News. Projections and Picking. Transforming View Volumes. Projections recap. Basic Perspective Projection. Basic Perspective Projection

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1 Universit of British Columbia CPSC 44 Computer Graphics Projections and Picking Wed 4 Sep 3 project solution demo recap: projections projections 3 picking News Project solution eecutable available idea of what s epected no need to cop look and feel eactl Readings reminder Chapter 5 Tamara Munner Week 4, Wed 4 Sep 3 Tamara Munner Universit of British Columbia CPSC 44 Computer Graphics Projections recap Transforming View Volumes perspective view volume left top bottom -near right -far orthographic view volume left bottom top right -near -far (-,-,-) (,,) Tamara Munner 3 Week 4, Wed 4 Sep 3 Tamara Munner 4 Basic Perspective Projection P(,,d) d ' d ' d P(,,) also nonuniform foreshortening not affine d ' similar triangles but ' d Week 4, Wed 4 Sep 3 Tamara Munner 5 Basic Perspective Projection can epress as homogenous 44 matri! / d / d / d Week 4, Wed 4 Sep 3 Tamara Munner 6 d / d / d

2 Projective Transformations determining the matri representation need to observe 5 points in general position, e.g. [left,,,] T [-,,,] T [,top,,] T [,,,] T [,,-f,] T [,,,] T [,,-n,] T [,,-,] T [left*f/n,top*f/n,-f,] T [-,,,] T solve resulting equation sstem to obtain matri Week 4, Wed 4 Sep 3 Tamara Munner 7 OpenGL Orthographic Matri scale, translate, reflect for new coord ss right + left right left right left top + bot top bot top bot far + near far near far near Week 4, Wed 4 Sep 3 Tamara Munner 8 OpenGL Perspective Matri shear, scale, reflect for new coord ss near right + left right left right left near top + bot top bot top bot ( far + near) far near far near far near Week 4, Wed 4 Sep 3 Tamara Munner 9 Projection Normaliation viewing clipping normalied CCS device projection perspective division alter w distort such that orthographic projection of distorted objects is desired persp projection separate division from standard matri multiplies division: normaliation Week 4, Wed 4 Sep 3 Tamara Munner Universit of British Columbia CPSC 44 Computer Graphics Projections 3 Demos Brown Projections Demos are/catalogs/viewing_techniques.html Nate Robbins tutorial (take ): Tamara Munner Week 4, Wed 4 Sep 3 Tamara Munner

3 n r l n t b Perspective Eample r + l r l t + b ( t f + b n) f n fn f n view volume left -, right bot -, top near, far 4 5/ 3 8 / 3 Week 4, Wed 4 Sep 3 Tamara Munner 3 Perspective Eample tracks in : left -, - right, top view real midpoint ( not shown) view volume left -, right bot -, top near, far 4 ma- ma- ( not shown) Week 4, Wed 4 Sep 3 Tamara Munner 4 Perspective Eample 5 / 3 8 / 3 5 / 3 / / 8 / 3 Week 4, Wed 4 Sep 3 Tamara Munner Viewport Transformation generate piel coordinates map, from range (normalied device coordinates) to piel coordinates on the displa involves D scaling and translation displa viewport Week 4, Wed 4 Sep 3 Tamara Munner 6 (-,-) Viewport Transformation ( +) w ( +) h ( +) (,) OpenGL (,) glviewport(,,a,b); default: glviewport(,,w,h); a (w,h) Week 4, Wed 4 Sep 3 Tamara Munner 7 b Projective Rendering Pipeline glverte3f(,,) object world viewing OCS alter w WCS glfrustum(...) modeling viewing projection clipping gltranslatef(,,) glulookat(...) glrotatef(th,,,) CCS... perspective division OCS - object coordinate sstem normalied glutinitwindowsie(w,h) device WCS - world coordinate sstem glviewport(,,a,b) - viewing coordinate sstem viewport CCS - clipping coordinate sstem device - normalied device coordinate sstem - device coordinate sstem Week 4, Wed 4 Sep 3 Tamara Munner 8 3

