Reading for This Module. Viewing. Using Transformations. Viewing. University of British Columbia CPSC 314 Computer Graphics Jan-Apr 2013

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1 Universit of British Columbia CPSC 34 Computer Graphics Jan-Apr 23 Tamara Munner Reaing for This Moule FCG Chapter 7 Viewing FCG Section 6.3. Winowing Transforms Viewing RB rest of Chap Viewing RB rest of App Homogeneous Coors RB Chap Selection an Feeback RB Sec Object Selection Using the Back Buffer in Chap Now That You Now ) 2 Viewing Using Transformations three was moelling transforms place objects within scene share worl) affine transformations viewing transforms place camera rigi bo transformations: rotate, translate projection transforms change tpe of camera projective transformation 3 4

2 Renering Pipeline Renering Pipeline Scene graph Object geometr Moelling Transforms Scene graph Object geometr Moelling Transforms result all vertices of scene in share 3D worl coorinate sstem Viewing Transform Viewing Transform Projection Transform Projection Transform 5 6 Renering Pipeline Renering Pipeline Scene graph Object geometr Moelling Transforms result scene vertices in 3D view camera) coorinate sstem Scene graph Object geometr Moelling Transforms result 2D screen coorinates of clippe vertices Viewing Transform Viewing Transform Projection Transform Projection Transform 7 8

3 Viewing an Projection Renering Pipeline nee to get from 3D worl to 2D image projection: geometric abstraction what ees or cameras o Geometr Database Moel/View Transform. Lighting Perspective Transform. Clipping two pieces viewing transform: where is the camera, what is it pointing at? perspective transform: 3D to 2D flatten to image Scan Conversion Teturing Depth Test Blening Framebuffer 9 Renering Pipeline OpenGL Transformation Storage Geometr Database Moel/View Transform. Lighting Perspective Transform. Clipping moeling an viewing store together possible because no intervening operations perspective store in separate matri Scan Conversion Teturing Depth Test Blening Framebuffer specif which matri is target of operations common practice: return to efault moelview moe after oing projection operations glmatrimoegl_modelview); glmatrimoegl_projection); 2

4 Coorinate Sstems result of a transformation names convenience animal: leg, hea, tail stanar conventions in graphics pipeline object/moelling worl camera/viewing/ee screen/winow raster/evice 3 Projective Renering Pipeline object worl viewing O2W W2V OCS V2C WCS moeling viewing projection transformation transformation transformation OCS - object/moel coorinate sstem WCS - worl coorinate sstem - viewing/camera/ee coorinate sstem CCS - clipping coorinate sstem NDCS - normalie evice coorinate sstem DCS - evice/ispla/screen coorinate sstem C2N perspective ivie N2D viewport transformation clipping CCS normalie evice NDCS evice DCS 4 Pee Viewing Transformation image plane WCS object worl viewing OCS WCS moeling transformation viewing transformation OCS Basic Viewing starting spot - OpenGL camera at worl origin probabl insie an object ais is up looking own negative ais wh? RHS with horiontal, vertical, out of screen translate backwar so scene is visible move istance = focal length where is camera in P template coe? 5 units back, looking own - ais M mo M cam OpenGL MoelView matri 5 6

5 Convenient Camera Motion rotate/translate/scale versus ee point, gae/lookat irection, up vector emo: Robins transformation, projection OpenGL Viewing Transformation glulookate,e,e,l,l,l,u,u,u) postmultiplies current matri, so to be safe: glmatrimoegl_modelview); glloaientit); glulookate,e,e,l,l,l,u,u,u) // now ok to o moel transformations 7 emo: Nate Robins tutorial projection 8 Convenient Camera Motion Placing Camera in Worl Coors: V2W rotate/translate/scale versus ee point, gae/lookat irection, up vector WCS ee Pee up lookat view Pref 9 treat camera as if it s just an object translate from origin to ee rotate view vector lookat ee) to w ais rotate aroun w to bring up into vw-plane WCS ee w v up Pee u lookat view Pref 2

