7/30/2019 09-texturas

1/59

Cap. 9

Texturas

Engenharia Informtica (5385) - 2 ano, 2 semestre

7/30/2019 09-texturas

2/59

Sumrio Objectivos" Noo de textura" Motivao" Mapeamento de textura, padres de textura e texels" Mapeamento de texturas em polgonos, interpolao de texturas" Rasterizao: modos de aplicao de texturas" Mapeamento de texturas em objectos geomtricos"

mapeamento planar" mapeamento cilndrico" mapeamento esfrico" mapeamento paralepipdico"

Modos de revestimento (wrapping)" ..."

7/30/2019 09-texturas

3/59

Objectivos Introduzir mtodos de mapeamento

Mapeamento de textura (texture mapping) Mapeamento ambiental (environmental mapping) Mapeamento rugoso (bump mapping) Mapeamento de luz (light mapping)

Considera-se duas estratgias bsicas: Especificao manual de coordenadas Mapeamento automtico em duas fases

7/30/2019 09-texturas

4/59

Noo de Textura Uma textura uma imagem com

componentes RGB e alpha..." Mapeamento de textura: um mtodo

para criar complexidade numa imagemsem o nus de construir grandes

modelos geomtricos"

7/30/2019 09-texturas

5/59

Motivao:

(1) adicionarrealismo

texture map

light map

bump map

reflection map

7/30/2019 09-texturas

6/59

Motivao: (2) adicionardetalhe

superfcie A soluo mais bvia no a melhor"

Dividir uma cena em polgonos cada vez mais pequenos aumenta odetalhe"

Mas muito difcil de modelar e muito oneroso de renderizar emtermos de tempo"

A soluo preferida usar mapeamento de textura" tipicamente uma imagem 2D decalcada em objectos"

Exemplos:" Modelo de t-shirt com logo"

no h necessidade de modelar as letras nem nenhum processamentode tringulos"

usa-se um polgono de dimenses grandes" colora-se o polgono com uma foto

Iluminao sbtil da parede

no h necessidade de calcul-la em cada frame"

no h necessidade de model-la com vrios tringulos de cor constante" decalca-se a foto num polgono grande

Tambm funciona em superfcies no complanares subdivide surface into planar patches" assign photograph subregions to each individual patch"

Exemplos de modulao de cor, rugosidade, brilho, e transparnciacom a mesma geometria esfrica"

7/30/2019 09-texturas

7/59

Texturas: em que ponto as coisas

comeam a parecer reais?

modelo geomtrico modelo geomtrico+

coloraomodelo geomtrico

+colorao

+texturas

Superfcies de objectos do mundo selvagem so muito complexas No podem modelar as mais finas variaes Precisamos de encontrar formas de adicionardetalhe superfcie. Como?"

7/30/2019 09-texturas

8/59

Mapeamento de textura, padro

de textura e texels Desenvolvido por Catmull (1974), Blinn e

Newell (1976), e outros investigadores." Mapeamento de textura: adiciona detalhe

superfcie atravs de mapeamento depadres de texturas sobre a superfcie. "

Padro repetido. Por exemplo, o padrode textura para o cubo ao lado o seguinte: "

Texel: abreviatura para texture element." Um texel um pixel da textura. Por

exemplo, uma textura de resoluo 128x128tem 128x128 texels. No ecr, isto poderesultar em mais ou menos pixels, o quedepender da distncia a que o objecto seencontra na cena, ou seja, de como atextura escalada para a superfcie."

