CG OpenGL 3D viewing-course 7
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The document discusses 3D viewing frameworks and how to generate 3D views of objects and scenes by setting up a camera position and orientation, projecting object descriptions onto a view plane using different projection types like parallel, perspective, and oblique projections, and transforming the view for output. It also covers topics like depth cueing, aspect ratios, and the steps involved in the 3D viewing process using computer graphics.
![Inquiring about values in
a matrix in OpenGL
• gluLookAt(4,4,4,0,1,0,0,1,0);
– Eye: (4,4,4), look: (0,1,0), up: (0,1,0)
n = eye-look ux uy uz dx
u = upxn
v vy vz dy
V x
v = nxu nx ny nz dz
(dx,dy,dz)=(-eye·unor, -eye·vnor, - 0 0 0 1
eye·nnor)
– To see what is stored in the modelview matrix
• Define an array GLFloat mat[16]
• Use glGetFloatv(GL_MODELVIEW_MATRIX,mat)
mat: matT = V Modelview
matrix will
copy to mat[]
Video Processing Lab 44
臺灣師範大學數位媒體中心視訊處理研究室](https://image.slidesharecdn.com/cg-3dviewing-course7-111015003853-phpapp01/85/CG-OpenGL-3D-viewing-course-7-44-320.jpg)
CG OpenGL 3D viewing-course 7
- 1. 3D Viewing Chen Jing-Fung (2006/12/1) Assistant Research Fellow, Digital Media Center, National Taiwan Normal University Video Processing Lab 臺灣師範大學數位媒體中心視訊處理研究室 Ch7: Computer Graphics with OpenGL 3th, Hearn Baker Ch5: Interactive Computer Graphics 3th, Addison Wesley
- 2. 3D viewing framework • How to view 3D • Some kind types of 3D projections • How to do 3D views Video Processing Lab 2 臺灣師範大學數位媒體中心視訊處理研究室
- 3. 3D viewing device • Virtual-Reality System-Amsterdam R.G. Belleman, PhD, (application at the company of Sara) 3 Video Processing Lab http://www.science.uva.nl/research/scs/projects/visualisation/index.php?page=hardware 臺灣師範大學數位媒體中心視訊處理研究室
- 4. How to make it ? Video Processing Lab 4 臺灣師範大學數位媒體中心視訊處理研究室
- 5. 2D -> 3D • 2D graphics application and viewing 2D view operations transfer positions no parallax – The world-coordinate plane -> pixel positions output plane – Rectangular boundaries for clipping window • Clip a scene and maps it to device coordinate monitor • 3D viewing (more choices than 2D) – How to construct a scene – How to generate views it on output device Video Processing Lab 5 臺灣師範大學數位媒體中心視訊處理研究室
- 6. Two eyes game • Two eyes = two separate vision angle – Close one eye – Put your free finger to aim “bowling” – Switch to close another eye Two eyes vision angle is same? Video Processing Lab 6 http://www.vision3d.com/stereo.html 臺灣師範大學數位媒體中心視訊處理研究室
- 7. How to see 3D? • Two eyes can see 3D – Two images be captured by two eyes – Images arrive simultaneously in the back of the brain – They are united into one picture brain A key point of 3D view is depth !! an object’s solid in three spatial dimensions: width, height and depth -- x, y and z. Video Processing Lab 7 http://www.vision3d.com/stereo.html 臺灣師範大學數位媒體中心視訊處理研究室
- 8. Overview 3D viewing concepts • Object in 3D scene – A set of surfaces (object descriptions) • Generate views of an object’s surface features – Closed boundary around the object • Provide routines – displaying internal components – Cross-sectional views of a solid object Video Processing Lab 8 臺灣師範大學數位媒體中心視訊處理研究室
- 9. Viewing 3D scene • Set up a coordinate reference for the viewing - “camera” parameters – The coordinate reference defines • Position and orientation for a view plane or projection plane – Object descriptions • Transferred to viewing coordinates • Projected onto the view plane Video Processing Lab 9 臺灣師範大學數位媒體中心視訊處理研究室
