Prog 2, Kangaroo Hall of Fame, Midterm Review, (Interpolation if - PowerPoint PPT Presentation

University of British Columbia CPSC 314 Computer Graphics Jan-Apr 2005 Tamara Munzner Prog 2, Kangaroo Hall of Fame, Midterm Review, (Interpolation if time) Week 6, Wed Feb 9 http://www.ugrad.cs.ubc.ca/~cs314/Vjan2005

Program 2 Corrections/Clarifications  handin 314 proj2 (not 414)  ‘f’ not ‘s’ to toggle flat/smooth shading  ‘s’ already in use for camera  add: ‘t’ to toggle between randomly colored and grey terrain  makes it easier to check if lighting correct  add: ‘u’ to replace terrain with new randomly generated geometry  consider adding for a bit of extra credit:  ‘+/-’ toggle to increment/decrement abs cam speed 2

Program 2 Corrections/Clarifications  roll/yaw confusion  first para. correct, second para. wrong  left horiz drag = yaw, right horiz drag = roll  image + flying expertise courtesy of Matt Baumann 3

Program 2 Quick Demo 4

Review: Midpoint Algorithm  moving incrementally along x direction  draw at current y value, or move up to y+1?  check if midpoint between two possible pixel centers above or below line  candidates  top pixel: (x+1,y+1),  bottom pixel: (x+1, y)  midpoint: (x+1, y+.5)  check if midpoint above or below line  below: top pixel  above: bottom pixel 0 < dy  assume , slope x < x dx < 1 1 2 5

Review: Bresenham Algorithm y=y0; e=0; for (x=x0; x <= x1; x++) { draw(x,y);  all integer arithmetic if (2(e+dy) < dx) {  cumulative error function e = e+dy; } else { y=y+1; e=e+dy-dx; y=y0; eps=0 }} for ( int x = x0; x <= x1; x++ ){ draw(x,y); eps += dy; if ( (eps << 1) >= dx ){ y++; eps -= dx; } } 6

Review: Flood Fill  draw polygon edges, seed point, recursively set all neighbors until boundary is hit to fill interior  drawbacks: visit pixels up to 4x, per-pixel memory storage needed P 7

Review: Scanline Algorithms  set pixels inside polygon boundary along horizontal lines one pixel apart  use bounding box to speed up 3 1 5=0 2 P 4

Review: Edge Walking  basic idea:  draw edges vertically  interpolate colors down edges  fill in horizontal spans for each scanline  at each scanline, interpolate edge colors across span 9

Review: General Polygon Rasterization  idea: use a parity test for each scanline edgeCnt = 0; for each pixel on scanline (l to r) if (oldpixel->newpixel crosses edge) edgeCnt ++; // draw the pixel if edgeCnt odd if (edgeCnt % 2) setPixel(pixel); 10

Hall of Fame 11

But Wait, There’s More!  nice comment :)  “this project is fun, only one of the very few that I actually enjoyed. Too bad there's only one CG course in UBC =(  two fourth year CG courses await you!  424 Geometric Modelling  426 Animation 12

Midterm Review 13

Midterm Exam  Friday Feb 11 10am-10:50am  you may use one handwritten 8.5”x11” sheet  one side of page  no other notes, no books  nonprogrammable calculators OK  arrive on time!  sit every other seat, ID out in front of you  coats and bags in front of room 14

What’s Covered  transformations  viewing and projections  coordinate systems of rendering pipeline  lighting and shading  not scan conversion 15

Reading  FCS book, Red book  see web page for details  you can be tested on material in book but not covered in lecture  you can be tested on material covered in lecture but not covered in book 16

Old Exams Posted  see course web page 17

The Rendering Pipeline  pros and cons of pipeline approach Model/View Model/View Perspective Geometry Model/View Perspective Geometry Perspective Geometry Lighting Lighting Clipping Clipping Lighting Clipping Transform. Transform. Transform. Database Database Transform. Transform. Transform. Database Frame- Frame- Frame- Scan Scan Depth Scan Depth Depth Texturing Texturing Texturing Blending Blending Blending buffer buffer Conversion buffer Conversion Conversion Test Test Test 18

Transformations translate(a,b,c) translate(a,b,c) scale(a,b,c) scale(a,b,c) x ' 1 a x x ' a x                         y ' 1 b y y ' b y             = = z ' c z z ' 1 c z                         1 1 1 1 1 1             Rotate ( x , ) Rotate ( z , ) Rotate ( y , ) θ θ θ cos sin x ' 1 x cos sin θ − θ θ θ                     sin cos y ' cos sin y 1 θ − θ θ θ           = z ' sin cos z 1 sin cos         θ θ   − θ θ           1 1 1 1 1           19