7/30/2019 09-texturas

9/59

Tcnicas de Mapeamento

Mapeamento de Texturas Mapeamento Ambiental

Mapeamento de Rugosidade Mapeamento de Luz

7/30/2019 09-texturas

10/59

Mapeamento (manual) de

Textura Questo: Que ponto da textura se usa

para um dado ponto da superfcie? A textura simplesmente uma imagem

com um sistema de coordenadas 2D (s,t) Parameteriza-se pontos da textura com

coordenadas: (s,t)

Define-se o mapeamento de (x,y,z) nodomnio da cena para o domnio datextura (s,t) Para determinar a cor em (x,y,z) usa-se o

correspondente (s,t) para determinar a cor

da textura nesse ponto Com polgonos:

Especifica-se (s,t) nos vrtices Interpola-se (s,t) para os pontos

intermdios entre os vrtices e no interiordo polgono

s

t

7/30/2019 09-texturas

11/59

s

t

u

v

(s,t) = (u,v)

Mapeamento automtico da

textura para a superfcie O problema bsico est em encontrar a

funo (mapping) que mapeia a texturapara a superfcie

Dada uma posio (s,t) da textura, qual a posio (x,y,z) na superfcie?

Este problema requer 3 funesparamtricas: x = X(s, t) y = Y(s, t) z = Z(s, t)

No caso de a superfcie j estar formuladaparametricamente, ento temos outros

sistemas de coordenadas envolvidos: o daimagem (s,t) e o da prpria superfcie (u,v)

s

t

(x,y,z)

7/30/2019 09-texturas

12/59

Como se define as coordenadas

paramtricas (u,v)?

Manualmente: Ns atribuimos as coordenadas da textura a cada vrtice da

superfcie

Automaticamente: Usa-se um algoritmo que atribui as coordenadas da textura

7/30/2019 09-texturas

13/59

Especificao manual de

coordenadas Podemos especificar manualmente as coordenadas da textura em cada vrtice

(0,0)texture 2D polygon textured polygon

+ =(1,1)

(0,0)

(1,1)

Podemos escolher coordenadas de textura alternativas

(0,0)

texture 2D polygon textured polygon

+ =

(1,1)

(0,0)

(1,0.5)

7/30/2019 09-texturas

14/59

Mapeamento de texturas em

polgonos Especificamos explicitamente

as coordenadas (u,v) nosvrtices do polgono

Ou seja, afixamos a textura nosvrtices

Faz-se ento a interpolaodentro do tringulo na altura darasterizao (scan conversion)no domnio de ecr.

uv

glTexCoord2f(0.5, 0.5);

glVertex3fv (10.2,3.4,4.5);

7/30/2019 09-texturas

15/59

Interpolao de texturas

A interpolao feita durantea fase de scan conversion, semelhana do que feito nacolorao de Gouraud

Mas e vez de interpolar osvalores RGB, obtemos osvalores (u,v) que permitemaceder correspondente corna textura.

Isto , o mapeamento datextura feito no domniocannico do ecr quando o

polgono rasterizado No entanto, quando se

descreve uma cena, assume-se muitas vezes que omapeamento feito nodomnio da cena

(x1, y1), (u1, v1)(x2, y2), (u2, v2)

(x3, y3), (u3, v3)

R

LR

L

L

LR

Ls

xx

xxs

xx

xxs

+

= 1

sR = 1y y

1

y3 y

1

u1 +

y y1

y3 y

1

u3

sL = 1y y

2

y3 y

2

u2 +

y y2

y3 y

2

u3

7/30/2019 09-texturas

16/59

Rasterizao:

modos de aplicao de texturas Aps saber os valores de uma textura,

podemos us-los para modificar um oumais atributos de um polgono/superfcie atravs das chamadasfunes de mistura (combinefunctions ou texture blendingoperations): replace: substitui cor da superfcie pela

cor da textura decal: substitui cor da superfcie pela

cor da textura, misturando ento a corcom o valor alpha da textura, ainda quea componente alpha no sejamodificado no framebuffer

modulate: multiplica a cor da superfciepela cor da textura (shaded + texturedsurface). Precisa-se disto para a multi-texturizao (i.e., lightmaps).

blend: semelhante modulao mascom mistura alpha

Textura Polgono Textura Mapeada

Textura Polgono Textura Mapeada

operao REPLACE

operao MODULATE

7/30/2019 09-texturas

17/59

Questes relevantes em

mapeamento de texturas O que acontece quando se faz zoom aumentativo e zoom

diminuitivo?

