University of British Columbia CPSC 314 Computer Graphics Jan-Apr Tamara Munzner. Viewing 4. Page 1

Transcription

1 University of British Columbia CPSC 34 Computer Graphics Jan-Apr 206 Tamara Munzner Viewing 4 Page

2 2 Projective Rendering Pipeline object world viewing O2W OCS WCS W2V VCS modeling OCS - object/model coordinate system WCS - world coordinate system viewing VCS - viewing/camera/eye coordinate system CCS - clipping coordinate system NDCS - normalized device coordinate system DCS - device/display/screen coordinate system V2C projection C2N perspective divide N2D viewport clipping CCS normalized device NDCS device DCS 2 Page 2

3 3 NDC to Device Transformation map from NDC to pixel coordinates on display NDC range is x = -..., y = -..., z = -... typical display range: x = , y = maximum is size of actual screen z range max and default is (0, ), use later for visibility - gl.viewport(0,0,w,h); gl.depthrange(0,); // depth = by default NDC y x x 500 y viewport 3 Page 3

4 4 Origin Location yet more (possibly confusing) conventions GL origin: lower left most window systems origin: upper left then must reflect in y when interpreting mouse position, have to flip your y coordinates - - NDC y x x 500 y viewport 4 Page 4

5 5 N2D Transformation general formulation reflect in y for upper vs. lower left origin scale by width, height, depth translate by width/2, height/2, depth/2 FCG includes additional translation for pixel centers at (.5,.5) instead of (0,0) y 0 0 x 500 y height - - NDC x 300 viewport width 5 Page 5

6 6 - - NDC y N2D Transformation é width ù é width ù é width (x é x D ù N + ) - ù 2 2 y D 0 0 height - 2 é 0 0 0ù é x N ù 2 height height( = y y N +) - N 2 2 z D 2 = depth depth z N 2 depth(z N +) ë û 2 2 ë û ë û 2 ë û ë û ë û reminder: NDC z range is - to x Display z range is 0 to. gl.depthrange(n,f) can constrain further, but depth = is both max and default 0 x y height 300 width viewport 6 Page 6

7 7 Device vs. Screen Coordinates viewport/window location wrt actual display not available within GL usually don t care use relative information when handling mouse events, not absolute coordinates could get actual display height/width, window offsets from OS loose use of terms: device, display, window, screen... 0 x x y y offset 0 y x offset display viewport viewport height 300 display 768 display width 7 Page 7

8 8 Projective Rendering Pipeline vertex(x,y,z) object world viewing O2W OCS WCS W2V VCS V2C modeling translatef(x,y,z) lookat(...) rotatef(a,x,y,z)... OCS - object coordinate system WCS - world coordinate system VCS - viewing coordinate system CCS - clipping coordinate system NDCS - normalized device coordinate system DCS - device coordinate system viewing alter w projection C2N canvas.{w,h} viewport(x,y,a,b) / w perspective division N2D viewport frustum(...) clipping CCS normalized device NDCS device DCS 8 Page 8

9 9 Questions? 9 Page 9

10 Coordinate Systems viewing (4-space, W=) projection matrix clipping (4-space parallelepiped, with COP moved backwards to infinity divide by w normalized device (3-space parallelepiped) scale & translate device (3-space parallelipiped) framebuffer 0 Page 0 0

11 Perspective Example tracks in VCS: left x=-, y=- right x=, y=- view volume left = -, right = bot = -, top = near =, far = 4 x=- x= ymax- z=-4 z=- real midpoint x NDCS 0 0 DCS xmax- z VCS top view (z not shown) (z not shown) Page

12 2 Perspective Example é 2n r + l ù 0 0 r - l r - l 2n t + b 0 0 t - b t - b -( f + n) -2 fn 0 0 f - n f - n ë û view volume left = -, right = bot = -, top = near =, far = 4 é ù /3-8 /3 ë û 2 Page 2

13 3 Perspective Example é ù é - = -5z VCS /3-8/ 3 ë û ë -z VCS ù é ù - -5/ 3-8/3 z VCS - û ë û / w x ND CS = -/ z VCS y ND CS = /z VCS z ND CS = z VCS 3 Page 3

14 4 Projective Rendering Pipeline following pipeline from top/left to glvertex3f(x,y,z) bottom/right: moving object POV object world viewing alter w O2W OCS WCS W2V VCS V2C modeling gltranslatef(x,y,z) glrotatef(a,x,y,z)... OCS - object coordinate system glutinitwindowsize(w,h) WCS - world coordinate system glviewport(x,y,a,b) VCS - viewing coordinate system CCS - clipping coordinate system NDCS - normalized device coordinate system DCS - device coordinate system viewing glulookat(...) projection C2N / w perspective division N2D viewport glfrustum(...) clipping CCS normalized device NDCS device DCS 4 Page 4

15 5 gl.viewport(0,0,w,h); OpenGL Example go back from end of pipeline to beginning: coord frame POV! object world viewing clipping O2W W2V VCS V2C OCS WCS CCS CCS modeling viewing projection VCS THREE.PerspectiveCamera(view angle, aspect, near, far) WCS OCS u_xformmatrix = Identidy() gl.uniformmatrix4fv(u_xformmatrix, false, xformmatrix); torsogeometry.applymatrix(u_xformmatrix ); var torso = new THREE.Mesh(torsoGeometry,normalMaterial); scene.add(torso); 5 Page 5

16 6 Coord Sys: Frame vs Point read down: transforming between coordinate frames, from frame A to frame B OpenGL command order DCS D2N NDCS N2V V2W W2O VCS WCS OCS read up: transforming points, up from frame B coords to frame A coords display gl.viewport(x,y,a,b) glfrustum(...) normalized device viewing glulookat(...) world glrotatef(a,x,y,z) object glvertex3f(x,y,z) N2D V2N W2V O2W 6 pipeline interpretation Page 6

17 7 Questions? 7 Page 7