Texture MappingTexture Mapping

ScopeScope

BuffersBuffersVarious of graphics imageVarious of graphics imageTexture mappingTexture mapping

IntroductionIntroduction

When we deal with texture When we deal with texture 2D image may use as texture for surface2D image may use as texture for surface

Frame Buffers

Color bufferColor buffer Front bufferFront buffer Back bufferBack buffer 32 bit for RGBA32 bit for RGBA

Depth bufferDepth buffer Deal with z valueDeal with z value

Image formatImage format Bitmap (bmp)Bitmap (bmp) TIFFTIFF

2 forms: uncompress and compressed2 forms: uncompress and compressed JPGJPG

Compressed imageCompressed image Post Script (PS)Post Script (PS)

used in printer controlused in printer control Coded in 7 bit of ASCII character setCoded in 7 bit of ASCII character set Understood by a large class of printerUnderstood by a large class of printer Large in sizeLarge in size

Encapsulated Post Script (EPS)Encapsulated Post Script (EPS) PS similar but add additional information for previewing images.

GIFGIF For index images with color table and an array of image indices.

Writes into BuffersWrites into Buffers

OpenGL Buffers and the Pixel OpenGL Buffers and the Pixel PipelinePipeline

Color buffersFront and back buffer

Depth bufferHidden surface removal

Accumulation bufferCombination of multiple image

Stencil bufferMasking operation

Pixels and ImagesPixels and Images

Screen smallest elementScreen smallest element Image just 2DImage just 2D

Mapping MethodsMapping Methods

Texture mappingTexture mappingPattern (texture) determined the color of Pattern (texture) determined the color of

fragmentfragmentMap on smooth surfaceMap on smooth surface

Bump mappingBump mappingDistort the normal vector Distort the normal vector Make some bump on surfaceMake some bump on surface

Environmental mappingEnvironmental mapping Image that have the appearance of ray traceImage that have the appearance of ray trace

Texture MappingTexture Mapping

Some patternsSome patternsRegardless of patternRegardless of pattern

1D for stripe, curve etc1D for stripe, curve etc2D use to map on surface2D use to map on surface3D map on solid box3D map on solid box

Two-Dimensional Texture MappingTwo-Dimensional Texture Mapping

Mapping involved among 3 or 4 different coordinate systems.Mapping involved among 3 or 4 different coordinate systems. Screen coordinate at first, Final at world coordinate systemScreen coordinate at first, Final at world coordinate system World coordinate: object is described hereWorld coordinate: object is described here Texture coordinate: describe textureTexture coordinate: describe texture Parametric coordinate: for the relation of curve or surfaceParametric coordinate: for the relation of curve or surface

Texture processTexture process Start out with 2D image may come fromStart out with 2D image may come from

Photo scanningPhoto scanning Form by applicationForm by application

Brought into the memory arrayBrought into the memory array Smallest element call texel (texture element) Smallest element call texel (texture element) texel is represented by T(s,t) texel is represented by T(s,t) (texel coordinate)(texel coordinate)

where s where s and and tt are texture coordinate. are texture coordinate. Often range between 0 and 1Often range between 0 and 1

Mapping approachMapping approach

General form of General form of mappingmapping

Let (x,y,z,w) object Let (x,y,z,w) object coordinate and coordinate and

( , )

( , )

( , )

( , )

x x s t

y y s t

z z s t

w w s t

Texture mapping function

( , , , )

( , , , )

s s x y z w

t t x y z w

Inverse function

A method of texture mappingA method of texture mapping

Texture maps for a parametric surface.

Map texture together with parametric on to geometric coordinate Last project onto the screen coordinate

Map the texture coordinate to geometric Map the texture coordinate to geometric coordinatecoordinate

Texture to screen coordinateTexture to screen coordinateWe interested in mapping area to areaWe interested in mapping area to area

Aliasing problem may happenAliasing problem may happen

Direct mapping between texel Direct mapping between texel coordinate to parametric coordinatecoordinate to parametric coordinate

( )

p( )= ( )

( )

x u,v

u,v y u,v

z u,v

=

=

u as+bt +c

v ds+et + f( )

( )

minmin max min

max min

minmin max min

max min

s su u u u

s s

t tv v v v

t t

Two-part mappingTwo-part mapping

Use for map on curve surface Use for map on curve surface 2 steps2 steps

Map texture on intermediate surfaceMap texture on intermediate surfaceMap intermediate surface to surface being Map intermediate surface to surface being

renderedrenderedUseable both parametric and geometric Useable both parametric and geometric

coordinatecoordinate

Suppose that map on the cylinder surfaceSuppose that map on the cylinder surface

cos(2 )

sin(2 )

/

x r u

y r u

z v h

Texture mapping with a cylinder

s u

t v

What happen if the object is sphere? Some distortion happen at the pole. Why ?