Como geramos as coordenadas de texturas?

O que acontece quando usamos coordenadas de textura menoresdo que 0 e maiores do que 1?

Ser que as aplicaes (maps) de textura s servem para por cornos objectos?

7/30/2019 09-texturas

18/59

Aplicao de uma textura numa

superfcie A aplicao de uma textura numa

superfcie tem lugar durante arenderizao.

semelhante ao mtodo decolorao de Gouraud: Tringulo rasterizado Cada pixel do tringulo mapeado de

volta textura Usa-se valores conhecidos nos

vrtices para interpolar sobre a textura Cada pixel est associado com uma

pequena regio da superfcie e a umapequena rea da textura. H 3 possibilidades de associao:

1. um texel a um pixel (raramente)2. magnificao: um texel a muitos pixels3. minificao: muitos texels a um pixel

Magnificao

Minificao

7/30/2019 09-texturas

19/59

Aplicao de uma textura numa

superfcie (cont.): zoom in: filtro de

magnificao Um pixel mapeado para uma pequena poro de um texel O resultado que muitos pixels so mapeados para o mesmo texel Sem um mtodo de filtragem surge o fenmeno de aliasing Filtro de magnificao: suaviza a transio entre pixels

Magnificao

muitos pixels correspondem a um texel blockiness / jaggies / aliasing

soluo: aplicar mdia(magnification filter)

7/30/2019 09-texturas

20/59

Aplicao de uma textura numa

superfcie (cont.): zoom out: filtro

de minificao Um pixel mapeado para muitos texels comum em perspectiva (foreshortening)

Minificao

Perspectiva (foreshortening)e mapeamento pobre detextura provoca adeformao visual dopavimento

Mipmaps melhoram o mapeamento,restaurando a forma do pavimento

7/30/2019 09-texturas

21/59

Aplicao de uma textura numa

superfcie (cont.): melhor filtro de

minificao: Mipmaps mip significa multum in parvo, ou muitas coisas num pequeno

lugar Ideia bsica: criar muitas texturas de tamanho decrescente e usar

uma delas quando for apropriado

Texturas pr-filtradas = mipmaps

Minificao

7/30/2019 09-texturas

22/59

Aplicao de uma textura numa

superfcie (cont.): Mipmaps:

otimizao de armazenamento obrigatrio fornecer

todos os tamanhos datextura em potncias de2 em relao originalem 1x1

7/30/2019 09-texturas

23/59

Sumrio: filtragem Zoom-in requer a utilizaao dum filtro de magnificao

Zoom-out requer a utilizaao dum filtro de minificao

Filtros mais avanados requerem mais tempo/computao, masproduzem melhores resultados

Mipmapping um filtro de minificao avanado

Precauo: mipmapping sem pr-definir mipmaps desligar (turn off)a texturizao (veja-se Filtering in OpenGL)

7/30/2019 09-texturas

24/59

Wrapping Modes Can assign texture coords outside of

[0,1] and have them eitherclamp orrepeatthe texture map

Wrapping modes:

repeat: start entire texture over Repeat Issue: making the texture borders

match-up

mirror: flip copy of texture in eachdirection get continuity of pattern

clamp to edge: extend texture edgepixels

clamp to border: surround with bordercolor

courtesy of Microsoft

(0, 0) (3, 0)

(3, 3)(3, 0)

REPEAT

MIRROR

CLAMP

TO EDGE

CLAMP TO

BORDER

7/30/2019 09-texturas

25/59

Wrapping modes:

Repetitive texture tiling A texture can also be repeatedly tiled across the surface by repeating the

(s,t) parameterization over the surface

But, best results are obtained when the texture is seamlessly tilable This means that the right side of the texture joins seamlessly with the left side

