Projective Texture

Spring 2006 2

Projective Texture

Texture projected on a scene as if by a projectorCan also be used to generate spot light and shadows

Spring 2006 3

Idea

Generate texture coordinates based on the projector coordinate system

Spring 2006 4

In Projector Space …

xp

yp

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

Spring 2006 5

Review: Pipeline

Fall 2009 revised 6

Model Transform

Viewing Transform

ModelviewMatrix

worldcoordinates

Pipeline Review

Spring 2006 7

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.

Spring 2006 8

Review: Texgen (Eye_linear)

If the texture generation function is GL_EYE_LINEAR, the functiong =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.

Spring 2006 9

Review: Texgen Matrix

Concatenate texgen planes into a 4-by-4 matrix

Object-linear

Eye-linear

objectw

z

y

x

v

v

v

vpppp

q

r

t

s

4321

To

Spring 2006 10

Coordinate Transformation

opp MvVv From Object to Projector:

epp vVVv 1From Eye to Projector:

ppp vPc Clip coordinate of Projector Space:

M: model matrixVp: view matrix to projector spaceV : view matrix to eye

Pp: projection matrix to projector space

Spring 2006 11

Scale to Texture Coordinates

Scale-and-bias matrix (S)

1000

00

00

00

21

21

21

21

21

21

Clip Coordinate[-1,1]

Texture Coordinate[0,1]

Note: we only care about [s,t] (and then [x,y]). Hence, frustum clipping on z is of no importance

Spring 2006 12

Use Texgen for Coord. Transform1

objectw

z

y

x

T

pp

v

v

v

v

MVSP

q

r

t

s

o

p

T Scqrts ,,,

opp MvVv

ppp vPc

Need to keep track of model matrix MTexgen planes To should be updated whenever M changes (model moves)

Not explicitly available in

OpenGL!

Spring 2006 13

Use Texgen for Coord. Transform2

pT Scqrts ,,,

ppp vPc epp vVVv 1

eyew

z

y

x

T

pp

v

v

v

v

VVSP

q

r

t

s

e

1

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

Spring 2006 14

Alternatively,

For the rest of transformations, set the texture matrix instead

q

r

t

s

VP

q

r

t

s

texture

pp

matrix

21

21

21

21

21

21

1000

00

00

00

eyew

z

y

x

e

v

v

v

v

V

q

r

t

s

1

eqns plane eye

1

1

1

1

We can use OpenGL matrix facility for matrix

multiplication

Tex coordsafter texgen

Tex coordsafter texture

transformation

Spring 2006 15

Summary

Texgen: eye-linearWhen texgen is called, set modelview to contain Ve only

Specify the other transforms (SPpVp) as texture matrix

eyew

z

y

x

epp

v

v

v

v

VVP

q

r

t

s

1

matrix texture

21

21

21

21

21

21

1000

00

00

00

Spring 2006 16

Summaryneed to generate the texture coordinate according to the projector coordinate system

Spring 2006 17

Demo (myprojspot - blended)

Scene: textured plane and untextured teapot, subject to a textured spotlightTwo rendering passes blended together (with polygon offset to resolve z-fighting)

Spring 2006 18

Demo

Projective PassRegular Pass

Blended

Polygon offset is critical to resolve z-fighting!

GL_ONE GL_ONE

Spring 2006 19

Implementation Note

Border pixels The projected

texture needs to be padded with black boundary pixels so that the clamped texture appears Ok

Spring 2006 20

Multitexture Implementation

Rather than using two blended passes, use a single (multitextured) passAssign 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: equivalent to one/one blending

The padding is black (0,0,0); GL_ADD plays no role.

Spring 2006 21

Projective Texture Shadow

Esp. good for non-planar shadow receivers

Spring 2006 22

Projective Shadow Texture

Generate a shadow texture from light coordinate system Render unlit occluder only

Render the shadow receiver with the projected shadow; then render the occluderNote the shadow texture is padded with white pixels. The texture environment used is GL_MODULATE (white (1,1,1) plays no role)

spot or point light

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

Spring 2006 25

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

Spring 2006 26

s -f

gluLookAt (eye, center, up)

worldT

worldeye

eyeworld

z

y

x

z

y

x

xLxLx

Lxx

eye

eye

eye

fus

fus

fus

world

world

world

1

]2[]2[]2[

]1[]1[]1[

]0[]0[]0[

LT

Change of Basis

gluLookAt is equivalent to:

s

ss

M T

Spring 2006 27

Model Transform

Viewing Transform

ModelviewMatrix

worldcoordinates

[-1,1]3

MT

[clip] = [Proj] [MT] [world][world] = [MT]-1[Proj]-1[clip] = T-1 M-1 P-1 [clip]

Spring 2006 28

glFrustum (l,r,b,t,n,f)n,f must be positiven cannot be zero

n

f r

rf/n

zx

y

1

11

1

1

1

1

1

11

1

1

1

1

12

22

22

1

12

22

22

1

fR

n

b

l

R

ntfnrf

f

nt

nr

fnnffn

nbt

nbt

nlr

nlr

n

nb

nl

fnnfnf

nbt

nbt

nlr

nlr

(1,1,1)

(-1,-1,-1)

Spring 2006 29

Implementation