Texture Mapping

+

=

ObjectTexture

Texture Mapped Object

Texture Mapping Basics

Basic Concepts

Texture (2D Texture): A two-dimensional array of data

Texel : An individual data element in a texture

Texture Space : A normalized coordinate space in which the texture is specified.

s

t

0 1

1

(s, t): Texture Coordinates0.0 s 1.0, 0.0 t 1.0

Surface-Texture Transformation

Transform from object space (x, y, z) to texture space (s, t)

Parametric equation P = P(u, v). Usually transform from parametric space (u, v) to texture space (s, t)

Example: Sphere

x

y

z

P = (x, y, z)

r

sin

sincos

coscos

rz

ry

rxParametric equation:

5.05.0 ,20

Surface-Texture Transformation

5.0

2

t

s

Curved surface

Polygon surface

Specify texture coordinates for each vertex. Then linearly interpolate texture coordinates across projected polygon.

x

y

1

2

3

4 5p(x, y)

),(),(),( 2221

111

21

244 ts

yy

yyts

yy

yyts

),(),(),( 2223

333

23

255 ts

yy

yyts

yy

yyts

Scan line y

),(),(),( 5545

444

45

5 tsxx

xxts

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xxts pp

Texture Mapping Procedure

s

t

xd

yd

Pixel Area

Object Surface

Device Space Object Space Texture Space

STM1MVPM

Projected Pixel Area

Pixel Center

ModelViewProjection MMMM MVP

Surface-texture transformationSTM

Texture Wrapping Methods

Methods to deal with texture coordinates outside [0, 1] range.

Texture

Polygon surface with texture coordinates for four corners

(0, 0) (3, 0)

(3, 3)(0, 3)

Repeat Mirrored Repeat

n s < n 1s s n

n s < n 1if (n is even number) s s nif (n is odd number) s n 1 s

Clamp

if (s < 0) s 0if (s > 1) s 1

Border Clamp

if (s < 0) {s 0; Use border color;}if (s > 1) {s 1; Use border color;}

Border Color:

One-Dimensional and Three-Dimensional Texture

One-Dimensional Texture (Linear Texture)

One-dimensional array of data.Texture coordinate s.

Three-Dimensional Texture (Volume Texture, Solid Texture)

Three-dimensional array of data.Texture coordinates (s, t, r).

s0 1

s t

r

Texture Mapping Examples

Texture Filtering

Texture Filtering: Determine screen pixel color from texel color values using projected pixel area in texture space.

Nearest Filtering

Linear Filtering

Mipmap Nearest Filtering

Mipmap Linear Filtering

Anisotropic Filtering

Texture Minification and Magnification

s

t Projected Pixel Area

Minification: Projected pixel area in texture space is larger than a single texel.

s

t Projected Pixel Area

Magnification: Projected pixel area in texture space is smaller than a single texel.

Nearest Filtering (Point Sampling)

Select the texel whose center lies nearest to the projected pixel center. Use the color of this texel as pixel color.

s

t Projected Pixel Center

Nearest Texel Center

Nearest filtering can result in severe aliasing effects and blocky images.

Linear Filtering (Bilinear Filtering)

Select 22 array of texels that lie nearest to the projected pixel center. The pixel color is linearly interpolated from these texels.

s

t Projected Pixel Center

Linear filtering produces better and smooth texture mapped images.

(s, t)

(s0, t0) (s0+s, t0)

(s0+s, t0+t)(s0, t0+t)Texture array mn

nt

ms

1,

1

),(),(),( 000

000

0 tsss

ssts

s

sssts

CCC

),(),(),( 000

000

0 ttsss

sstts

s

ssstts

CCC

),(),(),( 00

00 tts

t

ttts

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tttts

CCC

Mipmap

Mipmap (multum in parvo, many things in a small place): A series of prefiltered texture images with decreasing resolution.

Level 0 (8 8) Level 1 (4 4) Level 2 (2 2) Level 3 (1 1)

Using a single texture, when object surface moves further away from the viewer, texture mapping may result in artifacts such as shimmering and flashing.

Mipmap is only used for texture minification. Higher mipmap level should be chosen for longer distance between object surface and the viewer.