4 Universit of British Columbia CPSC 44 Computer Graphics Picking Tamara Munner 9 Interactive Object Selection move cursor over object, click how to decide what is below? ambiguit man 3D world objects map to same D point four common approaches manual ra intersection bounding etents backbuffer color coding selection region with hit list Week 4, Wed 4 Sep 3 Tamara Munner Manual Ra Intersection do all computation at application level map selection point to a ra intersect ra with all objects in scene. no librar dependence Week 4, Wed 4 Sep 3 Tamara Munner Manual Ra Intersection do all computation at application level map selection point to a ra intersect ra with all objects in scene. no librar dependence difficult to program slow: work to do depends on total number and compleit of objects in scene Week 4, Wed 4 Sep 3 Tamara Munner Bounding Etents keep track of ais-aligned bounding rectangles conceptuall simple eas to keep track of boes in world space Bounding Etents low precision must keep track of object-rectangle relationship etensions do more sophisticated bound bookkeeping Week 4, Wed 4 Sep 3 Tamara Munner 3 Week 4, Wed 4 Sep 3 Tamara Munner 4 4

5 Backbuffer Color Coding use backbuffer for picking create image as computational entit never displaed to user redraw all objects in backbuffer turn off shading calculations set unique color for each pickable object store in table read back piel at cursor location check against table Backbuffer Color Coding conceptuall simple variable precision number of color bits must be adequate introduce redraw dela Week 4, Wed 4 Sep 3 Tamara Munner 5 Week 4, Wed 4 Sep 3 Tamara Munner 6 Backbuffer Eample glcolor3f(.f,.f,.f); for(int i ; i < ; i++) for(int j ; j < ; j++) { glpushmatri(); gltranslatef(i*3.,,-j * 3.); glcolor3f(.f,.f,.f); glcalllist(snowman_displa_list); glpopmatri(); for(int i ; i < ; i++) for(int j ; j < ; j++) { glpushmatri(); switch (i*+j) { case : glcolor3ub(55,,);break; case : glcolor3ub(,55,);break; case : glcolor3ub(,,55);break; case 3: glcolor3ub(5,,5);break; gltranslatef(i*3.,,-j * 3.) glcalllist(snowman_displa_list); glpopmatri(); Select/Hit use small region around cursor for viewport assign per-object integer kes (names) redraw in special mode store hit list of objects in region eamine hit list OpenGL support Week 4, Wed 4 Sep 3 Tamara Munner 7 Week 4, Wed 4 Sep 3 Tamara Munner 8 Viewport small rectangle around cursor change coord ss so fills viewport wh rectangle instead of point? people aren t great at positioning mouse Fitts s Law: time to acquire a target is function of the distance to and sie of the target allow several piels of slop Viewport trick to compute invert viewport matri, set up new orthogonal projection simple utilit command glupickmatri(,,w,h,viewport),: cursor point w,h: sensitivit/slop (in piels) push old setup first, so can pop it later Week 4, Wed 4 Sep 3 Tamara Munner 9 Week 4, Wed 4 Sep 3 Tamara Munner 3 5

6 Render Modes glrendermode(mode) GL_RENDER: normal color buffer default GL_SELECT: selection mode for picking (GL_FEEDBACK: report objects drawn) Name Stack names are just integers glinitnames() flat list glloadname(name) or hierarch supported b stack glpushname(name), glpopname can have multiple names per object Week 4, Wed 4 Sep 3 Tamara Munner 3 Week 4, Wed 4 Sep 3 Tamara Munner 3 Hierarchical Names Eample for(int i ; i < ; i++) { glpushname(i); for(int j ; j < ; j++) { glpushmatri(); glpushname(j); gltranslatef(i*.,,j *.); glpushname(head); glcalllist(snowmanheaddl); glloadname(body); glcalllist(snowmanboddl); glpopname(); glpopname(); glpopmatri(); glpopname(); Week 4, Wed 4 Sep 3 Tamara Munner 33 Hit List glselectbuffer(buffersie, *buffer) where to store hit list data on hit, cop entire contents of name stack to output buffer. hit record number of names on stack minimum and minimum depth of object vertices depth lies in the -buffer range [,] multiplied b ^3 - then rounded to nearest int Week 4, Wed 4 Sep 3 Tamara Munner 34 Separate Pick Function? use same function to draw and pick simpler to code name stack commands ignored in render mode customie functions for each potentiall more efficient can avoid drawing unpickable objects Week 4, Wed 4 Sep 3 Tamara Munner 35 Select/Hit faster OpenGL support means hardware accel onl do clipping work, no shading or rasteriation fleible precision sie of region controllable fleible architecture custom code possible, e.g. guaranteed frame rate more comple Week 4, Wed 4 Sep 3 Tamara Munner 36 6