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CAP 4703 Computer Graphic Methods

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

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CAP 4703 Computer Graphic Methods

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  1. CAP 4703Computer Graphic Methods Prof. Roy Levow Lecture 2

  2. 2-Dimensional Drawingwith 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

  3. Sierpinski 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

  4. Sierpinski Gasket Construction

  5. OpenGL Program forSierpinski Gasket main() { initialize_the_system(); for (some_number_of_points) { pt = generate_a_point(); display_the_point(pt); } cleanup(); return 0; }

  6. Points or Vertices • Points are represented by vectors with an entry for each coordinate • p = (x, y, z) in 3 dimensions • p = (x, y, 0) gives 2 dimensions by always setting z to 0 • OpenGL allows up to 4 dimensions • Internal representation is always the same

  7. OpenGL Vertices • Vertex creating functions have general name glVertex* • 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

  8. Underlying Representation • OpenGL data types are defined in header file #define GLfloat float so a header might look like glVertex2i(GLint xi, GLint yi) or glVertex3f(GLfloat xf, GLfloat yf, GLfloat zf)

  9. Representation (cont.) • For the vector form GLfloat vertex[3]; and then use glVertex3fv(vertex);

  10. Defining Geometric Objects • Objects are defined by collections of point constructors bounded by calls to glBegin and glEnd • A line is defined by glBegin(GL_LINES); glVertex2f(x1, y1); glVertex2f(x2, y2); glEnd();

  11. OpenGL Code for Sierpinski Gasket • See p. 41 of text • Code leaves many open questions by using default values • colors • image position • size • clipping? • persistence

  12. A Resulting Image

  13. 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

  14. Coordinates • 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

  15. App to Device Mapping

  16. Classes for OpenGL Functions • Primitives – draw points, line 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, …

  17. Function Classes (cont) • Transformations – change appearance or characteristics of objects: rotate, scale, translate • Input – handle keyboard, mouse, etc. • Control – communicate with window system • Inquiry – get display information: size, raster value, …

  18. OpenGL Interface • Graphics Utility Interface (GLU) • Creates common objects like spheres • GL Utility Toolkit (GLUT) • Provides generic interface to window system • GLX for Unix/Linux and wgl for Microsoft Windows • provide low-level glue to window system

  19. Library Organization

  20. Using Libraries • Header files • #include <GL/glut.h> • #include <GL/gl.h> • #include <GL/glu.h> • On some systems the GL/ is not used

  21. Primitives • OpenGL supports both geometric primitives and raster primitives

  22. Geometric Primitives • 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

  23. Primitive Examples

  24. Properties of Polygons • Defined by line loop border • Simple if no edges cross • Convex if every line segment connecting pair of points on boundary or inside lies completely inside

  25. 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 line loop

  26. Special Polygons • GL_TRIANGLES, GL_QUADS • Groups of 3 or 4 points are grouped as triangles or quadrilaterals

  27. Special Polygons • GL_TRIANGLE_STRIPE, GL_QUAD_STRIPE, GL_TRIANGEL_FAN • Contiguous stripe or fan of triangles or quadrilaterals

  28. Drawing a Sphere • Draw great circles • Fill between latitudes with quad strips • Fill caps with triangle fans • Code on p.52

  29. 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

  30. Raster text

  31. Color • The physiology of vision leads to 3-color theory • Any color can be produced by a combination of red, green, and blue at intensities that produce the same response in the cones as the true color

  32. 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 value • 0 – 255 for 24-bit color • Real numbers between 0.0 and 1.0

  33. 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.

  34. Clearing Frame Buffer • To get predictable results a program must first clear the frame buffer glClearColor(1.0, 1.0, 1.0, 1.0) • sets color to white

  35. Indexed Color • OpenGL also supports indexed color • Saves space when only a limited number of distince colors are used

  36. Indexed Color (cont) • Set color in table with glutSetColor(int color, GLfloat red, GLfloat blue, GLfloat green) • Access color in table with glIndexi(element)

  37. 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

  38. Two-Dimensional Viewing • Selected rectangle from 2-dimensional world is displayed • Called viewing rectangle or clipping rectangle

  39. 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)

  40. Orthographic Projection • Projects point (x,y,z) onto (x,y,0) • View is perpendicular to plane x=0 • Set viewing rectagle with void glOrtho(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top)

  41. Matrix Modes • Graphic pipelines perform matrix transformations on images at each stage • Most important matrices are • model-view • projection • State includes both

  42. Manipulating Mode Matrices • Matrix mode operations operate on matrix 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

  43. Control Functions • Depend on particular window system • GLUT provides standard set of basic operations • We will consider only these

  44. 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

  45. Example Code glutInit(&argc, argv); glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH); glutInitWindowSize(480, 480); glutWindowPosition(0, 0); glutCreateWindow(“sample");

  46. Aspect Ratio and Viewports • Ratio of width to length is aspect 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

  47. Distortion

  48. Viewport • Set viewport with void glViewport(GLint x, GLint y, GLsizei w, GLsizei h)

  49. GLUT Main Loop • If 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 event void glutMainLoop(void)

  50. Glut Display • To display an image, code 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))

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