1 3D modelling with OpenGL Brian Farrimond Robina Hetherington

2 A standard 3D OpenGL Program Draws a wire cube Ex02

3 Looking at the wire cube Default position

4 Program overview Drawing the scene Initialising the graphics Program start

5 Program overview What to do when the window is created, resized or moved Response to keyboard presses

6 main

7 Always there

8 main Setting up the window

9 main Initialise the graphics

10 init

11 init Does nothing in this case

12 main Name of the function that will draw the scene

13 main Name of the function that will respond to the keyboard

14 keyboard ASCII code of pressed key ASCII code for Esc key Terminate the program

15 main Name of the function that will be called when the window is created, resized or moved

16 reshape

17 Getting OpenGL to view the wire cube Two separate tasks: –Controlling the camera settings –Positioning the camera and the objects to be photographed Achieved by using matrices Matrix = Mathematical representation of a sequence of operations

18 OpenGL Matrices Controlling the camera settings –PROJECTION MATRIX Positioning the camera and the objects –MODELVIEW MATRIX

19 Ex02 The state of the matrices after the program has drawn the wire cube

20 Using orthographic projection The state of the matrices after the program has drawn the wire cube with orthographic projection

21 reshape Always the same

22 reshape PROJECTION Setting up the camera settings: perspective projection

23 reshape MODELVIEW Getting ready to position the camera and objects

24 Nate Robin’s Tutorial example Projection

25 display Position the camera

26 Where the camera is

27 Where the camera is looking

28 gluLookAt Always the same

29 gluLookAt

30 Changing the camera position gluLookAt(0, 5, 6, 0, 0, 0, 0, 1, 0);

31 display Position the camera Draw the object

32 Interacting with OpenGL

33 Interacting through the keyboard We have already met: Use Esc key to stop the program

34 Ex03 Now look at this … If key ‘a’ is pressed Increase variable g_yeye by 1 Redraw the scene

35 display Camera position stored in three variables

36 Declaring and initialising the camera position

37 Exercise Modify the code so that, in addition, ‘n’ moves the viewer left and ‘m’ moves the viewer right.

38 Using special keys

39 Using special keys GLUT codes for special keys

40 Other special keys

41 Exercise Modify Ex03.cpp to use the arrow keys to move the viewer left, right, up and down.

42 Animation Objects change position and appearance over time In an animation program: Repeat change the position/appearance data redraw the scene Until end of program

43 Example – rotating a cube Ex04 Note the poor quality of the animation

44 Example – rotating a cube If this continually changes then redrawing would visualise the change

45 The matrices Camera settings Camera and object positions

46 Repeatedly calling spin Tells OpenGL to call spin whenever there is nothing else to do

47 Handling the rotation angle Calling this function changes the rotation angle and redraws the scene This sets the initial rotation angle to 0 The rotation angle

48 The overall main function

49 Improving the quality – double buffering The problem –The OpenGL program continually writes new image data into the frame buffer –Before previous version has been fully displayed

50 Improving the quality – double buffering The solution –Two buffers (double buffering) –The OpenGL program writes new image data into one buffer –Digital to Analogue Converter reads from the other buffer –Buffers swapped as DAC prepares to draw another picture

51 Double buffering in OpenGL

52 Transformations Positioning objects in a scene is achieved by combinations of –Translation –Scaling –Rotation

53 Translation This performs a movement: –3 units in the positive x direction, –7 units in the negative y direction and –2 units in the positive z direction

54 Scaling stretches the scene –twofold in the x direction –and leaves the other directions unchanged.

55 Rotation Performs a rotation about an axis defined by a line joining the origin to the point (x, y, z). Rotations are usually made around one of the axes

56 Applying sets of transformations Object vertices can be expressed as column vectors Here is point P with coordinates x, y, z:

57 Applying sets of transformations The extra 1 at the bottom of the column vector enables the all transformations to be represented by 4x4 matrices.

58 Applying sets of transformations A 3D transformation is performed mathematically as a matrix multiplication. Here a transformation by matrix A moves the point P to (x’, y’, z’)

59 Applying sets of transformations We can represent this more neatly as P’ = A.P If another transformation, B, is carried out on P’ we get P’’ P’’ = B.P’ Hence we have: P’’ = B.A.P

60 Applying sets of transformations Modelling transformations are held in the modelview matrix In a sequence of transformations, the modelview matrix is multiplied by the corresponding sequence of 4x4 transformation matrices Order is crucial –A.B is not the same as B.A

61 Example 1 The cube is drawn Wire cube MODELVIEW MATRIX

62 Example 2 The cube is drawn, the cube is scaled Scale / Wire cube MODELVIEW MATRIX

63 Example 3 The cube is drawn, the cube is scaled, the cube is rotated, the cube is translated Translate / Rotate / Scale / Wire cube MODELVIEW MATRIX

64 Example 4 The cube is drawn, the cube is scaled, the cube is translated, the cube is rotated Rotate / Translate / Scale / Wire cube MODELVIEW MATRIX