Transformations III. Week 3, Mon Jan 18

Transcription

1 Universit of British Columbia CPSC 34 Computer Graphics Jan-Apr 2 Tamara Munzner Transformations III Week 3, Mon Jan 8

2 News CS dept announcements Undergraduate Summer Research Award USRA) applications due Feb 26 see Guiliana for more details 2

3 Department of Computer Science Undergraduate Events Events this week Drop-in Resume/Cover Letter Editing Date: Tues., Jan 9 Time: 2:3 2 pm Location: Rm 255, ICICS/CS Bldg. Interview Skills Workshop Date: Thurs., Jan 2 Time: 2:3 2 pm Location: DMP 2 Registration: dianejoh@cs.ubc.ca Project Management Workshop Speaker: David Hunter e-vp, SAP) Date: Thurs., Jan 2 Time: 5:3 7 pm Location: DMP CSSS Laser Tag Date: Sun., Jan 24 Time: 7 9 pm Location: Planet Braid St., New Westminster Event net week Public Speaking Date: Mon., Jan 25 Time: 5 6 pm Location: DMP 3

4 Assignments 4

5 project Assignments out toda, due 5pm sharp Fri Jan 29 projects will go out before we ve covered all the material so ou can think about it before diving in build iguana out of cubes and 44 matrices think cartoon, not beaut template code gives ou program shell, Makefile written homework out toda, due 5pm sharp Wed Feb 6 theoretical side of material 5

6 Demo animal out of boes and matrices 6

7 Real Iguanas green-iguana--iguana-iguana-.jpg 7

8 Armadillos 8

9 Armadillos 9

10 Monkes

11 Monkes

12 Giraffes 2

13 Giraffes 3

14 Project Advice do not model everthing first and onl then worr about animating interleave modelling, animation for each bod part: add it, then jumpcut animate, then smooth animate discover if on wrong track sooner dependencies: can t get anim credit if no model use bod as scene graph root check from all camera angles 4

15 Project Advice finish all required parts before going for etra credit plaing with lighting or viewing ok to use glrotate, gltranslate, glscale ok to use glutsolidcube, or build our own where to put origin? our choice center of object, range -.5 to +.5 corner of object, range to 5

16 visual debugging Project Advice color cube faces differentl colored lines sticking out of glutsolidcube faces make our cubes wireframe to see inside thinking about transformations move phsical objects around pla with demos Brown scenegraph applets 6

17 Project Advice smooth transition change happens graduall over X frames ke click triggers animation one wa: redraw happens X times linear interpolation: each time, param += new-old)/3 or redraw happens over X seconds even better, but not required 7

18 transitions Project Advice safe to linearl interpolate parameters for glrotate/gltranslate/glscale do not interpolate individual elements of 44 matri 8

19 Stle ou can lose up to 5 for poor stle most critical: reasonable structure es: parametrized functions no: cut-and-paste with slight changes reasonable names variables, functions) adequate commenting rule of thumb: what if ou had to fi a bug two ears from now? global variables are indeed acceptable 9

20 Version Control bad idea: just keep changing same file save off versions often after got one thing to work, before ou tr starting something else just before ou do something drastic how? not good: commenting out big blocks of code a little better: save off file under new name p.almostworks.cpp, p.fiedbug.cpp much better: use version control software strongl recommended 2

21 Version Control Software eas to browse previous work eas to revert if needed for maimum benefit, use meaningful comments to describe what ou did started on tail, fied head breakoff bug, leg code compiles but doesn t run useful when ou re working alone critical when ou re working together man choices: RCS, CVS, svn/subversion all are installed on lab machines svn tutorial is part of net week s lab 2

22 Graphical File Comparison installed on lab machines fdiff4 side b side comparison) wdiff in-place, with crossouts) Windows: windiff Macs: FileMerge in /Developer/Applications/Utilities 22

23 Readings for Transformations I-IV FCG Chap 6 Transformation Matrices ecept 6..6, 6.3. FCG Sect 3.3 Scene Graphs RB Chap Viewing Viewing and Modeling Transforms until Viewing Transformations Eamples of Composing Several Transformations through Building an Articulated Robot Arm RB Appendi Homogeneous Coordinates and Transformation Matrices until Perspective Projection RB Chap Displa Lists 23

24 24 Review: Shear, Reflection shear along ais push points to right in proportion to height reflect across ais mirror + = sh + =

25 25 Review: 2D Transformations = + + = + b a b a ) ) ) ) = cos sin sin cos = b a scaling matri rotation matri = d c b a translation multiplication matri?? vector addition matri multiplication matri multiplication ), b a,), )

26 Review: Linear Transformations linear transformations are combinations of shear scale rotate reflect a c b d properties of linear transformations satisifes Ts+t) = s T) + t T) origin maps to origin lines map to lines parallel lines remain parallel ratios are preserved closed under composition = = = a c + + b d 26

27 Review: Homogeneous Coordinates w w w w homogeneous,, w) w= / w cartesian w, w point in 2D cartesian + weight w = point P in 3D homog. coords multiples of,,w) form 3D line L all homogeneous points on L represent same 2D cartesian point homogenize to convert homog. 3D point to cartesian 2D point: divide b w to get /w, /w, ) projects line to point onto w= plane like normalizing, one dimension up ) 27

28 28 Review: Homogeneous Coordinates 2D transformation matrices are now 33: = ) cos ) sin ) sin ) cos Rotation = b a Scale = T T Translation + + = + + = b a b a b a use rightmost column

29 29 Review: Affine Transformations affine transforms are combinations of linear transformations translations properties of affine transformations origin does not necessaril map to origin lines map to lines parallel lines remain parallel ratios are preserved closed under composition = w f e d c b a w

