewport defines region of screen in which to display image Can eliminate distortion,Distortion,Viewport,Set viewport with void glViewport(GLint x, GLint y,GLsizei w, GLsizei h),GLUT Main Loop,If
25、 we simply run an OpenGL program it will display the image and exit may not allow time to see it could sleep program to keep window open but this is limited solution GLUT provides controls to avoid this Keep program running waiting for eventvoid glutMainLoop(void),Glut Display,To display an image, c
26、ode a function to create the image and have GLUT call it image drawing function takes no arguments and returns no result Any parameters must be passed through global variables void glutDisplayFunc(void (*func)(void),Simple Main Program,#include void main(int argc, char *argv) glutInit(,Simple Main P
27、rogram (cont),glutCreateWindow(“My Image“);glutDisplayFunc(display);myinit();glutMainLoop(); ,Program Structure,Key components initialization display callback function mainGasket Program codegasket.c 2-d codegasket2.c 3-d with colors /code/gasket3.c 3-d with polygons,Hidden Surface Removal,Z-buffer algorithm Z coordinate determines depth Point nearer camera obscures one with greater depth Steps Init with GLUT_DEPTH glEnable(GL_DEPTH_TEST can also disable clear before redrawing,Sample HSR Program,void display() glClear(GL_COLOR_BUFFER_BIT |GL_DEPTH_BUFFER_BIT)tetrahedron(n)glFlush(); ,
