11-texture-mapping.pptx

Texture Mapping

•

_{The fragment operations can access a specialized}

RAM

–

_{The Texture RAM}

–

_{Organized in a set of Textures}

•

_{Each texture is an array}

1D, 2D o 3D

Texels

•

_{Typical examples of texels:}

–

_{each texel is a color (components: R-G-B, or R-G-B-A)}

•

_{The texture is a "}

_color-map

_"

–

_{each texel is an alpha value}

•

_{the texture is an "}

_alpha-map

_"

–

_{each texel is a normal (components: X-Y-Z)}

•

_{the texture is a "}

_normal-map

_{" or "}

_bump-map

_"

–

_{each texel contains a specularity value}

•

_{the texture is a "}

_{shininess-map}

_"

Typical application: mapping images on geometry

3D geometry

(quads mesh

+

RGB texture

2D

(color-map)

More examples

Texture Mapping: History

•

_{1974 introduced by Ed Catmull}

–

_{In its Phd Thesis}

•

_{Only in 1992 (!) we have texture mapping hardware}

–

Silicon Graphics RealityEngine

•

_{1992 on:}

increasingly used and integrated in graphic cards

–

_{First of all by low end graphic boards}

•

_Today:

a fundamental rendering primitive

–

_{the main image-based technique}

Ed Catmull

Notation

Texture 2D

u

v

texel

Texture Space

(or "parametric space" or "u-v space")

A Texture is defined

In the region [0,1] x [0,1]

of the "parametric space"

5

1

2

te

xe

ls

1024 texels

Texture Space

u

v

Texture Mapping

•

_{We associate to each vertex (of each triangle) its}

u,v

coordinates in the texture space

Screen Space

x

,y

x

,y

x

,y

u

,v

u

,v

u

,v

Position of the 1st vertex

Attributes of the 1st vertex

u

,v

u

,v

Texture Mapping

•

_{More precisely, we define a mapping between the}

3D triangle 3D and a texture triangle

Texture Mapping

•

_{each fragment has its own}

_u,v

_coordinates

_{in the}

texture space

Texture Space

Screen Space

Problem: linear interpolation of texture coordinates

•

_{Not true for perspective projection!}

–

_{It is only an approximation}

–

_{It works fine to interpolate colors, normals, ..}

–

_{Not applicable to interpolate texture coordinates...}

V

V

V

p

3

R

R

2

f(p)

f( v

)

f( v

)

f( v

)

projection

f

p

has barycentric coordinates

a,b,c

In the triangle

v

v

v

f(p)

has barycentric coordinates

Problem: linear interpolation of texture coordinates

•

_Example:

u

v

1

1

u,v= (1,0)

u

,v

= (1,1)

u

,v

= (0,1)

Problem: linear interpolation of texture coordinates

Solution: Perspective Correction

•

p

has

barycentric coordinates

c

c

c

V

V

V

A

,B

...

A

,B

...

A

,B

...

p

p

=

c

₀

v

₀

+

c

₁

v

₁

+

c

₂

v

₂

Attributes of

p

:

(not considering the

“

perspective correction

")

A

_p

=

c

₀

A

₀

+

c

₁

A

₁

+

c

₂

A

₂

B

_p

=

c

₀

B

₀

+

c

₁

B

₁

+

c

B

Solution: Perspective Correction

•

p

has

barycentric coordinates

c

c

c

V

V

V

A

,B

...

A

,B

...

A

,B

...

p

p

=

c

₀

v

₀

+

c

₁

v

₁

+

c

₂

v

₂

Attributes of

p

:

(not considering the

“

perspective correction

")

w

₀

w

₁

A

_p

=

c

₀

A

A

₀

0

+

c

₁

A

₁

+

c

₂

A

₂

w

₀

A

₁

w

₁

A

₂

w

₂

A

_p

=

A

_p

=

c

₀

A

1

₀

+

c

₁

A

1

₁

+

c

₂

A

1

₂

w

₂

Solution: Perspective Correction

Screen

buffer

Original

attribute

A

Apply

transformatio

ns

compute:

A'

= A / w

and

w'