(same with the bottom and top)

Seams will appear for most textures when tiled:

But, we can edit or re-synthesize textures to be seamlessly repeatable (this isanother topic onto itself):

7/30/2019 09-texturas

26/59

Texturing in OpenGL

Procedure" Example"

7/30/2019 09-texturas

27/59

Texturing in OpenGL

Procedure: Texture Mapping" uploading of the texture to the video memory" set up texture parameters" enable texturing" the application of the texture onto geometry"

7/30/2019 09-texturas

28/59

Texturing in OpenGL:

main steps1. Create texture and load with

glTexImage() Three methods:

read in an image in a jpg, bmp, ... File generate the texture yourself within application copy image from color buffer

2. define texture parameters as to how texture is applied glTexParameter*() wrapping, filtering, etc

3. enable texturing

glEnable(GL_TEXTURE_*D)

4. assign texture coordinates to vertices the mapping function is left up to you glTexCoord*(s,t); glVertex*(x,y,z);

7/30/2019 09-texturas

29/59

Step 1: Specifying Texturing

Image Define a texture image as an array oftexels

(texture elements) in CPU memory:

Glubyte myTexture[width][height][3];

Each RGB value is specified to be an unsignedbyte, between 0 and 255

For example, a blue color would be (0, 0, 255)

Warning:

this [3]

seems to be

missing in

thetextbook

7/30/2019 09-texturas

30/59

Step 1: Defining an Image as a

Texture Call glTexImage2D. It uploads the texture to the video memory where it will be ready for

us to use in our programs.

void glTexImage2D(target,level,components,w,h,border,format,type,texture);"Parameters: target : type of texture, e.g. GL_TEXTURE_2D level : used for mipmapping = 0 (discussed later) components : elements per texel (for RGB) w, h : width and height of texture in pixels border : used for smoothing = 0 (dont worry about this) format : texel format e.g. GL_RGB type : rgb component formate.g. GL_UNSIGNED_BYTE texture : pointer to the texture array

Example, set the current texture:glTexImage2D(GL_TEXTURE_2D, 0, 3, 512, 512, 0, GL_RGB, GL_UNSIGNED_BYTE, texture);

7/30/2019 09-texturas

31/59

Step 1 (alternative):

Generating a Random Texture Here is a function for a random texture:

GLubyte texture[64][64][3];

int u, v;

for(u=0; u

7/30/2019 09-texturas

32/59

Step 2:

Specifying Texture Parameters OpenGL has a variety of parameters that determine how textures are

applied: Wrapping parameters determine what happens if s and t are outside the

(0,1) range

Filter modes allow us to use area averaging instead of point samples Mipmapping allows us to use textures at multiple resolutions

The glTexParameter() function is a crucial part of OpenGL texturemapping, this function determines the behavior and appearance oftextures when they are rendered.

Take note that each texture uploaded can have its own separateproperties, texture properties are not global.

7/30/2019 09-texturas

33/59

Step 2:

glTexParameter()Texture Paramete r Accepted value s Descripti o n

GL_TEXTURE_MIN_FILTER GL_NEAREST , GL_LINEAR,

GL_NEAREST_MIPMAP_NEAREST,GL_LINEAR_MIPMAP_NEAREST,GL_NEAREST_MIPMAP_LINEAR and

GL_LINEAR_MIPMAP_LINEA R

The texture minification function is used

when a single screen pixel maps tomore than one texel, this means thetexture must be shrunk in size.

Default setting isGL_NEAREST_MIPMAP_LINEAR.

GL_TEXTURE_MAG_FILTE R GL_NEAREST or GL_LINE A R

The texture magnification function isused when the pixel being texturedmaps to an area less than or equal to

one texel, this means the texture mustbe magnified.

Default setting is GL_LINE A R .