- 10. 3D viewing process Clipping Project to Viewport process projection plane transformation Object Output Clipping (scene) - device - (Camera) - coordinate coordinate coordinate Video Processing Lab 10 臺灣師範大學數位媒體中心視訊處理研究室
- 11. Classical views Front elevation Elevation oblique Plan oblique One-point perspective Three-point perspective isometric Video Processing Lab 11 臺灣師範大學數位媒體中心視訊處理研究室
- 12. Three projections • Introduction projection & views • Axonometric projections • Oblique projections • Perspective projections Video Processing Lab 12 臺灣師範大學數位媒體中心視訊處理研究室
- 13. Parallel-projection views • Orthographic projection: show accurate dimensions – Used in engineering and architectural side front top Video Processing Lab 13 臺灣師範大學數位媒體中心視訊處理研究室
- 14. multi-view orthographic Plan view • projection plane is (top view) parallel to one of the object’s principal faces. • display at least three views- such as the front, top and right side view front view (right view) Video Processing Lab 14 臺灣師範大學數位媒體中心視訊處理研究室
- 15. Axonometric projections • Preserve how many views direct by original object **projected lines is parallel but angles are not • Foreshortening: an object appears compressed plane (projected) which extracted by a particular viewpoint • Dimetric view • Two different foreshortening ratios • Trimetric view (general case) • Three different foreshortening ratios • Isometric view • Symmetrical projection of three principal directions Q: Symmetrical two principal faces? Video Processing Lab 15 臺灣師範大學數位媒體中心視訊處理研究室
- 16. Projected vs. original • Lines are scaled and can find scale ratios • Angles are not related projected • • View box-like object on projection plane • Not look real: – No matter how objectproj is near or far, it has the same projection axonometric views are used extensively in architectural and mechanical design Video Processing Lab 16 臺灣師範大學數位媒體中心視訊處理研究室
- 17. Clipping window projection • Orthogonal-projection view volume (view plane) Clipping window – 2D rectangular clipping Far plane window -> 3D near-far Near plane clipping planes (box-like) Normalized view volume Orthogonal-projection yview (xwmax,ywmax,zfar) ynorm znorm view volume (1,1,1) zview xview Project xnorm (xwmin,ywmin,znear) (-1,-1,-1) glMatrixMode (GL_PROJECTION) glLoadIdentity() glOrtho(xwmin,xwmax,ywmin,ywmax,znear,zfar) Video Processing Lab 17 臺灣師範大學數位媒體中心視訊處理研究室
- 18. Real case about Axonometric projections • Technically some games (strategy or simulation) use this projection to show object’s distance whether near or far Video Processing Lab 18 臺灣師範大學數位媒體中心視訊處理研究室
- 19. Oblique projections • Oblique views are the most general views – Can make an arbitrary angle with projection plane • Angles can be preserved – projected • The most difficult to construct by hand • Bellows camera is flexible to produce approximations to parallel oblique views **Oblique view are somewhat unnatural. Video Processing Lab 19 臺灣師範大學數位媒體中心視訊處理研究室
- 20. Clipping – Oblique projections • CG-Oblique projections – Objectworld -> objectrotate -> objectproj Clipping window Clipping window View plane Near plane Transformed Oblique view volume Shear View volume Vp transformation Far plane Oblique-projection view volume Moblique,norm=Mortho,norm * Moblique Video Processing Lab 20 臺灣師範大學數位媒體中心視訊處理研究室
- 21. Orthogonal projection vectors • DOP = -VPN VUP: view-up vector to this plane View plane DOP: projection’s direction VPN: view-plane normal VPN: view-plane normal • Vector u & v in plane A v Plane A – viewPN=uxv/det|uv| u Video Processing Lab 21 http://www.cmlab.csie.ntu.edu.tw/~robin/courses/ 臺灣師範大學數位媒體中心視訊處理研究室