6 Deriving V2W Transformation translate origin to ee T = e e e Deriving V2W Transformation rotate view vector lookat ee) to w ais w: normalie opposite of view/gae vector g w = ˆ g = g g WCS ee v up lookat view Pref WCS ee v up lookat view Pref w Pee u 2 w Pee u 22 Deriving V2W Transformation Deriving V2W Transformation rotate aroun w to bring up into vw-plane u shoul be perpenicular to vw-plane, thus perpenicular to w an up vector t v shoul be perpenicular to u an w u = t w v = w u t w WCS ee w v up Pee u lookat view Pref 23 rotate from WCS into uvw coorinate sstem with matri that has columns u, v, w u = t w t w e e T = e v = w u w = ˆ g = g g u v w u R = v w u v w M V2W =TR reminer: rotate from uvw to coor ss with matri M that has columns u,v,w 24

7 M V2W =TR V2W vs. W2V e e T = e u v w u R = v w u v w we erive position of camera as object in worl invert for glulookat: go from worl to camera M W2V =M V2W ) - =R - T - u u u e e R = v v v T = w w w e inverse is transpose for orthonormal matrices inverse is negative for translations M W2V =M V2W ) - = R- T - V2W vs. W2V u u u e u u u e u v M = v v e = v v v e v worl2view w w w e w w w e w u u u e u + e u + e u ) v M = v v e v + e v + e v ) W 2V w w w e w + e w + e w ) ) Moving the Camera or the Worl? Worl vs. Camera Coorinates Eample two equivalent operations move camera one wa vs. move worl other wa eample initial OpenGL camera: at origin, looking along - ais create a unit square parallel to camera at = - translate in b 3 possible in two was camera moves to = -3 Note OpenGL moels viewing in left-han coorinates camera stas put, but worl moves to -7 resulting image same either wa possible ifference: are lights specifie in worl or view coorinates? a C2 c b C a =,) W b =,) C = 5,3) W c =,) C2 =,3) C = 5,5) W W 27 28

8 Pinhole Camera Projections I ingreients bo, film, hole punch result picture Pinhole Camera theoretical perfect pinhole light shining through tin hole into ark space iels upsie-own picture Pinhole Camera non-ero sie hole blur: ras hit multiple points on film plane perfect pinhole one ra of projection actual pinhole multiple ras of projection film plane 3 film plane 32

9 Real Cameras Graphics Cameras pinhole camera has small aperture lens opening) minimie blur real pinhole camera: image inverte problem: har to get enough light to epose the film aperture image plane ee point solution: lens permits larger apertures permits changing istance to film plane without actuall moving it cost: limite epth of fiel where image is in focus lens epth of fiel computer graphics camera: convenient equivalent ee point center of projection image plane General Projection image plane nee not be perpenicular to view plane Perspective Projection our camera must moel perspective image plane ee point ee point image plane 35 36

10 Perspective Projection our camera must moel perspective Projective Transformations planar geometric projections planar: onto a plane geometric: using straight lines projections: 3D -> 2D aka projective mappings countereamples? Projective Transformations properties lines mappe to lines an triangles to triangles parallel lines o NOT remain parallel e.g. rails vanishing at infinit Perspective Projection project all geometr through common center of projection ee point) onto an image plane affine combinations are NOT preserve e.g. center of a line oes not map to center of projecte line perspective foreshortening)

11 Perspective Projection Basic Perspective Projection projection plane similar triangles P,, ) P,,) center of projection ee point) how tall shoul this bunn be? = but = nonuniform foreshortening not affine 4 42 Perspective Projection esire result for a point [,,, ] T projecte onto the view plane: =, = = =, = =, = what coul a matri look like to o this? Simple Perspective Projection Matri / / 43 44

12 45 Simple Perspective Projection Matri / / is homogenie version of where w = / / 46 Simple Perspective Projection Matri = / / / is homogenie version of where w = / / 47 Perspective Projection epressible with 44 homogeneous matri use previousl untouche bottom row perspective projection is irreversible man 3D points can be mappe to same,, ) on the projection plane no wa to retrieve the unique values 48 Moving COP to Infinit as COP moves awa, lines approach parallel when COP at infinit, orthographic view