GL_TEXTURE_WRAP_ S GL_CLAMP or GL_REPEATSets the wrap parameter for the stexture coordinate. Can be set to eitherGL_CLAMP or GL_REPEAT .

Default setting is GL_REPEAT.

GL_TEXTURE_WRAP_T GL_CLAMP or GL_REPEATSets the wrap parameter for the t

texture coordinate. Can be set to eitherGL_CLAMP or GL_REPEAT .

Default setting is GL_REPEAT. GL_TEXTURE_BORDER_COLO R Any four values in the [0, 1] range

Sets the border color for the texture, if

border is present .

Default setting is (0, 0, 0, 0) .

GL_TEXTURE_PRIORITY [0, 1]Specifies the residence priority of thetexture, use to prevent OpenGL from

swapping textures out of video memory.Can be set to values in the [0, 1] range.See glPrioritizeTextures() for more

information or this article onGamasutra.

Target Specifies the target textur e GL_TEXTURE_1 D One dimensional texturing. GL_TEXTURE_2 D Two dimensional texturing.

7/30/2019 09-texturas

34/59

Step 2:

glTexParameter()Parameter Value DescriptionGL_CLAMP Clamps the texture coordinate in the [0,1] range. GL_REPEAT

Ignores the integer portion of the texture coordinate, only thefractional part is used, which creates a repeating pattern. Atexture coordinate of 3.0 would cause the texture to tile 3 timeswhen rendered .

GL_NEAREST Returns the value of the texture element that is nearest (inManhattan distance) to the center of the pixel being textured.Use this parameter if you would like your texture to appear

sharp when rendered .

GL_LINE A R Returns the weighted average of the four texture elements thatare closest to the center of the pixel being textured. These caninclude border texture elements, depending on the values ofGL_TEXTURE_WRAP_S and GL_TEXTURE_WRAP_T, and onthe exact mapping. Use this parameter if you would like yourtexture to appear blurred when rendered .

GL_NEAREST_MIPMAP_NEARESTChooses the mipmap that most closely matches the size of thepixel being textured and uses the GL_NEAREST criterion (thetexture element nearest to the center of the pixel) to produce atexture value.

GL_LINEAR_MIPMAP_NEARESTChooses the mipmap that most closely matches the size of thepixel being textured and uses the GL_LINEAR criterion (aweighted average of the four texture elements that are closestto the center of the pixel) to produce a texture value.

GL_NEAREST_MIPMAP_LINE A R Chooses the two mipmaps that most closely match the size ofthe pixel being textured and uses the GL_NEAREST criterion(the texture element nearest to the center of the pixel) toproduce a texture value from each mipmap. The final texture

value is a weighted average of those two values.

GL_LINEAR_MIPMAP_LINE A R Chooses the two mipmaps that most closely match the size ofthe pixel being textured and uses the GL_LINEAR criterion (aweighted average of the four texture elements that are closestto the center of the pixel) to produce a texture value from eachmipmap. The final texture value is a weighted average of thosetwo values.

7/30/2019 09-texturas

35/59

Step 2:

Wrapping Modes Clamping : if s,t> 1 use color at 1, ifs,t< 0 use color at 0

glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP);

Repeating : uses,tmodulo 1

glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);

textures

t

Wrap S : GL_REPEATWrap T : GL_REPEAT

Wrap S : GL_REPEATWrap T : GL_CLAMP

Wrap S : GL_CLAMPWrap T : GL_REPEAT

Wrap S : GL_CLAMPWrap T : GL_CLAMP

7/30/2019 09-texturas

36/59

Step 2:

Filter Modes Minification and magnification

7/30/2019 09-texturas

37/59

Step 2:

Mipmapping

7/30/2019 09-texturas

38/59

Step 3: Enable Texturing

To enable/disable just call: glEnable(GL_TEXTURE_2D) glDisable(GL_TEXTURE_2D);