Mipmap Nearest Filtering

Choose the nearest mipmap level.

Mipmap Linear Filtering

Choose the two nearest mipmap levels. Linearly interpolate between texels sampled from these two levels.

Trilinear Filtering: Use mipmap linear filtering for sampling between mipmap levels and use bilinear filtering for sampling within each mipmap level.

Without Mipmap With Mipmap

Anisotropic Filtering

Texture anisotropy: The projected pixel area in texture space has elongated shape if the object surface forms a steep angle with respect to view plane.

xd

yd

Pixel Area

s

t

Object Surface

Projected Pixel Area

View Plane

xd

yd

Pixel Area

s

t

Object Surface Projected

Pixel Area

Anisotropic Filtering: Use multiple samples in projected pixel area. Different sample patterns are used for different projected pixel area shape.

View Plane

Trilinear Filtering Anisotropic

OpenGL Texture Mapping

OpenGL Texture Mapping Procedures:

1. Create Texture Object.

2. Specify Texture Image for Texture Object.

3. Specify Texture Parameters (Texture Wrapping and Filtering Modes) for Texture Object.

4. Specify Texture Environment (The way in which texel color is combined with fragment color).

5. Enable Texture Mapping and Bind Texture Object.

6. Render Primitives. Specify Texture Coordinates for Each Vertex.

Texture Objects

A texture object stores texture image data and texture parameters. Each texture object is identified by a positive integer index number.

Procedures to use texture objects:

1. Generate texture object names.

2. Initially bind texture objects and set texture image data and parameters.

3. Bind and rebind texture objects for rendering.

4. Delete texture objects when they are no longer needed.

Generate Texture Object Names

void glGenTextures(GLsizei n, GLuint *textureNames)

Return n currently unused integer index names for texture objects and store them in array textureNames.

GLboolean glIsTexture(GLuint textureName)

Return GL_TRUE if textureName is currently used as the name for a texture object. Otherwise return GL_FALSE.

Delete Texture Objects

void glDeleteTextures(GLsizei n, const GLuint *textureNames)

Delete n texture objects whose names are stored in array textureNames. Their data is released and their names are freed.

Bind Texture Objects

void glBindTexture(GLenum target, GLuint textureName)When using textureName for the first time, a new texture object is created. When binding to a previously created texture object, that texture object becomes active.target: Texture targettextureName: Texture object name

target Meaning

GL_TEXTURE_1D One-dimensional Texture

GL_TEXTURE_2D Two-dimensional Texture

GL_TEXTURE_3D Three-dimensional Texture

GL_TEXTURE_CUBE_MAP Cube Environment Map

Use glEnable(target) to enable texture mapping.Use glDisable(target) to disable texture mapping.

Specify Texture Image

• Texture image can be specified from system memory or frame buffer.

• Texture image of a texture object can be replaced entirely or partly after it is initially specified.

• Texture image can be 1D, 2D or 3D. 3D texture support was added in OpenGL 1.2.

• Cube environment map texture consists of six 2D square texture images. Cube map support was added in OpenGL 1.3.

Specify or Replace Texture Image from System MemoryglTexImage*(), glTexSubImage*()

SystemMemory

FrameBuffer

PixelStorageModes

Pixel TransferOperations(Pixel Map)

Unpack Pack

Rasterization(Pixel Zoom)

FragmentOperations

TextureMemory

Specify or Replace Texture Image from Frame BufferglCopyTexImage*(), glCopyTexSubImage*()

SystemMemory

FrameBuffer

PixelStorageModes

Pixel TransferOperations(Pixel Map)

Unpack Pack

Rasterization(Pixel Zoom)

FragmentOperations

TextureMemory

Two-Dimensional Texture

void glTexImage2D(GLenum target, GLint level, GLint internalFormat,GLsizei width, GLsizei height, GLint border, GLenum format, GLenum type, const GLvoid *texels)

target: 2D texture image target.level: Mipmap level. Base level is 0.internalFormat: Internal format for texel data. Indicates how texture im

age is stored internally in texture memory.width: Width of the texture image.height: Height of the texture image.border: Width of the texture image border. Must be 0 or 1.format: Texel data format of source image.type: Texel data type of source image.texels: System memory that stores source image data.