13 Orthographic Camera Projection camera s back plane parallel to lens infinite focal length no perspective convergence just throw awa values p p = p p = p p Perspective to Orthographic transformation of space center of projection moves to infinit view volume transforme from frustum truncate prami) to parallelepipe bo) Frustum - Parallelepipe View Volumes specifies fiel-of-view, use for clipping restricts omain of store for visibilit test perspective view volume =left =top =bottom =-near =right orthographic view volume =left =-far =bottom =top =right =-near =-far Canonical View Volumes stanarie viewing volume representation perspective or front plane or = +/- back plane - front plane orthographic orthogonal parallel or - back plane

14 Wh Canonical View Volumes? permits stanariation clipping easier to etermine if an arbitrar point is enclose in volume with canonical view volume vs. clipping to si arbitrar planes renering projection an rasteriation algorithms can be reuse Normalie Device Coorinates convention viewing frustum mappe to specific parallelepipe Normalie Device Coorinates NDC) same as clipping coors onl objects insie the parallelepipe get renere which parallelepipe? epens on renering sstem Normalie Device Coorinates Unerstaning Z left/right =+/-, top/bottom =+/-, near/far =+/- Camera coorinates NDC right left = Frustum - = - = - = =-n =-f 55 ais flip changes coor sstem haneness RHS before projection ee/view coors) LHS after projection clip, norm evice coors) =left =bottom =top =right =-near =-far NDCS -,-,-),,) 56

15 Unerstaning Z Unerstaning Z near, far alwas positive in OpenGL calls glortholeft,right,bot,top,near,far); glfrustumleft,right,bot,top,near,far); glperspectivefov,aspect,near,far); perspective view volume =left =top =bottom =-near =right =-far orthographic view volume =left =bottom =top =right =-near =-far wh near an far plane? near plane: avoi singularit ivision b ero, or ver small numbers) far plane: store epth in fie-point representation integer), thus have to have fie range of values ) avoi/reuce numerical precision artifacts for istant objects Orthographic Derivation Orthographic Derivation scale, translate, reflect for new coor ss scale, translate, reflect for new coor ss = top = = a + b = bot = NDCS NDCS =left =top =right -,-,-),,) =left =top =right -,-,-),,) =bottom =-near =-far =bottom =-near =-far 59 6

16 Orthographic Derivation scale, translate, reflect for new coor ss = top = = a top + b = a + b = bot = = a bot + b 2 b = a top, b = a bot = top + b top bot a top = a bot 2 top b = ) = a bot a top ) top bot 2 = a bot + top ) top bot ) 2 top b = 2 top bot a = top bot top bot b = top bot 6 Orthographic Derivation scale, translate, reflect for new coor ss = top = = a + b = bot = 2 a = top bot =left =bottom =top =right =-near =-far top + bot b = top bot same iea for right/left, far/near 62 Orthographic Derivation scale, translate, reflect for new coor ss Orthographic Derivation scale, translate, reflect for new coor ss 2 right left P = 2 top bot 2 far near right + left right left top + bot top bot P far + near far near 2 right left P = 2 top bot 2 far near right + left right left top + bot top bot P far + near far near 63 64

17 Orthographic Derivation scale, translate, reflect for new coor ss Orthographic Derivation scale, translate, reflect for new coor ss 2 right left P = 2 top bot 2 far near right + left right left top + bot top bot P far + near far near 2 right left P = 2 top bot 2 far near right + left right left top + bot top bot P far + near far near Orthographic OpenGL glmatrimoegl_projection); glloaientit); glortholeft,right,bot,top,near,far); Demo Brown applets: viewing techniques parallel/orthographic cameras projection cameras catalogs/viewing_techniques.html 67 68

18 Asmmetric Frusta our formulation allows asmmetr wh bother? Projections II right left Frustum - right left Frustum - 69 =-n =-f 7 Asmmetric Frusta our formulation allows asmmetr wh bother? binocular stereo view vector not perpenicular to view plane Right Ee Left Ee Simpler Formulation left, right, bottom, top, near, far nonintuitive often overkill look through winow center smmetric frustum constraints left = -right, bottom = -top 7 72