What does texture mapping affect? the current shading color of a pixel (after lighting) is multiplied by the

corresponding texture color

So, if the object is a near white color (0.8, 0.8, 0.8) at some point and thecurrent texture color at that point is red (1, 0, 0), then when multiplied, itproduces (0.8, 0, 0)

7/30/2019 09-texturas

39/59

Step 4:

Mapping a Texture Assign the texture coordinates glTexCoord*() is specified at each vertex

s

t1, 1

0, 1

0, 0 1, 0

(s, t) = (0.2, 0.8)

(0.4, 0.2)

(0.8, 0.4)

A

B C

a

b

c

Texture Space Object Space

7/30/2019 09-texturas

40/59

Step 4:

Mapping a Texture: example How to texture a quad? The following code assumes that texturing has been enabled

and that there has been a texture uploaded with the id of 13. "glBindTexture (GL_TEXTURE_2D, 13);!

glBegin (GL_QUADS); !glTexCoord2f (0.0, 0.0); glVertex3f (0.0, 0.0, 0.0); !glTexCoord2f (1.0, 0.0); glVertex3f (10.0, 0.0, 0.0); !glTexCoord2f (1.0, 1.0); glVertex3f (10.0, 10.0, 0.0);!glTexCoord2f (0.0, 1.0); glVertex3f (0.0, 10.0, 0.0); !

glEnd ();"

(0.0f,0.0f) (1.0f,0.0f)

(1.0f,1.0f)(0.0f,1.0f)

texture coordinates

7/30/2019 09-texturas

41/59

Texturing Mapping in OpenGL:

summing up

7/30/2019 09-texturas

42/59

What about complex 3D

objects? It is easy to set texture coordinate for a single 2D

polygon, but can be difficult to set the texturecoordinates for complex 3D regions or objects.

Besides: in rendering based on pixel-to-pixel approach, the

inverse mapping from screen coordinates to texturecoordinates is needed

because of shading, mapping areas-to-areas and notpoint-to-point is required, which causes antialisingproblems, moire patterns etc.

Two-Stage Mapping: An automatic solution to themapping problem is to first map the texture to asimple intermediate surface then map the simpleintermediate surface to the target surface

7/30/2019 09-texturas

43/59

Automatic: cylindrical mapping

Example: first map to a cylinder Like wrapping a label around a can of soup

Convert rectangular coordinates (x, y, z) to cylindrical (r, , h), use only (h, ) to indextexture image

h

u

v

7/30/2019 09-texturas

44/59

Automatic: cylindrical mapping

Example: first map to a cylinder Like wrapping a label around a can of

soup

Convert rectangular coordinates (x, y, z) tocylindrical (r, , h), use only (h, ) to indextexture image

Parametric cylinder:x = rcos (2u)y = v/hz= rsin (2u)

Maps rectangle in u, vspace to cylinderof radius r and height h in worldcoordinates:

s = ut = v

h

u

v

7/30/2019 09-texturas

45/59

Automatic: spherical mapping

Example: first map to a sphere

Convert rectangular coordinates (x,y,z)to spherical (,)

Parametric sphere:x = rcos (2u)y = rsin (2u) cos (2v)z= rsin (2u) sin (2v)

For example: paste a world map onto asphere to model the earth. But in the

case of the sphere there is distortion atthe poles (north and south)

7/30/2019 09-texturas

46/59

Automatic: box mapping

Example: first map to a box

7/30/2019 09-texturas

47/59

Automatic: stage-two mapping

Now, we still need to map from an intermediate object (sphere, cylinder, or box) to thetarget object

1. Intersect the normals from intermediate surface to target surface2. Intersect the normals from target surface to intermediate surface3. Intersect vectors from center of target surface to intermediate

7/30/2019 09-texturas

48/59

Mapping Techniques

Texture Mapping Environmental Mapping Bump Mapping Light Mapping

7/30/2019 09-texturas

49/59

Environmental Maps

Use texture to represent reflectedcolor Texture indexed by reflection

vector

Approximation works whenobjects are far away from thereflective object

Environment mapping producesreflections on shiny objects

Texture is transferred in thedirection of the reflected ray fromthe environment map onto theobject

