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Lecture 4: 3D Rendering Pipeline (I)
Prof. Hsien-Hsin Sean LeeSchool of Electrical and Computer
EngineeringGeorgia Institute of Technology
Interactive Game Loop
Game Input(Keyboard,
Mouse)
PhysicsStrategy, AI
RenderTriangles
(one frame)
Exit?
CleanupStates
30 to 60 frames per second
3D Graphics Rendering Pipeline
• Geometry Pipeline– Processing Vertices– Mainly floating-point operations
• Rasterization Pipeline– Processing Pixels– Mainly dealing with Integer
operations
Geometry Processing
xy
z
xy
z
xy
z
xy
z
xy
z
x
y
Rasterization Processing
x
y
3D Graphics Rendering Pipeline
• Geometry Pipeline– Processing Vertices– Mainly floating-point operations
• Rasterization Pipeline– Processing Pixels– Mainly dealing with Integer operations– MMX was originally designed to
accelerate this functionality
Geometry Processing
xy
z
xy
z
xy
z
xy
z
xy
z
x
y
Rasterization Processing
x
y
MMX ISAMMX ISA
3D Graphics Rendering Pipeline
• Geometry Pipeline– Processing Vertices– Mainly floating-point operations– SSE/SSE2 were designed for this
part• Rasterization Pipeline
– Processing Pixels– Mainly dealing with Integer operations– MMX was originally designed to
accelerate this functionality
Geometry Processing
xy
z
xy
z
xy
z
xy
z
xy
z
x
y
Rasterization Processing
x
y
MMXMMX ISAISASSE/SSE2 ISASSE/SSE2 ISA
Fixed Function 3D Graphics Pipeline
• Geometry Pipeline– Processing Vertices– Mainly floating-point operations– SSE/SSE2 were designed for this
part• Rasterization Pipeline
– Processing Pixels– Mainly dealing with Integer operations– MMX was originally designed to
accelerate this functionality
Geometry Processing
xy
z
xy
z
xy
z
xy
z
xy
z
x
y
Rasterization Processing
x
yPerformed by (GP)GPU
3D Coordinates
• Left-handed system is more common for graphics viewing space
• Camera or viewer position can be set up using 3D API
+z
+x
+y
Right-Handed System
+z
+x
+y
Left-Handed System
Geometry Format ─ Vertex Coordinates
(X1, Y1, Z1)
(X2, Y2, Z2)
(X3, Y3, Z3)
+Z
+X
+Y
X1
Z1
Y1
Geometry Format ─ Vertex Normals
(NX1, NY1, NZ1)
(NX2, NY2, NZ2)
(NX3, NY3, NZ3)
+Z
+X
+Y
Geometry Format ─ Vertex Colors
(R1, G1, B1, A1)
(R2, G2, B2, A2)
(R3, B3, B3, G3)
+Z
+X
+Y
Triangle-based Geometry Representation
V5V4
V3
V2
V1
V1V2
V3V4
V5
V6V7
V8
V9
V5V4
V1V1
V3
V2
Triangle List(note the vertex order)
Triangle Strip Triangle Fan
Specifying a 3D object
• Vertex ordering is critical
V1
V2 V3
V4
V5
V6V7Triangle list{v1, v3, v2},{v1, v5, v3},{v5, v6, v3},{v4, v3, v6},{v1, v7, v6},{v1, v6, v5}
Triangle strip{v5, v3, v1, v2},{v5, v6, v3, v4},{v7, v6, v1, v5}
V8
Specifying a 3D object
• Vertex ordering is critical• We will discuss normal computation later in this lecture
V1
V2 V3
V4
V6V7Triangle list{v1, v2, v7},{v2, v8, v7},{v2, v3, v4},{v2, v4, v8},{v4, v7, v8},{v4, v6, v7}
Triangle strip{v1, v2, v7, v8},{v3, v4, v2, v8},{v6, v7, v4, v8}
3D Rendering Pipeline
Clip
ping
Pers
pect
ive D
ivide
View
port
Tran
sfor
m
Rast
eriza
tion
Proj
ectio
n Tr
ansf
orm
Wor
ld T
rans
form
View
Tra
nsfo
rm
Ligh
ting
Back
face
Cul
ling
Transformation Pipeline• World Transformation
– Model coordinates World coordinates
• View Transformation– World coordinates Camera space
• Projection Transformation – Camera space View Plane
• These are a series of matrix multiplications
World Transformation
• Translation• Rotation• Scaling