19 Fiel-of-View Formulation FOV in one irection + aspect ratio w/h) etermines FOV in other irection also set near, far reasonabl intuitive) α Frustum - fov/2 fov/2 w h Perspective OpenGL glmatrimoegl_projection); glloaientit); glfrustumleft,right,bot,top,near,far); or glperspectivefov,aspect,near,far); =-n =-f Demo: Frustum vs. FOV Projective Renering Pipeline Nate Robins tutorial take 2): 75 object worl viewing O2W W2V OCS V2C WCS moeling viewing projection transformation transformation transformation OCS - object/moel coorinate sstem WCS - worl coorinate sstem - viewing/camera/ee coorinate sstem CCS - clipping coorinate sstem NDCS - normalie evice coorinate sstem DCS - evice/ispla/screen coorinate sstem C2N perspective ivie N2D viewport transformation clipping CCS normalie evice NDCS evice DCS 76

20 Projection Warp warp perspective view volume to orthogonal view volume rener all scenes with orthographic projection aka perspective warp Perspective Warp perspective viewing frustum transforme to cube orthographic renering of cube prouces same image as perspective renering of original frustum =α = = = Z Z Preistortion Projective Renering Pipeline 79 object worl viewing O2W W2V OCS V2C WCS moeling viewing projection transformation transformation transformation OCS - object/moel coorinate sstem WCS - worl coorinate sstem - viewing/camera/ee coorinate sstem CCS - clipping coorinate sstem NDCS - normalie evice coorinate sstem DCS - evice/ispla/screen coorinate sstem C2N perspective ivie N2D viewport transformation clipping CCS normalie evice NDCS evice DCS 8

21 8 Separate Warp From Homogeniation warp requires onl stanar matri multipl istort such that orthographic projection of istorte objects is esire persp projection w is change clip after warp, before ivie ivision b w: homogeniation CCS NDCS alter w / w projection transformation viewing normalie evice clipping perspective ivision V2C C2N 82 Perspective Divie Eample specific eample assume image plane at = - a point [,,,] T projects to [-/,-/,-/,] T [,,,-] T - 83 Perspective Divie Eample = ) = * * * * * +, / / / T alter w / w projection transformation perspective ivision after homogeniing, once again w= Perspective Normaliation matri formulation warp an homogeniation both preserve relative epth coorinate) ) * +, -. - = / / / / / ) ) * +, - - = p p p.. / / 2

22 Demo Perspective To NDCS Derivation Brown applets: viewing techniques parallel/orthographic cameras projection cameras catalogs/viewing_techniques.html =top =left =bottom =-near =right =-far NDCS -,-,-),,) Perspective Derivation Perspective Derivation simple eample earlier: = w / earlier: = w / complete: shear, scale, projection-normaliation complete: shear, scale, projection-normaliation E A = F B C D w ) E A = F B C D w ) 87 88

23 Perspective Derivation earlier: = w / complete: shear, scale, projection-normaliation E A = F B C D w ) 89 Recorrection: Perspective Derivation E A F B = C D w = F + B, w = E + A = F + B = C + D w= F + B =, = w = F + B, = F B, = F top near) B, = F top near B L/R sign error = left / w = = right / w = = top / w = = bottom / w = = near / w = = far / w = ais flip F + B F + B, =, w 9 Perspective Derivation similarl for other 5 planes 6 planes, 6 unknowns 2n r + l r l r l 2n t + b t b t b f + n) 2 fn f n f n 9 Projective Renering Pipeline object worl viewing O2W W2V OCS V2C WCS moeling viewing projection transformation transformation transformation OCS - object/moel coorinate sstem WCS - worl coorinate sstem - viewing/camera/ee coorinate sstem CCS - clipping coorinate sstem NDCS - normalie evice coorinate sstem DCS - evice/ispla/screen coorinate sstem C2N perspective ivie N2D viewport transformation clipping CCS normalie evice NDCS evice DCS 92