- 22. Projection tunnel Clipping window projection plane view plane Any point DOP VRP CW ∞ PRP VPN (umin,vmin) (umav,vmax) Video Processing Lab 22 臺灣師範大學數位媒體中心視訊處理研究室
- 23. Orthogonal projection - Oblique Clipping window View Near plane Transformed Oblique- Oblique view projection view Shear volume Vp volume Far • Translate the VRPclip to the origin • Rotate VRC to projected plane (PRP) • Shear that let the DOP become parallel to the projected plane (PRPshear) • Translate and scale into the parallel-projection normal view volume No =Sp_prp Tp_prp SHprp Rvrc T(VRP) Video Processing Lab 23 http://www.cmlab.csie.ntu.edu.tw/~robin/courses/ 臺灣師範大學數位媒體中心視訊處理研究室
- 24. Perspective projections monitor Video Processing Lab 24 http://groups.csail.mit.edu/graphics/classes/6.837/F04/calendar.html 臺灣師範大學數位媒體中心視訊處理研究室
- 25. Projection tunnel view plane projection plane VRP Clipping window PRP VPN COP COP Video Processing Lab 25 臺灣師範大學數位媒體中心視訊處理研究室
- 26. Depth cueing • Depth information is important in 3D scene – Easy identify the particular viewing direction • The front and back of each displayed object No depth information Downward from above Upward from below base vertex Video Processing Lab 26 臺灣師範大學數位媒體中心視訊處理研究室
- 27. Perspective-projection view volume Rectangular view Frustum window view volume Projection reference point θ (xprp,yprp,zvp) (xprp,yprp,zprp) Near clipping Far clipping plane plane Video Processing Lab 27 臺灣師範大學數位媒體中心視訊處理研究室
- 28. OpenGL Perspective- Projection (p.p) Function θ/2 • Symmetric p.p function View plane gluPerspective(theta, aspect, dnear, dfar) zprp-zvp • Four parameters: double or float point • Theta (field-of-view angle): angle between top and bottom • Aspect ratio: (width/height) • dnear & dfar: negative, because clipping plane must always be somehow along the –zview axis (behind the view position) Video Processing Lab 28 臺灣師範大學數位媒體中心視訊處理研究室
- 29. Aspect ratio (width)x (height) Sony PSP 4.3” ST-International 19” Panasonic 42 ” 80mmx15mm 500mmx485mm ~1:1 16:9 Video Processing Lab 29 臺灣師範大學數位媒體中心視訊處理研究室
- 30. OpenGL p.p function (2) Frustum view volume • General p.p function gluFrustum(xwmin, xwmax, ywmin, ywmax, zwnear, zwfar) Near plane Far plane • All parameters: double or float point numbers • zwnear & zwfar : negative (behind the view position) as tha same as dnear & dfar • Clipping window can be specified anywhere on the near plane. – Xwmin = -xwmax & ywmin = -ywmax Video Processing Lab 30 臺灣師範大學數位媒體中心視訊處理研究室
- 31. 3D viewing process Clipping Project to Viewport process projection plane transformation Object Output Clipping (scene) - device - (Camera) - coordinate coordinate coordinate Video Processing Lab 31 臺灣師範大學數位媒體中心視訊處理研究室
- 32. 3D scene process by CG • Choose a viewing position (camera) – Point to where camera (camera position) • Choose a viewing position (object) – Display a front, back, side, top, or bottom view Video Processing Lab 32 臺灣師範大學數位媒體中心視訊處理研究室
- 33. Synthetic camera • First, pick a position (object fixed) COP – Middle of a group of objects – Inside a single object • Camera located in COP – Focus on camera’s motion – Rotate it – Choose a parallel or perspective projection • Eliminate parts of a scene along the line of sight Video Processing Lab 33 臺灣師範大學數位媒體中心視訊處理研究室
- 34. Projections (views) Perspective projection (views): •center of projection (COP) Parallel projection (views): •More realistic like •Direction of projection (DOP) our eyes and camera lens •View space: near & far object projector object projector Projection plane finite COP infinite COP Projection plane **depth!! Video Processing Lab 34 臺灣師範大學數位媒體中心視訊處理研究室
- 35. One-point perspective view Video Processing Lab 35 http://www.richardmurphyarchitects.com/projects/images 臺灣師範大學數位媒體中心視訊處理研究室
