3D OpenGL
Introduction
Topics
:
3D graphic modeling approach
1.
Hierarchical approach
2.
Drawing 3D models
using
:
2
D
surface
Volume
Function
approximations
3.
Matrix approach
:
3D points
Homogenous
coordinates
Matrix Multiplication
Affecting models
Communicating
with hardware
by
using a state machine:
1.
The sequence of displaying
a 3D point
.
2.
Projection mod
e
–
view port definition
.
3.
View mod
e
–
placing world
models
.
OpenGL drawing tools
1.
Drawing 3D models
2.
3D realization tools
3D drawing graphic

advanced
3D graphic
:
M
odeling approach
1.
Hierarchical approach
In order to
handle
complex model
we will split
it in
to
small
and
basic
models
.
Each
of these models
is
drawn with
respect to the origin
(0,0,0)
.
Using the basic models, we
will
compose
the required complex
model
by positioning the basic
models with respect to the center of
the final model.
2.
Common methods for 3D
modeling
:
Basic
3D models
approximations
–
sphere, to
r
us
2
D
surface
–
way
meshes
–
dragon
statue
surface
Volume
–
human
brain
–
MRI
–
additional
un
pre
pared
cut
Function
approximations
–
waving flag
animation
3.
Positioning by m
atrix
approach:
3D points
–
As
vectors (x,y,z).
Homogenous
coordinates
–
3D
points with a forth
coordinate of which
value is equal to 1.
Matrix Multiplication
–
Using
homogenous coo
rdinates, each
composition of
geometrical
function
s
, such as
“
rotate
”
,
“scale”
and
“
translate
”
, is
expressible as a
multiplication of
the function’s corresponding
matrices.
Affecting models
–
If a complex
model is represented by a
composition of basic m
odels and
their respected matrices, and we
want to apply geometrical
functions to that model, we may
manipulate the complex model by
apply
ing
a single matrix to all of
the basic models of which th
e
complex model is comprised.
Communicating
with hardware b
y
using a state
machine:
1.
The sequence of displayin
g a
3D point
–
A point undergoes
two major stages before
presented on the screen: The
modeling stage, in which it is
applied by the current
modeling matrix.
In the
second stage, the Projection
stage, the mo
dified point is
projected to the screen by the
current projection matrix.
2.
Project
ion mode
–
view port
definition
–
The graphic
hardware contains a matrix
which is used to project 3D
points onto the screen.
We
can modify this matrix while
in the “Projection
” state.
In
or
der to enter this state, we
use the
glMatrixMode
(
GL_PROJECTION)
command in the draw
function. In this state, we can
use the following commands:
glLoadIdentity()
–
Initiate the
current state
matrix into the
identity matrix.
glFrustum(…)
–
mult
iplies
the current projection matrix
with a
perspective
matrix
built according to the
parameters given.
glOrthogonal(…)

multiplies
the current projection matrix
with an orthogonal
projection
matrix built according to the
parameters given.
3.
Vi
ew mode
–
pla
cing world
models

The graphic
hardware contains a matrix
which is used to position 3D
points before the use of
projection. We can modify
this matrix while in the
“
Model View
” state. In order
to enter this state, we use the
glMatrixMode
(
GL_MODELVIEW
)
comm
and in the draw
function. In this state, we can
use the following commands:
glLoadIdentity()
–
Same as
before.
glRotate, glTranslate, glScale
–
fun
ctions for modifying the
current state matrix a
ccording
to the given operation and
parameters.
NOTE: Using
th
ese functions in projection
mode is for manipulating the
camera position, while using
them in Model View mode is
for manipulating the model
itself.
glVertex3f
–
send a point to
the hardware.
This command
should be inside the glBegin
hierarchy, as studied.
glPushMatrix(),glPopMatrix()
–
the
hardware holds a stack, you may use it
to save an achieved matrix you
will
use
in the future. (
F
or example
save the
matrix that represents
the complex
model
center
position
.
Use it to return
the start position before you
multiply
the
each
simple part matrix)
OpenGL drawing
tools
:
Drawing 3D models
Depth
test
–
depth buffer
Coloring
–
color buffer
Polygon face
–
left hand basic rule
3D realization tools
Light
o
Smooth VS. flat shading
o
Normal
o
Material properties
o
Ray tracing
Image reflecting
3D drawing
graphic

advanced
Textures
Project texture to model
Project model to texture
Bump map
Polygons normal
randomization
Bump map & Texture
Animating
Parametric surface
Geometrical error functions
Quadratic error metric
Level of De
tail approach
Occlusion Culling
Hardware occlusion culling
LOD & occlusion culling
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