24 NDC to Device Transformation map from NDC to piel coorinates on ispla NDC range is = -..., = -..., = -... tpical ispla range: =...5, =...3 maimum is sie of actual screen - range ma an efault is, ), use later for visibilit - glviewport,,w,h); gldepthrange,); // epth = b efault NDC 5 3 viewport 93 Origin Location et more possibl confusing) conventions OpenGL origin: lower left most winow sstems origin: upper left then must reflect in when interpreting mouse position, have to flip our coorinates - - NDC 5 3 viewport 94 N2D Transformation general formulation reflect in for upper vs. lower left origin scale b with, height, epth translate b with/2, height/2, epth/2 FCG inclues aitional translation for piel centers at.5,.5) instea of,) - - NDC 5 height 3 with viewport NDC N2D Transformation with D with with 2 2 N + ) D height 2 height N 2 = height N +) N D = epth epth N 2 epth N +) reminer: NDC range is - to Displa range is to. gldepthrangen,f) can constrain further, but epth = is both ma an efault 5 height 3 with viewport 96

25 Device vs. Screen Coorinates viewport/winow location wrt actual ispla not available within OpenGL usuall on t care use relative information when hanling mouse events, not absolute coorinates coul get actual ispla height/with, winow offsets from OS loose use of terms: evice, ispla, winow, screen offset offset ispla viewport viewport height 3 ispla 768 ispla with 97 Projective Renering Pipeline glverte3f,,) object worl viewing O2W OCS WCS W2V V2C alter w glfrustum...) moeling viewing projection transformation transformation transformation clipping gltranslatef,,) glulookat...) C2N / w CCS glrotatefa,,,)... perspective OCS - object coorinate sstem ivision normalie glutinitwinowsiew,h) WCS - worl coorinate sstem N2D evice glviewport,,a,b) NDCS - viewing coorinate sstem viewport transformation CCS - clipping coorinate sstem evice NDCS - normalie evice coorinate sstem DCS DCS - evice coorinate sstem 98 viewing 4-space, W=) projection matri Coorinate Sstems clipping 4-space parallelepipe, with COP move backwars to infinit Perspective Eample tracks in : left =-, =- right =, =- view volume left = -, right = bot = -, top = near =, far = 4 ivie b w normalie evice 3-space parallelepipe) =- = ma- scale translate evice 3-space parallelipipe) =-4 =- real mipoint NDCS DCS ma- framebuffer 99 top view not shown) not shown)

26 Perspective Eample Perspective Eample 2n r + l r l r l 2n t + b t b t b f + n) 2 fn f n f n view volume left = -, right = bot = -, top = near =, far = 4 5/3 8 /3 = 5 /3 8/ 3 / w ND CS = / ND CS = / ND CS = / 3 8 /3 2 OCS2 OpenGL Eample object worl viewing O2W W2V OCS WCS moeling viewing transformation transformation CCS WCS OCS glmatrimoe GL_PROJECTION ); glloaientit); gluperspective 45,.,., 2. ); glmatrimoe GL_MODELVIEW ); glloaientit); gltranslatef.,., -5. ); glpushmatri) gltranslate 4, 4, ); W2O glutsoliteapot); glpopmatri); gltranslate 2, 2, ); W2O glutsoliteapot); V2C projection transformation clipping CCS transformations that are applie to object first are specifie last 3 Reaing for Net Time RB Chap Color FCG Sections FCG Chap 2 Color FCG Chap Visual Perception Color) 4

27 Fl Through The Lens: Roll/Pitch/Yaw Viewing: More Camera Motion 5 6 Viewing: Incremental Relative Motion how to move relative to current camera coorinate sstem? what ou see in the winow computation in coorinate sstem use to raw previous frame is simple: incremental change I to current C at time k, want p = I k I k- I k-2 I k-3... I 5 I 4 I 3 I 2 I Cp each time we just want to premultipl b new matri p =ICp but we know that OpenGL onl supports postmultipl b new matri p =CIp 7 Viewing: Incremental Relative Motion sneak trick: OpenGL moelview matri has the info we want ump out moelview matri from previous frame with glgetdoublev) C = current camera coorinate matri wipe the matri stack with glientit) appl incremental upate matri I appl current camera coor matri C must leave the moelview matri unchange b object transformations after our ispla call use push/pop using OpenGL for storage an calculation quering pipeline is epensive but safe to o just once per frame 8