Specify a 2D texture image from system memory. The image is set for texture object currently bound to target.

target Meaning

GL_TEXTURE_2D 2D texture image

GL_TEXTURE_CUBE_MAP_POSITIVE_X Cube map +x face

GL_TEXTURE_CUBE_MAP_NEGATIVE_X Cube map x face

GL_TEXTURE_CUBE_MAP_POSITIVE_Y Cube map +y face

GL_TEXTURE_CUBE_MAP_NEGATIVE_Y Cube map y face

GL_TEXTURE_CUBE_MAP_POSITIVE_Z Cube map +z face

GL_TEXTURE_CUBE_MAP_NEGATIVE_Z Cube map z face

width and height must be (2n + 2border), where n is an integer.

format and type have the same meaning as in glReadPixels() and glDrawPixels(), except that format can not be GL_STENCIL_INDEX.

2D Texture Image Target

Base Internal Format Texel data components

GL_RGB (R, G, B, 1)

GL_RGBA (R, G, B, A)

GL_ALPHA (0, 0, 0, A)

GL_LUMINANCE (L, L, L, 1)

GL_LUMINANCE_ALPHA (L, L, L, A)

GL_INTENSITY (I, I, I, I)

GL_DEPTH_COMPONENT Depth Value

Internal Format

R = Red, G = Green, B = Blue, A = AlphaL = Luminance, I = Intensity

Base Internal Format Internal FormatGL_RGB GL_RGB, GL_R3_G3_B2, GL_RGB4, GL_RGB5, GL_RGB8,

GL_RGB10, GL_RGB12, GL_RGB16

GL_RGBA GL_RGBA, GL_RGBA2, GL_RGBA4, GL_RGB5_A1, GL_RGBA8, GL_RGB10_A2, GL_RGBA12, GL_RGBA16

GL_ALPHA GL_ALPHA, GL_ALPHA4, GL_ALPHA8, GL_ALPHA12, GL_ALPHA16

GL_LUMINANCE GL_LUMINANCE, GL_LUMINANCE4, GL_LUMINANCE8, GL_LUMINANCE12, GL_LUMINANCE16

GL_LUMINANCE_ALPHA GL_LUMINANCE_ALPHA, GL_LUMINANCE4_ALPHA4, GL_LUMINANCE6_ALPHA2, GL_LUMINANCE8_ALPHA8, GL_LUMINANCE12_ALPHA4, GL_LUMINANCE12_ALPHA12, GL_LUMINANCE16_ALPHA16

GL_INTENSITY GL_INTENSITY, GL_INTENSITY4, GL_INTENSITY8, GL_INTENSITY12, GL_INTENSITY16

GL_DEPTH_COMPONENT GL_DEPTH_COMPONENT, GL_DEPTH_COMPONENT16, GL_DEPTH_COMPONENT24, GL_DEPTH_COMPONENT32

Use glGetIntegerv(GL_MAX_TEXTURE_SIZE, …) to obtain maximum supported texture size without border.Use glGetIntegerv(GL_MAX_CUBE_MAP_TEXTURE_SIZE, …) to obtain maximum supported cube map texture size without border.

To use an image with width or height that is not power of two (without border) as texture image, it must be scaled first.

int gluScaleImage(GLenum format, GLint widthin, GLint heightin, GLenum typein, const void *datain, GLint widthout, GLint heightout, GLenum typeout, const void *dataout)

Scale an image. Return 0 if succeeds, otherwise return a GLU error code.format: Pixel data formatwidthin, heightin: Width and height of input imagetypein: Pixel data type of input imagedatain: Input image datawidthout, heightout: Width and height of output imagetypeout: Pixel data type of output imagedataout: Output image data

void glCopyTexImage2D(GLenum target, GLint level, GLint internalFormat,

GLint x, GLint y, GLsizei width, GLsizei height, GLint border)

Specify a 2D texture image from frame buffer.target: 2D texture image target.level: Mipmap level. Base level is 0.internalFormat: Internal format for texel data.x, y: Lower left corner of the source image in frame buffer.width: Width of the texture image.height: Height of the texture image.border: Width of the texture image border. Must be 0 or 1.

target, level, internalFormat, width, height and border have the same meaning as in glTexImage2D().

void glTexSubImage2D(GLenum target, GLint level, GLint xoff, GLint yoff, GLsizei width, GLsizei height, GLenum format, GLenum type, const GLvoid *texels)

xoff, yoff: Texel offsets of the lower left corner of the subimage with respect to the lower left corner of the entire texture image.

width: Width of the texture subimage.height: Height of the texture subimage.