+x
+z
+y
World origin
World Coordinates
Local model coordinates
Local model coordinates
View Transformation
+x
+z
+y
World origin
World Coordinates
+y
+x
+z
• Camera position• Look vector
Projection Transformation• Set up camera internals
• Set up – Field of View (FOV)– View frustum – View planes
• Will discuss later
Homogeneous Coordinates• Enable all transformations to be done
by “multiplication” – Primarily for translation (See next few
slides)
• Add one coordinate (w) to a 3D vector
• Each vertex has [x, y, z, w]– W will be useful for perspective projection– W should be 1 in a Cartesian Coordinate
System
Transformation 1: Translation (Offset)
+x
+z
+y
+x
+z
+y
(x, y, z)
(xt, yt, zt)
Translation Matrix
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⋅=
1TTT
0100
0010
0001
]z,1y,x,[],1z,y,x[
zyx
ttt
Transformation 2: Scaling
+x
+z
+y
+x
+z
+y
Scaling Matrix
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⋅=
1000
0R00
00R0
000R
]z,1y,x,[],1z,y,x[z
y
x
rrr
Transformation 3: Rotation
+x
+z
+y
+y
+x
+z
2D Rotation
+x
+y
+x
+y
(x, y)
(x’, y’)
+x
+y
(x, y)
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−⋅=
100
0cossin
0sincos
]y,1x,[],1y',x'[ èè
èè
Rotate along which axis?
3D Rotation Matrix
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡−
⋅=
1000
0100
00cossin
00sincos
]z,1y,x,[],1z',y',x'[èè
èè
Rotation along Z axis
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡ −
⋅=
1000
0cos0sin
0010
0sin0cos
]z,1y,x,[],1z',y',x'[θθ
θè
Rotation along Y axis
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−⋅=
1000
0cossin0
0sincos0
0001
]z,1y,x,[],1z',y',x'[èè
èèRotation along X axis
Non-Commutative Property (1)
1. Counter-clockwise 90o along y
2. Clockwise 90o along x
+x
+z
+y
+x
+z
+y
1. Clockwise 90o along x
2. Counter-clockwise 90o along y
Non-Commutative Property (1)
+x
+z
+y
+x
+z
+y
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−
−
=
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
−⋅
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
−−
−−−
1000
0001
0100
0010
1000
0)2
cos()2
sin(0
0)2
sin()2
cos(0
0001
1000
0)2
cos(0)2
sin(
0010
0)2
sin(0)2
cos(
ππ
ππ
ππ
ππ
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−−
=
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
−−
−−−
⋅
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
−1000
0010
0001
0100
1000
0)2
cos(0)2
sin(
0010
0)2
sin(0)2
cos(
1000
0)2
cos()2
sin(0
0)2
sin()2
cos(0
0001
ππ
ππ
ππ
ππ
(x’’, y’’, z’’) = (-z, -x, y)
(x’’, y’’, z’’) = (-y, -z, x)
Non-Commutative Property (2)
1. Translation by (x, y, z)2. Scale by 2 times
+x
+z
+y
1. Scale by 2 times2. Translation by (x, y, z)
+x
+z
+y
Non-Commutative Property (2)
+x
+z
+y
+x
+z
+y
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⋅
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
1
000
000
000
1000
000
000
000
1
0100
0010
0001
RzTzRyTyRxTx
Rz
Ry
Rx
Rz
Ry
Rx
TzTyTx
(x’’, y’’, z’’) = (x*Rx+Rx*Tx, y*Ry+Ry*Ty, z*Rz+Rz*Tz)
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⋅
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
1
000
000
000
1
0100
0010
0001
1000
000
000
000
TzTyTx
Rz
Ry
Rx
TzTyTx
Rz
Ry
Rx
(x’’, y’’, z’’) = (x*Rx+Tx, y*Ry+Ty, z*Rz+Tz)
Offsets were scaled as well
Non-Commutative Property• Ordering matters !
• Be careful when performing matrix multiplication
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