CG OpenGL 3D viewing-course 7

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

3D viewing framework
• How to view 3D

• Some kind types of 3D projections

• How to do 3D views

Video Processing Lab 2

3D viewing device
• Virtual-Reality System-Amsterdam

R.G. Belleman, PhD, (application at the company of Sara)
3
http://www.science.uva.nl/research/scs/projects/visualisation/index.php?page=hardware

How to make it ?


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


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?

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

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.
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

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


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


3D viewing process

Clipping Project to Viewport
process projection plane transformation

Object Output
Clipping
(scene) - device -
(Camera) -
coordinate coordinate
coordinate


Classical views

Front elevation Elevation oblique Plan oblique

One-point perspective Three-point perspective
isometric

Three projections

• Introduction projection & views
• Axonometric projections
• Oblique projections
• Perspective projections


Parallel-projection views
• Orthographic projection:
show accurate dimensions
– Used in engineering and
architectural
side front
top


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)


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?


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


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)

Real case about
Axonometric projections
• Technically some games (strategy
or simulation) use this projection
to show object’s distance whether
near or far


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.


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


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

http://www.cmlab.csie.ntu.edu.tw/~robin/courses/

Projection tunnel

Clipping window projection plane view plane

Any point DOP VRP
CW ∞
PRP VPN
(umin,vmin)
(umav,vmax)


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)
http://www.cmlab.csie.ntu.edu.tw/~robin/courses/

Perspective projections

monitor

http://groups.csail.mit.edu/graphics/classes/6.837/F04/calendar.html

Projection tunnel

view plane
projection plane
VRP
Clipping window

PRP VPN
COP

COP


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


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


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)


Aspect ratio
(width)x (height)
Sony PSP 4.3” ST-International 19”

Panasonic 42 ”

80mmx15mm

500mmx485mm
~1:1

16:9


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


3D viewing process

Clipping Project to Viewport
process projection plane transformation

Object Output
Clipping
(scene) - device -
(Camera) -
coordinate coordinate
coordinate


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


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


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!!


One-point perspective
view

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

Two-point perspective
views

http://www.cityofmoorhead.com/whats_new/downtown/Perspective.jpg

Three-points views

37
The Music Lesson, c.1662-1665

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)


Positioning of the camera
frame
• Camera can be move by designer
– Follow the rotation steps COP
• glMatrixMode(GL_MODELVIEW)
• glLoadIdentity()
• glTranslatef()
• glRotatef()
• ….


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


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)


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


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)


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[]

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


reference
• http://graphics.im.ntu.edu.tw/~robin
/courses/
• http://www.cs.brown.edu/courses/cs
123/lectures.shtml


CG OpenGL 3D viewing-course 7

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