Mapping texture on the intermediate object to the Mapping texture on the intermediate object to the desire surfacedesire surface

3 possible strategies3 possible strategies a. Place the texture at the finding point of intersection a. Place the texture at the finding point of intersection

of normal from object edgeof normal from object edge b. place the texture at the interaction point of normal b. place the texture at the interaction point of normal

intersect the intermediate surfaceintersect the intermediate surface c. draw a line from the center of the object to edgec. draw a line from the center of the object to edge

Texture Mapping in OpenGLTexture Mapping in OpenGL

OpenGL pipelines merge at rendering (rasterization) stage

process: maps 3D points to pixels on the display. visibility is test (with the z-buffer) and is shaded if visible.Vertices are mapped to texture coordinates in object defined stage, values can then be obtained by interpolation like color to polygons

Define texel arrayDefine texel array

Assign to texture imageAssign to texture image

Enable textureEnable texture

GLubyte my_texels[512][512];

glTexImage2D(GL_TEXTURE_2D, 0, 3, 512, 512, 0, GL_RGB, GL_UNSIGNED_BYTE, my_texels);

glEnable(GL_TEXTURE_2D);

Defining texture to object.Defining texture to object.

t and s have value between 0 and 1 t and s have value between 0 and 1 correspond to texel array (mytexels)correspond to texel array (mytexels)

Mapping can happened at object definition Mapping can happened at object definition stage in glBegin and glEnd loopstage in glBegin and glEnd loop

Correspond of texel to image coordinate. Opengl use interpolate to match the image.

glBegin(GL_QUAD); glTexCoord2f(0.0,0.0); glVertex2f(x1, y1); glTexCoord2f(1.0,0.0); glVertex2f(x2, y2); glTexCoord2f(1.0,1.0); glVertex2f(x3, y3); glTexCoord2f(0.0,1.0); glVertex2f(x4, y4);glEnd();

Map texture using glTexCoord

Texture map condition (a) only 100% (b) 50% of texture

Mapping of texture to polygons. (a and b) Mapping of a checkerboard texture to a triangle. (c) Mapping of a checkerboard texture to a trapezoid.

When (s,t) outside (0,1)When (s,t) outside (0,1)

We can set for repeat or clamp when We can set for repeat or clamp when value is out of boundvalue is out of bound

For clamping use GL_CLAMP instead of For clamping use GL_CLAMP instead of GL_REPEATGL_REPEAT

glTexParameteri(GL_TEXTURE_WRAP_S, GL_REPEAT); // for sglTexParameteri(GL_TEXTURE_WRAP_T, GL_CLAMP); // clamp t

Alias problemAlias problem

Texel is rarely get the centerTexel is rarely get the center Use point samplingUse point sampling

Closet texel is use for interpolateCloset texel is use for interpolate

Weighted average of a group of texelWeighted average of a group of texel Linear filteringLinear filtering

Problem may occur at the edgeProblem may occur at the edge Add more texel row and columAdd more texel row and colum (2(2mm+1)x(2+1)x(2nn+1)+1)

Most of texel doesn’t math the pixelMost of texel doesn’t math the pixel

Mapping texels to pixels condition (a) Magnification. (b) Minification.

In both cases, use the value of the nearest point sampling. glTexParameteri(GL_TEXTURE_2D,GL_TEXTURE_MAG_FILTER,GL_NEAREST);glTexParameteri(GL_TEXTURE_2D,GL_TEXTURE_MIN_FILTER,GL_NEAREST);

More smooth use GL_LINEAR instead of GL_NEAREST

What do we do when texel is larger than pixel ?What do we do when texel is larger than pixel ?

Use mipmapping technique for minification Use mipmapping technique for minification We can reduce size of texel to match the image by let We can reduce size of texel to match the image by let

OpenGL interpolate for a small oneOpenGL interpolate for a small one

gluBuild2DMipmaps(GL_TEXTURE_2D,3,64,64,GL_RGB,GL_UNSIGNED_BYTE, my_texels);

Or control parameter level of glTexImage2D() instead

glTexImage2D(GL_TEXTURE_2D, level, components, width, height,border, format, type, tarray);

Texture and shading

2 options2 optionsMultiply the shading and texture by controlMultiply the shading and texture by control

Decal the texture to object Decal the texture to object

glTexEnvi(GL_TEX_ENV,GL_TEX_ENV_MODE, GL_MODULATE);

glTexEnvi(GL_TEX_ENV,GL_TEX_ENV_MODE, GL_DECAL);

Projection correctionProjection correction

No need for orthogonal projection if linear No need for orthogonal projection if linear interpolation is useinterpolation is use

For perspective projectionFor perspective projection due to non linear depth scaling due to non linear depth scaling a better interpolation is apply by usea better interpolation is apply by use

glHint(GL_PERSPECTIVE_CORRECTION, GL_NICEST);

Texture transformationTexture transformation

As vertices definitionAs vertices definitionTransformation such as scaling, rotating, Transformation such as scaling, rotating,

move etcmove etcTexture coordinate store in the form of 4D Texture coordinate store in the form of 4D

matrix call matrix call texture matrixtexture matrix Initially matrix is identicalInitially matrix is identicalManipulate by glMatrixMode()Manipulate by glMatrixMode()

glMatrixMode(GL_TEXTURE);

Environmental / Reflection MapsEnvironmental / Reflection Maps

appear on highly specular surface eg. mirrorappear on highly specular surface eg. mirror use physically base rendering method such as ray use physically base rendering method such as ray

tracertracer basic ideabasic idea

follow the r = 2(v.n)n-v until intersect the environmentfollow the r = 2(v.n)n-v until intersect the environment shad the reflect to the objectshad the reflect to the object approximate using step 2approximate using step 2