CSCE 441: Computer Graphics: Hierarchical Models

1. CSCE 441: Computer Graphics:Hierarchical Models Jinxiang Chai

2. Summary: 3D Geometry Pipeline Object space World space View space Normalized project space Image space 2

3. Complex Models

4. Outline Hierarchical Models Reading: HB chapter 14, OpenGL Programming Guide, chapter 3, and course slides

5. Symbols and Instances • Most graphics API supports a few primitives: - sphere - cube - cylinders • These symbols are instanced using instance transformation:

6. Symbols and Instances • Most graphics API supports a few primitives: - sphere - cube - cylinders • These symbols are instanced using instance transformation: What’s the matrix for the instance transformation above?

7. Symbols and Instances • Most graphics API supports a few primitives: - sphere - cube - cylinders • These symbols are instanced using instance transformation:

8. Sample Instance Trans. • In opengl, instance transformation is created by modifying the Model-view matrix: glMatrixMode(GL_MODELVIEW); glLoadIdentity(…);// set current matrix to the identity glTranslate(…); // translate glRotate(…); //rotate glScale(…);//scale house();

9. Sample Instance Trans. • In opengl, instance transformation is created by modifying the Model-view matrix: glMatrixMode(GL_MODELVIEW); glLoadIdentity(…); glTranslate(…); glRotate(…); glScale(…); house(); Does the transform seem to be backward?

10. Composite Transformation: Opengl Implementation • Opengl postmultiplies transformation matrices as they are called • Each subsequent transformation call concatenates the designated transformation matrix on the right of the composite matrix • We must invoke the transformation in the opposite order from which they are applied. glMatrixMode(GL_MODELVIEW); glLoadIdentity(…); M4; M3; M2; M1; …

11. Lamp What’s the current coordinate A ? 11

12. Lamp What’s the current coordinate A ? 12

13. Lamp What’s the current coordinate A ? 13

14. Lamp What’s the current coordinate A ? 14

15. Lamp What’s the current coordinate A ? 15

16. Lamp Implementation lamp() { M_model = base(); M_model = upper_arm(); M_model = middel_arm(); M_model = lower_arm(); } Matrix M_model; Main() { … lamp(); } The lamp can be displayed by computing a global matrix and computing it at each step

17. Lamp Implementation lamp() { M_model = base(); M_model = upper_arm(); M_model = middel_arm(); M_model = lower_arm(); } Matrix M_model; Main() { … lamp() } Can we make it more efficiently? The lamp can be displayed by computing a global matrix and computing it at each step

18. Better Implementation lamp() { M_model *= base(); M_model *= upper_arm(); M_model *= middel_arm(); M_model *= lower_arm(); } Matrix M_model; Main() { … M_model=Identity() lamp(); } • Instead recalculating the global matrix each time, we can just update it in place

19. Opengl Implementation • Opengl maintains a global state matrix called model-view matrix Main() { … glMatrixMode(GL_MODELVIEW); glLoadIdentity(); 2D_lamp(a,b,c,d,e,f) … } 2D_lamp(x, y, θ0,θ1,θ2,θ3) { glTranslatef(x,y,0) glRotatef(θ0,0,0,1,); base(); glTranslatef(0,l0,0) glRotatef(θ1,0,0,1,); upper_arm(); glTranslatef(0,l1,0) glRotatef(θ2,0,0,1,); middel_arm(); glTranslatef(0,l2,0) glRotatef(θ3,0,0,1,); lower_arm(); } //set current matrix to identity

20. Hierarchical Modeling • Consider a model of a car – how many symbols? – how many instances?

21. Hierarchical Modeling • Consider a model of a car – 2 symbols : – 5 instances :

22. Hierarchical Modeling Chasis system World system front-left wheel system • Consider a model of a car – 2 symbols : chassis + wheel – 5 instances : 1 chassis + 4 wheel

23. Hierarchical Modeling • Consider a model of a car – 2 symbols : chassis + wheel – 5 instances : 1 chassis + 4 wheel • We can represent our car as a tree to show the relationship between the parts

24. Hierarchical Modeling • Consider a model of a car – 2 symbols : chassis + wheel – 5 instances : 1 chassis + 4 wheel • We can represent our car as a tree to show the relationship between the parts • However, since all 4 wheels are instances of the same model, we’d like to only have that model appear once

25. Hierarchical Modeling • Hierarchical model can be composed of instances using trees or directed acyclic graphs (DAGs) - edges contains geometric transformations - nodes contains geometry

26. Hierarchical Modeling • Hierarchical model can be composed of instances using trees or directed acyclic graphs (DAGs) - edges contains geometric transformations - nodes contains geometry What might we draw the tree for the lamp?

27. Hierarchical Modeling • Hierarchical model can be composed of instances using trees or directed acyclic graphs (DAGs) - edges contains geometric transformations - nodes contains geometry

28. Hierarchical Modeling world base Upper arm middle arm lower arm • Hierarchical model can be composed of instances using trees or directed acyclic graphs (DAGs) - edges contains geometric transformations - nodes contains geometry

29. A More Complex Example: Human Figure torso

30. A More Complex Example: Human Figure torso

31. A More Complex Example: Human Figure torso What’s the most efficient way to draw this figure?

32. A More Complex Example: Human Figure torso What’s the most sensible way to traverse this tree?

33. A More Complex Example: Human Figure torso What’s the most sensible way to traverse this tree?

34. A More Complex Example: Human Figure torso What’s the most sensible way to traverse this tree?

35. A More Complex Example: Human Figure torso What’s the most sensible way to traverse this tree?

36. A More Complex Example: Human Figure torso What’s the most sensible way to traverse this tree?

37. A More Complex Example: Human Figure torso What’s the most sensible way to traverse this tree?

38. A More Complex Example: Human Figure torso What’s the most sensible way to traverse this tree?

39. A More Complex Example: Human Figure torso What’s the most sensible way to traverse this tree?

40. A More Complex Example: Human Figure torso What’s the most sensible way to traverse this tree?

41. A More Complex Example: Human Figure torso What’s the most sensible way to traverse this tree?

42. Opengl Implementation: Human Figure torso Mh Mlua Mlla

43. Opengl Implementation: Human Figure torso Mh Mlua Mlla Is this correct?

44. Opengl Implementation: Human Figure I torso Mh Mh*Mlua should be Mlua Mh*Mlua*Mlla should be Mlua*Mlla Is this correct? No

45. Matrix Stack • glMatrixMode(GL_MODELVIEW) - Initially, each of the stacks contains one matrix, an identity matrix. - The top matrix in the stack is “current matrix” - The depth is at least 32 Mc … I

46. Push and Pop the Current Matrix • glPushMatrix() copy the current matrix at the top of the stack Mc Mc Mc … I … I

47. Push and Pop the Current Matrix • glPopMatrix() destroies the matrix at the top of stack Mtop-1 Mtop Mtop-1 … … I I

48. Opengl Implementation: Human Figure

49. Opengl Implementation: Human Figure I Mh Mlua Mlua Mlla