Transcript Projective textures

Projective Texture
Projective Texture
Texture projected on a scene as if by a projector
Can also be used to generate spot light and shadows
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Idea
Generate texture coordinates based on
the projector coordinate system
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In Projector Space …
yp
xp
Whatever is in the projector frustum has clip coord. of
[-1,1]x[-1,1]xZ … (Z is irrelevant)
Convert [-1,1] to [0,1] to become the texture
coordinates
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Review: Pipeline
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Pipeline Review
Modelview
Matrix
Model
Transform
Viewing
Transform
world
coordinates
Fall 2009 revised
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Review: Texgen (Object_linear)
If the texture generation function is
GL_OBJECT_LINEAR, the function
g = p1 * xo + p2 * yo + p3 * zo + p4 * wo
is used, where g is the value computed for
the coordinate; p1, p2, p3, and p4 are the
four values supplied in params; and xo, yo, zo,
and wo are the object coordinates of the
vertex.
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Review: Texgen (Eye_linear)
If the texture generation function is
GL_EYE_LINEAR, the function
g =p1' * xe + p2' * ye + p3' * ze + p4' * we
is used, where
(p1' p2' p3' p4') = (p1 p2 p3 p4) * M -1
and xe, ye, ze, and we are the eye coordinates
of the vertex, p1, p2, p3, and p4 are the values
supplied in params, and M is the modelview
matrix when glTexGen is invoked.
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Review: Texgen Matrix
Concatenate texgen planes into a 4-by-4
matrix
Object-linear
 s   p1
t  
 
r  
  
q  
p2
p3
p4   v x 
 v 
 y 
  vz 
 
 vw  object
To
Eye-linear
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Coordinate Transformation
From Object to Projector:
v p  Vp Mvo
From Eye to Projector:
v p  VpV 1ve
Clip coordinate of Projector Space:
c p  Ppv p
M: model matrix
Vp: view matrix to projector space
V : view matrix to eye
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Pp: projection matrix to projector space
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Scale to Texture Coordinates
Scale-and-bias matrix (S)
Clip Coordinate
[-1,1]
 12 0 0 12 
0 1 0 1 
2
2

0 0 12 12 


0 0 0 1 
Texture Coordinate
[0,1]
Note: we only care about [s,t] (and then [x,y]). Hence,
frustum clipping on z is of no importance
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Use Texgen for Coord. Transform1
s
t 
   SPpV p M



r 
To
 
q 
 vx 
v 
 y
 vz 
 
vw  object
v p  Vp Mvo
c p  Ppv p
s, t, r, q
T
 Scp
Not explicitly
available in
OpenGL!
Need to keep track of model matrix M
Texgen planes To should be updated
whenever M changes (model moves)
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Use Texgen for Coord. Transform2
 vx 
s
v 
t 
   SPpV p V 1  y 
  vz 
r 
Te
 
 
q 
vw  eye
v p  VpV 1ve
c p  Ppv p
s, t, r, q
T
 Scp
The texture coordinate generated is A’xe + B’ye + C’ze +
D’we where (A’,B’,C’,D’) is (A,B,C,D)M−1, M is the
modelview matrix when glTexGen is invoked. Thus,
simply set the modelview matrix to contain only the
view matrix
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Alternatively,
For the rest of transformations, set the
texture matrix instead
 s   12 0 0 12 
s
 t   0 1 0 1 
t 
2
2
 
 
P
V
p
p
 r   0 0 12 12 
r 

  
 
q
0 0 0 1
q 



Tex coords
after texture
transformation
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texture matrix
We can use OpenGL matrix
facility for matrix
multiplication
 vx 
 s  1

v 
t   1

 
 Ve1  y 
 vz 
r  
1 
 
  

vw  eye
1
q  



Tex coords
after texgen
eye plane eqns
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Summary
Texgen: eye-linear
When texgen is called, set modelview to
contain Ve only
Specify the other transforms (SPpVp) as
texture matrix
s
t 
 
r 
 
q 
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 12 0 0 12 
 vx 
0 1 0 1 
v 
1  y 
2
2

P
V
V
0 0 12 12  p p e  vz 


 
vw  eye
0 0 0 1




texture matrix
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Summary
Spring 2006
need to generate the texture coordinate
according to the projector coordinate
system
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Demo (myprojspot - blended)
Scene: textured
plane and
untextured teapot,
subject to a textured
spotlight
Two rendering
passes blended
together (with
polygon offset to
resolve z-fighting)
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Demo
Polygon offset is
critical to resolve
z-fighting!
Projective Pass
Regular Pass
GL_ONE
GL_ONE
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Blended
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Implementation Note
Border pixels

The projected
texture needs to be
padded with black
boundary pixels so
that the clamped
texture appears Ok
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Multitexture Implementation
Rather than using two blended passes,
use a single (multitextured) pass
Assign a separate texture unit for spot
light texture


Projective texture coordinate set by texgen
Texture environment set to GL_ADD
 Base fragment/texture + spot light RGB:
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equivalent to one/one blending
 The padding is black (0,0,0); GL_ADD plays no
role.
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Projective Texture Shadow
Esp. good for non-planar shadow receivers
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Projective Shadow Texture
Generate a shadow texture from light
coordinate system

Render unlit occluder only
spot or
point light
Render the shadow receiver with the
projected shadow; then render the occluder
Note the shadow texture is padded with
white pixels. The texture environment used is
GL_MODULATE (white (1,1,1) plays no role)
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This is normal!
If you see something like this,
the artifact comes from
projective texture clamping: the
shadow touches the texture
border (not enough padding). It
can be alleviated by increasing
the fov or raising the light
position
Frustum Display
Shows the
location/orientation
of the spotlight
Idea
Projector is set by “gluLookAt” API

Eye, center, up
Vertices of the viewing frustum have
clip coordinates of [-1,1]3
Need to know their corresponding world
coordinates to render
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s -f
gluLookAt (eye, center, up)
s
s
s
LT
Change of Basis
 world x   s[0] u[0]  f [0] eyex 
 world    s[1] u[1]  f [1]  eye 
y


 y 
 world z   s[2] u[2]  f [2] eyez 
xworld  Lxeye
xeye  L1 xworld  LT xworld
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gluLookAt is equivalent to:
M
T
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Modelview
Matrix
Model
Transform
Viewing
Transform
MT
world
coordinates
[-1,1]3
[clip] = [Proj] [MT] [world]
[world] = [MT]-1[Proj]-1[clip]
= T-1 M-1 P-1 [clip]
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glFrustum (l,r,b,t,n,f)
n,f must be positive
n cannot be zero
 r l
r l
 1  2 n  2 n   nl   l 
 1  t b  t b   b  b 
2n
2n 
R 1    
 n  
 1   1   1 n 
   f n f  n   1   
 1   2 fn   n  1 
1  r2nl  r2nl   nr   rfn 
1  t b  t b   t   tf 
n
2n
2n 
R 1    
  n 
1   1   1  f 
   n f  f n   1   
1  2 fn   f   1 
y
(1,1,1)
rf/n
z
x (-1,-1,-1)
f
r
n
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Implementation
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