Replace a subimage of a 2D texture with image data from system memory.

Other parameters have the same meaning as in glTexImage2D().

void glCopyTexSubImage2D(GLenum target, GLint level, GLint xoff, GLint yoff, GLint x, GLint y, GLsizei width, GLsizei height)

Replace a subimage of a 2D texture with image data from frame buffer.x, y: Lower left corner of the source image rectangle in frame buffer.Other parameters have the same meaning as in glTexSubImage2D().

Sub-Image

Texture Imageyoff

xoff

width

height

Automatic Mipmap Generation

int gluBuild2DMipmaps(GLenum target, GLint internalFormat,GLsizei width, GLsizei height,GLenum format, GLenum type, const GLvoid *texels)

Construct a series of mipmaps down to resolution of 1 1, then call glTexImage2D() to load texture images on all mipmap levels. Also automatically scale the original image so that its width and height become power of two. All parameters have the same meaning as in glTexImage2D().Return 0 if succeeds, otherwise return a GLU error code.

One-Dimensional Texture

glTexImage1D(), glTexSubImage1D()

glCopyTexImage1D(), glCopyTexSubImage1D()

gluBuild1DMipmaps()

Three-Dimensional Texture

glTexImage3D(), glTexSubImage3D()

glCopyTexImage3D(), glCopyTexSubImage3D()

gluBuild3DMipmaps()

Specify Texture Parameters

void glTexParameteri(GLenum target, GLenum pname, GLint param)void glTexParameterf(GLenum target, GLenum pname, GLfloat param)void glTexParameteriv(GLenum target, GLenum pname, GLint *param)void glTexParameterfv(GLenum target, GLenum pname, GLfloat *param)Specify texture parameters for texture object that is currently bound to target.target: GL_TEXTURE_1D

GL_TEXTURE_2DGL_TEXTURE_3DGL_TEXTURE_CUBE_MAP

pname: Texture parameter nameparam: Texture parameter value

Texture parameter name Values

GL_TEXTURE_BORDER_COLOR (R, G, B, A)

GL_TEXTURE_MAG_FILTER GL_NEARESTGL_LINEAR

GL_TEXTURE_MIN_FILTER GL_NEARESTGL_LINEARGL_NEAREST_MIPMAP_NEARESTGL_NEAREST_MIPMAP_LINEARGL_LINEAR_MIPMAP_NEARESTGL_LINEAR_MIPMAP_LINEAR

GL_TEXTURE_WRAP_SGL_TEXTURE_WRAP_TGL_TEXTURE_WRAP_R

GL_REPEATGL_MIRRORED_REPEATGL_CLAMPGL_CLAMP_TO_EDGE

GL_CLAMP_TO_EDGE was added in OpenGL 1.2.GL_MIRRORED_REPEAT was added in OpenGL 1.4.

Constant Texture Border Color

pname = GL_TEXTURE_BORDER_COLOR

Constant texture border color is used as border color when the texture image does not have borders.

Texture Magnification Filter

pname = GL_TEXTURE_MAG_FILTER

param Meaning

GL_NEAREST Nearest filtering

GL_LINEAR Linear filtering

Texture Minification Filter

pname = GL_TEXTURE_MIN_FILTER

param Meaning

GL_NEAREST Nearest filtering (Mipmap is not used)

GL_LINEAR Linear filtering (Mipmap is not used)

GL_NEAREST_MIPMAP_NEAREST Nearest filtering within each mipmapNearest filtering between mipmaps

GL_NEAREST_MIPMAP_LINEAR Nearest filtering within each mipmapLinear filtering between mipmaps