28 Caution: OpenGL Matri Storage OpenGL internal matri storage is columnwise, not rowwise a e i m b f j n c g k o h l p opposite of stanar C/C++/Java convention possibl confusing if ou look at the matri from glgetdoublev) Viewing: Virtual Trackball interface for spinning objects aroun rag mouse to control rotation of view volume orbit/spin metaphor vs. fling/riving rolling glass trackball center at screen origin, surrouns worl hemisphere sticks up in, out of screen rotate ball = spin worl 9 Clarif: Virtual Trackball know screen click:,, ) want to infer point on trackball:,,) ball is unit sphere, so,, =. solve for ee Clarif: Trackball Rotation user rags between two points on image plane mouse own at i =, ), mouse up at i 2 = a, b) fin corresponing points on virtual ball p =,, ), p 2 = a, b, c) compute rotation angle an ais for ball ais of rotation is plane normal: cross prouct p p 2 amount of rotation θ from angle between lines p p 2 = p p 2 cos θ virtual ball hemisphere i =, ) screen plane i 2 = a, b) image plane,, ) screen plane 2

29 Clarif: Trackball Rotation fining location on ball corresponing to click on image plane ball raius r is screen plane, ) with/2, height/2) virtual ball hemisphere screen plane r=,, ), ) 3 Trackball Computation user efines two points place where first clicke p =,, ) place where release p 2 = a, b, c) create plane from vectors between points, origin ais of rotation is plane normal: cross prouct p - o) p 2 - o): p p 2 if origin =,,) amount of rotation epens on angle between lines p p 2 = p p 2 cos θ p p 2 = p p 2 sin θ compute rotation matri, use to rotate worl 4 Reaing Picking Re Book Selection an Feeback Chapter all Now That You Know Chapter onl Object Selection Using the Back Buffer 5 6

30 Interactive Object Selection move cursor over object, click how to ecie what is below? inverse of renering pipeline flow from piel back up to object ambiguit man 3D worl objects map to same 2D point four common approaches manual ra intersection bouning etents backbuffer color coing selection region with hit list Manual Ra Intersection o all computation at application level map selection point to a ra intersect ra with all objects in scene. avantages no librar epenence isavantages ifficult to program slow: work to o epens on total number an compleit of objects in scene 7 8 Bouning Etents keep track of ais-aligne bouning rectangles avantages conceptuall simple eas to keep track of boes in worl space Bouning Etents isavantages low precision must keep track of object-rectangle relationship etensions o more sophisticate boun bookkeeping first level: bo check. secon level: object check 9 2

31 Backbuffer Color Coing use backbuffer for picking create image as computational entit never isplae to user reraw all objects in backbuffer turn off shaing calculations set unique color for each pickable object store in table rea back piel at cursor location check against table avantages conceptuall simple variable precision isavantages Backbuffer Color Coing introuce 2 reraw ela backbuffer reaback ver slow 2 22 glcolor3f.,.,.); forint i = ; i < 2; i++) forint j = ; j < 2; j++) { glpushmatri); gltranslatefi*3.,,-j * 3.); glcolor3f.,.,.); glcalllistsnowman_ispla_list); glpopmatri); } Backbuffer Eample forint i = ; i < 2; i++) forint j = ; j < 2; j++) { glpushmatri); switch i*2+j) { case : glcolor3ub255,,);break; case : glcolor3ub,255,);break; case 2: glcolor3ub,,255);break; case 3: glcolor3ub25,,25);break; } } gltranslatefi*3.,,-j * 3.) glcalllistsnowman_ispla_list); glpopmatri); Select/Hit use small region aroun cursor for viewport assign per-object integer kes names) reraw in special moe store hit list of objects in region eamine hit list OpenGL support