Homogeneous Coordinates  x w x w ⋅  ⋅        y w y w w ⋅ w ⋅     w w         x x     w= 1 1 w=     y y     1 1         y y x x 20

Composing Transformations Ta Tb = Tb Ta, but Ra Rb Rb != != Rb Rb Ra and Ta Ra and Ta Rb Rb != != Rb Rb Ta Ta Ta Tb = Tb Ta, but Ra 21

Composing Transformations  example: rotation around arbitrary center 22

Composing Transformations  example: rotation around arbitrary center  step 1: translate coordinate system to rotation center 23

Composing Transformations  example: rotation around arbitrary center  step 2: perform rotation 24

Composing Transformations  example: rotation around arbitrary center  step 3: back to original coordinate system 25

Composing Transformations  rotation about a fixed point p’ = TRT -1 p  rotation around an arbitrary axis OpenGL:  considering frame vs. object D  p’ = DCBAp C frame B A draw p object 26

Transformation Hierarchies  hierarchies don’t fall apart when changed  transforms apply to graph nodes beneath 27

Matrix Stacks  push and pop matrix stack  avoid computing inverses or incremental xforms  avoid numerical error T 2 (x) T 2 (x) T 1 (x) T 1 (x) T 3 (x) T 3 (x) World coordinates World coordinates 28

Matrix Stacks D = C scale(2,2,2) trans(1,0,0) D = C scale(2,2,2) trans(1,0,0) glPushMatrix() () glPushMatrix glPopMatrix() () glPopMatrix C D C D DrawSquare() () DrawSquare C C C C C glPushMatrix() () C C glPushMatrix C glScale3f(2,2,2) glScale3f(2,2,2) B B B B B B B B glTranslate3f(1,0,0) glTranslate3f(1,0,0) A A A A A A A A DrawSquare() () DrawSquare glPopMatrix() () glPopMatrix 29

Transformation Hierarchies  example glTranslate3f(x,y,0); glTranslate3f(x,y,0); glRotatef( ,0,0,1); ( ,0,0,1); glRotatef θ 1 DrawBody(); (); DrawBody glPushMatrix(); (); glPushMatrix θ glTranslate3f(0,7,0); glTranslate3f(0,7,0); 2 DrawHead(); (); θ DrawHead 4 glPopMatrix(); (); glPopMatrix glPushMatrix(); (); glPushMatrix glTranslate(2.5,5.5,0); (2.5,5.5,0); glTranslate θ θ glRotatef( ,0,0,1); ( ,0,0,1); glRotatef θ θ 3 5 2 1 DrawUArm(); (); DrawUArm glTranslate(0,-3.5,0); (0,-3.5,0); glTranslate y y glRotatef( ,0,0,1); ( ,0,0,1); glRotatef θ 3 DrawLArm(); (); DrawLArm x x glPopMatrix(); (); glPopMatrix ... (draw other arm) ... (draw other arm) 30

Display Lists  reuse block of OpenGL code  more efficient than immediate mode  code reuse, driver optimization  good for static objects redrawn often  can’t change contents  not just for multiple instances  interactive graphics: objects redrawn every frame  nest when possible for efficiency 31

Double Buffering  two buffers, front and back  while front is on display, draw into back  when drawing finished, swap the two  avoid flicker 32

Projective Rendering Pipeline glVertex3f(x,y,z) glVertex3f(x,y,z) viewing/ object world camera alter w alter w WCS VCS WCS VCS OCS OCS glFrustum(...) (...) glFrustum projection projection modeling modeling viewing viewing transformation transformation transformation transformation transformation transformation clipping glTranslatef(x,y,z) (x,y,z) gluLookAt(...) (...) glTranslatef gluLookAt / w / w CCS CCS glRotatef( (th th,x,y,z) ,x,y,z) glRotatef perspective perspective .... .... normalized division division OCS - object coordinate system device glutInitWindowSize(w,h) (w,h) glutInitWindowSize WCS - world coordinate system glViewport(x,y,a,b) (x,y,a,b) glViewport NDCS NDCS viewport viewport VCS - viewing coordinate system transformation transformation CCS - clipping coordinate system device DCS DCS NDCS - normalized device coordinate system 33 DCS - device coordinate system

Projection  theoretical pinhole camera eye eye point point image image plane plane – image inverted, more convenient equivalent eye eye point point image image plane plane 34