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Coordinate Systems (2.1.2)

Coordinate Systems (2.1.2). Device coordinates, or screen coordinates (pixels) put limitations on programmers and the code is not portable generally expressed in integers World coordinates

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Coordinate Systems (2.1.2)

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  1. Coordinate Systems (2.1.2) • Device coordinates, or screen coordinates (pixels) • put limitations on programmers and the code is not portable • generally expressed in integers • World coordinates • an effort was made to hide the actual device coordinates from the programmer and allow ANY coordinate to be used • generally expressed in floats • programmer defines world space • Mapping • the mathematical transformation from one coordinate system to another • involves relatively simple algebra • Example • Device coordinates of 640 x 480 • World coordinates of 5000 x 4000 • Map (2500, 2000) to ___________ • Map (1000, 1000) to ___________

  2. OpenGL • Originally SGIs GL • modified to be more portable • Collection of functions that interface to graphics hardware • Works well on a network • Protocol (format of instructions) is the same regardless of the computer. This makes the code portable or system independent • It does NOT do • windows • input • modeling • It does do sophisticated rendering of 3D scenes

  3. uisGL (3D object library) • The book explains that OpenGL is not OO • This API helps to hide some ugly details • #include <uisGL.h> • Vertex • uisVertex P1, P2, P3(10,10,0); • P1.set(20,20,0); • P2.set(40,40,0); • P3 = P1 + P2; • P3 = P1 / 2; • P3 = P2 * 2.0; • cout << P3;

  4. Typical API Functions (2.2.1) • Primitives • draw points, lines, polygons (maybe curves) • Attributes • colors, fill patterns, fonts • Viewing • position, orientation and lens for the virtual camera • Input • handle events from keyboard and mouse • Control • initialize programs, create windows • Transformation • rotate, translate, and scale objects

  5. Drawing Primitives (2.1.1) • We will consider 2D to be a special case (x,y,0) • Point or Vertex define geometric objects • glVertex2f (x, y); • glVertex3f (x,y,z); • Array or Vector format • float vertex[3]; • glVertex3fv(vertex); • Drawing individual points • glBegin(GL_POINTS); • glVertex3f (x,y,z); • glVertex3f (x,y,z); • glEnd( ); <--- warning! • Drawing a line • glBegin(GL_LINES); • glVertex3f(x,y,z); • glVertex3f(x,y,z); • glEnd( );

  6. Polygons (2.3.1) • a series of connected lines • simple polygon edges do not cross • the interior can be filled with a color • convex polygons can be tested by connecting all vertices with each other. If all of the lines remain inside the polygon then it is covex. • concave polygons are not convex • Drawing a polygon • float P1[3] = {10, 10, 0}; • glBegin(GL_POLYGON); • glVertex3fv (P1); • glVertex3fv (P2); • glVertex3fv (P3); • glVertex3fv (P4); • glEnd(); • Interior can be filled with a color • Edges can be turned on or off

  7. Attributes (2.3.5) • the name for any property that determines how an object appears • a solid red line is different that a dashed green line • color, line thickness, fill pattern • The general approach is to set current attributes and then display the object. • Each geometric type has a set of attributes. A line has color, width and style. • glPointSize (2.0) // 2 pixels wide

  8. Color (2.4) • Ignore color theory and mathematics • Three colored spot lights analogy • Different than mixing paints • RGB color or true color • C = T1R + T2G + T3B • T is the intensity that ranges from 0 - 1 • glColor3f (0, 0, 0); // balck • glColor3f (1, 0, 0); // red • glClearColor (1, 1, 1, 0); // white background • glClear (); // clear the screen • The number of colors that can be displayed are determined by the number of bits available for each pixel • true color requires 24 bits - 8 bits for each

  9. Indexed Color • not often needed any longer • when the number of bits per pixel is limited • rather than limit the possible range of colors we limit the possible number of colors • painter example that can mix an unlimited number of paints but can only fit so many on the cardboard plate • Color-lookup Table • the 8-bit representation is used as an index into the color lookup table • contains a limited number of entries but each entry can represent any color • set current color by specifying an index • common configuration is 256 indices

  10. Viewing 2.5 • Viewing rectangle or window • items within the window will be seen and others will be clipped • 3D Viewing Volume • glOrtho(left,right,bottom,top,near,far) • Be aware of right handed coordinate system • positive Z comes out from screen • Viewport • a rectangular region within the window • glViewport(x,y,width,height) • Aspect Ratio • the ratio of the viewing rectangle should be the same as the viewport

  11. Matrix Mode (2.5.3) • Primitives are multiplied by matrices before being displayed. • OpenGL has two important matrices • MODELVIEW - for viewing parameters • PROJECTION - for display parameters • obj’ = obj x MV • obj’’ = obj’ x P • Typical initialization • glMatrixMode(GL_PROJECTION); • glLoadIdentity(); • glOrtho(0,10,0,10,0,10); • glMatrixMode(GL_MODELVIEW); • Leave in MODELVIEW mode

  12. GLUT (GL Untility Toolkit) 2.6 • Windowing system independent API for OpenGL applications • Allows one to • window management • simple menus • event processing loop • input • We will use an X11 implementation of GLUT. There could be a Windows version or Macintosh version. • X11 is a protocal that allows device independent display of graphics over a network. Using real X11 commands would be a pain. Somewhat equivalent to programming in assembler. • Client Server model. The client is the application and the computer that does the display is the server.

  13. Event Processing 2.6 • What stops the image from disappearing after it has been drawn? • Event Processing Loop • glutMainLoop() • this causes an infinite loop until closing the window by hand • Callback Mechanism • a programmer defined function that glutMainLoop will call when GLUT determines an event has occurred. • this is called “registering a call back” • Display function • glutDisplayFunc(*func(void)) • Additional Events • mouse button presses • keyboard • window movement

  14. Sample Code • look a source • discuss Makefile

  15. Sierpinski Gasket • interesting example from the book • Choose a random point within the triangle • Loop • Find midpoint between current point and a random vertex • Make a mark • Update current point • Extended to 3D requires a tetrahedron

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