= 1 / w

c

₀

_w

A

0

+

c

₁

+

c

₂

0

A

₁

w

₁

A

₂

w

₂

A

_p

=

1

w

₀

w

1

₁

w

1

₂

interpolat

e

A'

and

w'

Final

fragment

attribute:

A'

/

w'

c

0

+

c

1

+

c

2

Perspective Correction

Perspective Correction

•

_{Texture mapping with perspective correction}

–

_{Also known as (aka):}

•

_{Perfect texture mapping}

•

_{3 magic vectors method}

_{(out of fashion)}

Note: the texture must be loaded

Screen

buffer

Texture RAM

L

O

A

D

Note: the texture must be loaded

1.

From hard disk to main RAM memory

•

_{(in the}

_motherboard

₎

2.

From main RAM memory to Texture RAM

•

₍

_{on board}

_{of the graphics HW)}

In OpenGL

•

_{As an example:}

glEnable(GL_TEXTURE_2D);

glBindTexture (GL_TEXTURE_2D, ID);

glTexImage2D (

GL_TEXTURE_2D,

0,

// mipmapping

GL_RGB,

// original format

imageWidth, imageHeight,

0,

// border

GL_RGB,

// RAM format

Assigning texture coordinates to vertices

•

_{2 possibilities:}

–

_{Computing textures coordinates on the fly}

•

_{During the rendering…}

–

_Precomputing

•

_{(and store them within the mesh)}

Difficult problem: u-v mapping

•

_{Associate texture coordinates to each vertex of the}

mesh

–

_{During preprocessing}

u

v

Difficult problem: u-v mapping

In OpenGL

•

_{Like any other attribute}

Assigning texture coordinates to vertices

•

_{2 possibilities:}

–

_{Computing textures coordinates on the fly}

•

_{During the rendering…}

–

_Precomputing

Automatically computed

•

_{Idea: from (x,y,z) to (u,v) - Linearly}

•

_{Using object or view coordinate}

Automatically computed

•

_{Even 1D}

Assigning texture coordinates to vertices

•

_{2 possibilities:}

–

_{Computing textures coordinates on the fly}

•

_{During the rendering…}

–

_Precomputing

Environment mapping: spherical

Environment map: a texture containing the color

of the environment “reflexed by each normal of

the half-sphere”.

Environment mapping: spherical

Simulates a mirror-like object reflecting a far-away background

Environment mapping: cube

front right back

below

above

Environment mapping: cube

Screen

buffer

Texture RAM

interpolati

ng

3D texture

coordinate

s

interpolat

ed

coordinat

es

3D

texture

Project on the

cube, look-up the

corresponding

face

compute

3D Texture

coordinates

1,+1] x 1,+1] x [-1,+1]

As view ray

reflexed by the

Environment mapping: cube

front right back

below

above

Environment mapping: cube and spherical

•

_Spherical:

–

_{one texel for each direction}

in the half-sphere

•

_{Projected on a circle}

–

_{the texture coordinate is}

the

normal

–

_{It has the "headlight“ effect:}

•

_{I can only rotate the object}

while the viewpoint does not

change

•

_Cube

–

_{one texel for each direction}

in the

sphere

•

_{Projected on the surface of}

the

cube

–

_{the texture coordinate is}

the view direction reflexed

by the normal

–

_{The viewpoint can rotate}

Automated computation of texture coordinates

glEnable(GL_TEXTURE_GEN_S);

1- abilitate:

2- choice of the mode:

glTexGeni(GL_S , GL_TEXTURE_GEN_MODE ,

mode

)

S, T, R, Q

mode

=

GL_OBJECT_LINEAR

GL_EYE_LINEAR

GL_SPHERE_MAP

Computes the texture coordinates

from the position in object

coordinates

(before the trasformation)

_{Computes the texture}

coordinates from the position in

view coordinates

(after the MODEL-VIEW)

The texture coordinates is the

reflexed view ray (using the normal)

Automated computation of texture coordinates

glTexGenfv(GL_S, GL_EYE_PLANE , v);

3- choice of the plane

S, T, R, Q

EYE OBJECT

or

4 elements vector

The resulting texture coordinate = v

T

• pos_vertex

u

Texture Look-up out of bounds: “clamp” mode

if (u<0) u←0; if (u>1) u←1;

if (v<0) v←0; if (v>1) v←1;

1

1

Texture Look-up out of bounds: “repeat” mode

u

v

1

1

u ← u –

[ u ]

v ← v –

Repeated textures

•

_{Typical use:}

Very space-efficient!