Reflected ray: R=2(NV)N-V What is in the map? spherical map

7/30/2019 09-texturas

50/59

Approximations Made

The map should contain a viewof the world with the point ofinterest on the object as the eye We cant store a separate map

for each point, so one map is

used with the eye at the center ofthe object Introduces distortions in the

reflection, but the eye doesntnotice

Distortions are minimized for asmall object in a large room

The object will not reflect itself The mapping can be computed

at each pixel, or only at thevertices

cubic map

7/30/2019 09-texturas

51/59

Types of Environment Maps

The environment map may take one ofseveral forms: Cubic mapping

Easy to produce with rendering system Possible to produce from phtographs uniform resolution Sim ple texture coordinates calculation

Spherical mapping (two variants) Spatially variant resolution

Parabolic mapping Describes the shape of the surface on

which the map resides Determines how the map is generated

and how it is indexed What are some of the issues in

choosing the map?

cubic map

spherical maps

7/30/2019 09-texturas

52/59

Mapping Techniques

Texture Mapping Environmental Mapping Bump Mapping Light Mapping

7/30/2019 09-texturas

53/59

Bump Mapping

7/30/2019 09-texturas

54/59

Bump Mapping:

how does it work? To create a bump-like effect, we

use texture to perturb normals Many textures are the result of

small perturbations in thesurface geometry

Modeling these changes wouldresult in an explosion in thenumber of geometric primitives.

Bump mapping attempts to alterthe lighting across a polygon toprovide the illusion of texture.

We can model this as deviationsfrom some base surface.

The question is then how thesedeviations change the lighting.

N

N

S(u,v) +B(u,v) = S(u,v)original surface bumpedsurfacebump map

7/30/2019 09-texturas

55/59

Bump Mapping:

step 1 and 2 Step 1: Putting everything into

the same coordinate frame as B(u,v). x(u,v), y(u,v), z(u,v) this is given

for parametric surfaces, but easyto derive for other analyticalsurfaces.

OrS(u,v) Step 2: Define the tangent plane

to the surface at a point (u,v) byusing the two vectors S

uand S

v.

The normal is then given by:N= SuSv

N

Su

Sv

7/30/2019 09-texturas

56/59

Bump Mapping:

step 3, 4, and 5 Step 3: The new surface positions are then given by:

S(u,v) =S(u,v) +B(u,v)N where,N=N / |N|

Step 4: Differentiating leads to: Su = Su +BuN+B(N)uSu = Su +BuN Sv = Sv +BvN+B(N)v Sv = Sv +BvNIfB is small.

Step 5: This leads to a new normal: N(u,v) = SuSv -Bu(NSv) +Bv(NSu) +BuBv(NN)

= N -Bu(NSv) +Bv(NSu) = N+ D

N

Su

SvN

D

For efficiency, can store Bu and Bv in a 2-component texture map. The cross products are geometry terms only. Nwill of course need to be normalized after the calculation and before lighting.This

floating point square root and division makes it difficult to embed into hardware.

7/30/2019 09-texturas

57/59

Mapping Techniques

Texture Mapping Environmental Mapping Bump Mapping Light Mapping

7/30/2019 09-texturas

58/59

Light Mapping

Gouraud shading is establishedtechnique for rendering but haswell known limitations Vertex lighting only works well for

small polygons but we dont want lots of

polygons! Solution is to pre-compute some

canonical light effects as texturemaps

For example Suppose we want to show effect

of a wall light Create wall as a single polygon Apply vertex lighting Apply texture map In a second rendering pass, apply

light map to the wall

=

=reflectance irradiance radiosity

7/30/2019 09-texturas

59/59

Light Mapping

Widely used in games industry Latest graphics cards will allow

multiple texture maps per pixel