30 3 Review: 3D Transformations = z c b a z translatea,b,c) translatea,b,c) = cos sin sin cos z z ), Rotate = z c b a z scalea,b,c) scalea,b,c) cos sin sin cos ), Rotate cos sin sin cos ), Rotate z h hz h hz hz hz shear shearh h,hz hz,h h,hz hz,hz hz,hz hz)

31 Review: Composing Transformations Ta Tb = Tb Ta, but Ra Rb = Rb Ra and Ta Rb = Rb Ta translations commute rotations around same ais commute rotations around different aes do not commute rotations and translations do not commute 3

32 Review: Composing Transformations p= TRp which direction to read? right to left interpret operations wrt fied coordinates moving object left to right OpenGL pipeline ordering interpret operations wrt local coordinates changing coordinate sstem OpenGL updates current matri with postmultipl gltranslatef2,3,); glrotatef-9,,,); glvertef,,); specif vector last, in final coordinate sstem first matri to affect it is specified second-to-last 32

33 More: Composing Transformations p= TRp which direction to read? right to left interpret operations wrt fied coordinates moving object draw thing rotate thing b -9 degrees wrt origin translate it -2, -3) over 33

34 More: Composing Transformations p= TRp which direction to read? left to right interpret operations wrt local coordinates changing coordinate sstem translate coordinate sstem 2, 3) over rotate coordinate sstem 9 degrees wrt origin draw object in current coordinate sstem in OpenGL, cannot move object once it is drawn 34

35 General Transform Composition transformation of geometr into coordinate sstem where operation becomes simpler tpicall translate to origin perform operation transform geometr back to original coordinate sstem 35

36 Rotation About an Arbitrar Ais ais defined b two points translate point to the origin rotate to align ais with z-ais or or ) perform rotation undo aligning rotations undo translation 36

37 Arbitrar Rotation Y B A X Z C arbitrar rotation: change of basis given two orthonormal coordinate sstems XYZ and ABC A s location in the XYZ coordinate sstem is a, a, a z, ),...

38 Y B Arbitrar Rotation b, b, b z, ) B Y a, a, a z, ) A A X Z C arbitrar rotation: change of basis given two orthonormal coordinate sstems XYZ and ABC A s location in the XYZ coordinate sstem is a, a, a z, ),... Z C X c, c, c z, )

39 Y B Arbitrar Rotation b, b, b z, ) B Y a, a, a z, ) A A X Z C arbitrar rotation: change of basis given two orthonormal coordinate sstems XYZ and ABC A s location in the XYZ coordinate sstem is a, a, a z, ),... transformation from one to the other is matri R whose columns are A,B,C: a b c a RX) = b c = a a z b z c z,a,a z,) = A Z C X c, c, c z, )

40 Transformation Hierarchies 4

41 Transformation Hierarchies scene ma have a hierarch of coordinate sstems stores matri at each level with incremental transform from parent s coordinate sstem scene graph road stripe stripe2... car car2... w w2 w3 w4 4

42 Transformation Hierarch Eample world torso LUleg RUleg LUarm RUarm head LLleg RLleg LLarm RLarm Lfoot Rfoot Lhand Rhand trans.3,,) rotz, ) 42

43 Transformation Hierarch Eample 2 draw same 3D data with different transformations: instancing 43

44 Transformation Hierarchies Demo transforms appl to graph nodes beneath cs.brown..brown.edu/eploratories/freesoftware/catalogs/ scenegraphs.html 44

45 Transformation Hierarchies Demo transforms appl to graph nodes beneath cs.brown..brown.edu/eploratories/freesoftware/catalogs/ scenegraphs.html 45

46 Matri Stacks challenge of avoiding unnecessar computation using inverse to return to origin computing incremental T -> T 2 Object coordinates T ) T 2 ) T 3 ) World coordinates 46

47 Matri Stacks glpushmatri) D = C scale2,2,2) trans,,) glpopmatri) C D DrawSquare) C C C C glpushmatri) B A B A B A B A glscale3f2,2,2) gltranslate3f,,) DrawSquare) glpopmatri) 47

48 Modularization drawing a scaled square push/pop ensures no coord sstem change void drawblockfloat k) { glpushmatri); glscalefk,k,k); glbegingl_line_loop); glverte3f,,); glverte3f,,); glverte3f,,); glverte3f,,); glend); } glpopmatri); 48

49 Matri Stacks advantages no need to compute inverse matrices all the time modularize changes to pipeline state avoids incremental changes to coordinate sstems accumulation of numerical errors practical issues in graphics hardware, depth of matri stacks is limited tpicall 6 for model/view and about 4 for projective matri) 49

50 Transformation Hierarch Eample 3 F h F h F h F h F F h F h glloadidentit); gltranslatef4,,); glpushmatri); glrotatef45,,,); gltranslatef,2,); glscalef2,,); gltranslate,,); glpopmatri); F W 5

51 Transformation Hierarch Eample gltranslate3f,,); glrotatef,,,); DrawBod); glpushmatri); gltranslate3f,7,); DrawHead); glpopmatri); glpushmatri); gltranslate2.5,5.5,); glrotatef 2,,,); DrawUArm); gltranslate,-3.5,); glrotatef 3,,,); DrawLArm); glpopmatri);... draw other arm) 5

52 Hierarchical Modelling advantages define object once, instantiate multiple copies transformation parameters often good control knobs maintain structural constraints if well-designed limitations epressivit: not alwas the best controls can t do closed kinematic chains keep hand on hip can t do other constraints collision detection self-intersection walk through walls 52