In OpenGL

glTexParameteri(

GL_TEXTURE_2D,

GL_TEXTURE_WRAP_S,

GL_CLAMP );

glTexParameteri(

GL_TEXTURE_2D,

GL_TEXTURE_WRAP_S,

GL_REPEAT );

or

note:

u

and

v

treated

separately

example: repeat

u

and clamp

v

Texture parameters.

each texture loaded

Texture Look-up

•

_{A fragment can have non-integer coordinates}

(in texels)

Texture Space

Screen Space

pixel

Texture Look-up

Texture Space

Screen Space

pixel

texel

one pixel = less than one texel

one pixel = more than one texel

Magnification

Solution 1:

Use the texel containg the pixel

(that is, the texel whose center

is closest to the u,v coordinates

of the fragment)

Equivalent to rounding up

the texel coordinates

to the nearest integer

"Nearest Filtering"

0.5 1.5 2.5 3.5 4.5 5.5 6.5

0.5

1.5

2.5

3.5

4.5

5.5

6.5

7.5

u

v

Magnification

texture 128x128

Nearest Filtering: result

Magnification

Solution 2:

Compute the average of the four

closest texels

Bilinear Interpolation

0.5 1.5 2.5 3.5 4.5 5.5 6.5

0.5

1.5

2.5

3.5

4.5

5.5

6.5

7.5

u

v

Magnification

texture 128x128

Magnification

•

_{Nearest filtering:}

–

_{Texels are visible}

–

_{Ok if texel borders are useful}

–

_{More efficient}

•

_{Bilinear Interpolation}

–

_{Usually provides better quality}

–

_{Less efficient}

Minification

Minification: MIP-mapping

MIP-map

level 0

MIP-map

level 1

MIP-map

level 2

MIP-map

level 3

MIP-map

level 4

(only one texel)

Mipmap Math

•

_{Define a scale factor,}



_{=texels/pixel}

–



is the maximum between



and



–

_{It can vary in the same triangle}

–

_{Can be derived from the transformation matrices,}

computed for the

Vertices

and interpolated for the

fragments

•

_{The mipmap level to use is:}

log

2



–

_{level 0 = maximum resolution}

–

_{if level<0 what is the reason?}

Minification: MIP-mapping

Minification: MIP-mapping

0

1

2

3

4

5

In OpenGL

glTexParameteri(

GL_TEXTURE_2D,

GL_TEXTURE_MAG_FILTER,

GL_NEAREST);

glTexParameteri(

GL_TEXTURE_2D,

GL_TEXTURE_MAG_FILTER,

GL_LINEAR );

or

In OpenGL

glTexParameteri(

GL_TEXTURE_2D,

GL_TEXTURE_MIN_FILTER,

mode

);

mode

= GL_NEAREST

GL_LINEAR

GL_NEAREST_MIPMAP_NEAREST

GL_LINEAR_MIPMAP_NEAREST

GL_NEAREST_MIPMAP_LINEAR

GL_LINEAR_MIPMAP_LINEAR

where

Choose the minification filter:

In OpenGL

•

_{Load on the graphics card all the mipmapping}

levels.

–

_One-by-one:

glTexImage2D (

GL_TEXTURE_2D,

i,

// MIP-map level

GL_RGB,

// original format

imageWidth, imageHeight,

0,

// border

GL_RGB,

// RAM format

In OpenGL

•

_{Load on the graphics card all the mipmapping}

levels.

–

_{All together (using the glu library):}

glTexImage2D (

GL_TEXTURE_2D,

0,

// MIP-map level

GL_RGB,

// original format

imageWidth, imageHeight,

0,

// border

GL_RGB,

// RAM format

GL_UNSIGNED_BYTE,

imageData);