- 36. Two-point perspective views Video Processing Lab 36 http://www.cityofmoorhead.com/whats_new/downtown/Perspective.jpg 臺灣師範大學數位媒體中心視訊處理研究室
- 37. Three-points views 37 The Music Lesson, c.1662-1665 Video Processing Lab 臺灣師範大學數位媒體中心視訊處理研究室
- 38. Multi-perspective views • Advantage – Objects can display multi-view and show the relation about near and far • Look realistic • Disadvantage – Object has not parallel lines – Difficult by hand ( easy by computer design) Video Processing Lab 38 臺灣師範大學數位媒體中心視訊處理研究室
- 39. Positioning of the camera frame • Camera can be move by designer – Follow the rotation steps COP • glMatrixMode(GL_MODELVIEW) • glLoadIdentity() • glTranslatef() • glRotatef() • …. Video Processing Lab 39 臺灣師範大學數位媒體中心視訊處理研究室
- 40. VPN VUP VRP v Two viewing APIs u Camera frame • Only one view direction is a little unsatisfying – Starting points in the world frame • Describe the camera’s position and orientation in this • glLoadIdentity() -> set_view_reference_point(x,y,z) • The orientation of the camera divide two parts – VPN: set_view_plane_normal (xn, yn, zn) – VUP: set_view_up(xvup, yvup,zvup) • Do transformation operators Video Processing Lab 40 臺灣師範大學數位媒體中心視訊處理研究室
- 41. Look-at function • A more direct method is appropriate the camera (xref, yref, zref) gluLookAt(xeye, yeye, zeye, xref, yref, zref, xup, yup, zup) (xup, yup, zup) • (xeye, yeye, zeye) = world- coordinate position P0 Ex: (0,0,0) camera (xeye, yeye, zeye) • VUP= (xup, yup, zup) Ex: y-axis (0,1,0) monitor • VRP=(xref, yref, zref) = projection position Pref Ex: (0,0,-1) • VPN=P0-Pref **viewing direction is along to any axis (maybe z-axis or –z-axis) Video Processing Lab 41 臺灣師範大學數位媒體中心視訊處理研究室
- 42. Set up a typical camera • Cameras are often set to “look down” on a scene from some nearby position • Ex: eye=(4,4,4), look=(0,1,0), upward up=(0,1,0), view volume width=6.4 & height=4.8 (aspect ratio = 640/480), near =1 & far =50 glMatixMode(GL_PROJECTION);//set the view volume y glLoadIdentity(); look at glOrtho(-3.2,3.2,-2.4,2.4, 1,50);//or use Frustumview volume z glMatrixMode(GL_MODELVIEW);//place and aim the camera glLoadIdentity(); gluLookAt(4,4,4,0,1,0,0,1,0); x Video Processing Lab 42 臺灣師範大學數位媒體中心視訊處理研究室
- 43. What does gluLookAt() do? • gluLookAt() builds a matrix (V) that converts world coordinates into eye coordinates (eyeu,v,n). n = eye-look up u = upxn v v = nxu n u gluLookAt() ux uy uz dx eye matrix V vx vy vz dy nx ny nz dz 0 0 0 1 look (dx,dy,dz)=(-eye·unor, -eye·vnor, -eye·nnor) Video Processing Lab 43 臺灣師範大學數位媒體中心視訊處理研究室
- 44. Inquiring about values in a matrix in OpenGL • gluLookAt(4,4,4,0,1,0,0,1,0); – Eye: (4,4,4), look: (0,1,0), up: (0,1,0) n = eye-look ux uy uz dx u = upxn v vy vz dy V x v = nxu nx ny nz dz (dx,dy,dz)=(-eye·unor, -eye·vnor, - 0 0 0 1 eye·nnor) – To see what is stored in the modelview matrix • Define an array GLFloat mat[16] • Use glGetFloatv(GL_MODELVIEW_MATRIX,mat) mat: matT = V Modelview matrix will copy to mat[] Video Processing Lab 44 臺灣師範大學數位媒體中心視訊處理研究室
- 45. Homework & next class • Homework – A. Multi-points views, B. 3D projection • create one polyhedron such as cube or others • A. multi-points views and observe what happen – Perspective and Axonometric projections • B. 3D projection – Change x, y, z (axis) projection and observe what happen • Next class will introduce how to construct 3D object Video Processing Lab 45 臺灣師範大學數位媒體中心視訊處理研究室
- 46. reference • http://graphics.im.ntu.edu.tw/~robin /courses/ • http://www.cs.brown.edu/courses/cs 123/lectures.shtml Video Processing Lab 46 臺灣師範大學數位媒體中心視訊處理研究室