32 Viewport small rectangle aroun cursor change coor ss so fills viewport wh rectangle instea of point? people aren t great at positioning mouse Fitts Law: time to acquire a target is function of the istance to an sie of the target Viewport nontrivial to compute invert viewport matri, set up new orthogonal projection simple utilit comman glupickmatri,,w,h,viewport),: cursor point w,h: sensitivit/slop in piels) push ol setup first, so can pop it later allow several piels of slop Rener Moes glrenermoemoe) GL_RENDER: normal color buffer efault GL_SELECT: selection moe for picking GL_FEEDBACK: report objects rawn) Name Stack again, names are just integers glinitnames) flat list glloanamename) or hierarch supporte b stack glpushnamename), glpopname can have multiple names per object 27 28

33 Hierarchical Names Eample forint i = ; i < 2; i++) { glpushnamei); forint j = ; j < 2; j++) { glpushmatri); glpushnamej); gltranslatefi*.,,j *.); glpushnamehead); glcalllistsnowmanheadl); glloanamebody); glcalllistsnowmanbodl); glpopname); glpopname); glpopmatri); } glpopname); } 29 Hit List glselectbufferbuffersie, *buffer) where to store hit list ata on hit, cop entire contents of name stack to output buffer. hit recor number of names on stack minimum an maimum epth of object vertices epth lies in the NDC range [,] format: multiplie b 2^32 - then roune to nearest int 3 Integrate vs. Separate Pick Function integrate: use same function to raw an pick simpler to coe name stack commans ignore in rener moe separate: customie functions for each potentiall more efficient can avoi rawing unpickable objects avantages faster Select/Hit OpenGL support means harware acceleration avoi shaing overhea fleible precision sie of region controllable fleible architecture custom coe possible, e.g. guarantee frame rate isavantages more comple 3 32

34 Hbri Picking select/hit approach: fast, coarse object-level granularit manual ra intersection: slow, precise eact intersection point hbri: both spee an precision use select/hit to fin object then intersect ra with that object OpenGL Precision Picking Hints gluunproject transform winow coorinates to object coorinates given current projection an moelview matrices use to create ra into scene from cursor location call gluunproject twice with same,) mouse location = near:,,) = far:,,) subtract near result from far result to get irection vector for ra use this ra for line/polgon intersection Projective Renering Pipeline following pipeline from top/left to glverte3f,,) bottom/right: moving object POV object worl viewing alter w O2W OCS WCS W2V V2C moeling transformation gltranslatef,,) glrotatefa,,,)... OCS - object coorinate sstem glutinitwinowsiew,h) WCS - worl coorinate sstem glviewport,,a,b) - viewing coorinate sstem CCS - clipping coorinate sstem NDCS - normalie evice coorinate sstem DCS - evice coorinate sstem viewing transformation glulookat...) projection transformation C2N / w perspective ivision N2D viewport transformation glfrustum...) clipping CCS normalie evice NDCS evice DCS 35 OCS2 OpenGL Eample go back from en of pipeline to beginning: coor frame POV object worl viewing clipping O2W W2V V2C OCS WCS CCS CCS WCS OCS moeling transformation viewing transformation glmatrimoe GL_PROJECTION ); glloaientit); gluperspective 45,.,., 2. ); glmatrimoe GL_MODELVIEW ); glloaientit); gltranslatef.,., -5. ); glpushmatri) gltranslate 4, 4, ); W2O glutsoliteapot); glpopmatri); gltranslate 2, 2, ); W2O glutsoliteapot); projection transformation V2W transformations that are applie to object first are specifie last 36

35 Coor Ss: Frame vs Point rea own: transforming between coorinate frames, from frame A to frame B OpenGL comman orer DCS D2N NDCS N2V V2W W2O WCS OCS rea up: transforming points, up from frame B coors to frame A coors ispla glviewport,,a,b) glfrustum...) normalie evice viewing glulookat...) worl glrotatefa,,,) object glverte3f,,) N2D V2N W2V O2W 37 pipeline interpretation Coor Ss: Frame vs Point is glulookat viewing transformation V2W or W2V? epens on which wa ou rea coorinate frames: V2W takes ou from view to worl coorinate frame points/objects: W2V point is transforme from worl to view coors when multipl b glulookat matri H2 uses the object/pipeline POV Q/4 is W2V glulookat) Q2/5-6 is V2N glfrustum) Q3/7 is N2D glviewport) 38