GL_LINEAR_MIPMAP_NEAREST Linear filtering within each mipmapNearest filtering between mipmaps

GL_LINEAR_MIPMAP_LINEAR Linear filtering within each mipmapLinear filtering between mipmaps

Texture Wrapping Modes

pname Meaning

GL_TEXTURE_WRAP_S Texture wrapping mode for s coordinate

GL_TEXTURE_WRAP_T Texture wrapping mode for t coordinate

GL_TEXTURE_WRAP_R Texture wrapping mode for r coordinate

param Meaning

GL_REPEAT Integer part of texture coordinate is ignored.Border color is always ignored. For linear filtering, 22 texel array wraps to the opposite edge of the texture.

GL_MIRRORED_REPEAT Integer part of texture coordinate is ignored. Fractional part is reversed at every integer boundary. The rest is the same as GL_REPEAT.

GL_CLAMP Texture coordinate is clamped to [0, 1]. Edge color is used for nearest filtering. Border color is used in 22 texel array for linear filtering.

GL_CLAMP_TO_EDGE Texture coordinate is clamped to [0, 1]. Border color is always ignored. Texels at or near the edge are used.

Specify Texture Environment

void glTexEnvi(GLenum envtarget, GLenum pname, GLint param)void glTexEnvf(GLenum envtarget, GLenum pname, GLfloat param)void glTexEnviv(GLenum envtarget, GLenum pname, GLint *param)void glTexEnvfv(GLenum envtarget, GLenum pname, GLfloat *param)

Specify texture environment. Texture environment determines how texture color is combined with incoming fragment color.envtarget: Must be GL_TEXTURE_ENV

pname param

GL_TEXTURE_ENV_MODE GL_REPLACE GL_MODULATE GL_DECALGL_BLEND

GL_TEXTURE_ENV_COLOR Constant environment color (Rc, Gc, Bc, Ac)

Base Internal Format Texture source color (Rs, Gs, Bs, As)

GL_RGB (R, G, B, 1)

GL_RGBA (R, G, B, A)

GL_ALPHA (0, 0, 0, A)

GL_LUMINANCE (L, L, L, 1)

GL_LUMINANCE_ALPHA (L, L, L, A)

GL_INTENSITY (I, I, I, I)

• Texture source color (Rs, Gs, Bs, As)

• Incoming fragment color (Rf, Gf, Bf, Af)

• Constant environment color (Rc, Gc, Bc, Ac)

• Final combined color (R, G, B, A)

Replace Mode

Base Internal Format GL_REPLACE

GL_ALPHA R = Rf, G = Gf , B = Bf

A = As

GL_RGBGL_LUMINANCE

R = Rs, G = Gs , B = Bs

A = Af

GL_RGBAGL_LUMINANCE_ALPHAGL_INTENSITY

R = Rs, G = Gs , B = Bs

A = As

The texture source color components replace corresponding fragment color components.

Modulation Mode (default mode)

Base Internal Format GL_MODULATE

GL_ALPHA R = Rf, G = Gf , B = Bf A = AfAs

GL_RGBGL_LUMINANCE

R = RfRs, G = GfGs , B = BfBs

A = Af

GL_RGBAGL_LUMINANCE_ALPHAGL_INTENSITY

R = RfRs, G = GfGs , B = BfBs

A = AfAs

The texture source color components multiply corresponding fragment color components.

Decal Mode

Base Internal Format GL_DECAL

GL_RGB R = Rs, G = Gs , B = Bs

A = Af

GL_RGBA R = Rf(1 As) + RsAs

G = Gf(1 As) + GsAs

R = Bf(1 As) + BsAs

A = Af

GL_ALPHAGL_LUMINANCEGL_LUMINANCE_ALPHAGL_INTENSITY

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For GL_RGB format, The texture source color replace fragment color.For GL_RGBA format, The texture source color is linearly blended with fragment color, using source alpha as blending weight.

Blending Mode

Base Internal Format GL_BLEND

GL_ALPHA R = Rf, G = Gf , B = Bf A = AfAs

GL_RGBGL_LUMINANCE

R = Rf(1 Rs) + RcRs

G = Gf(1 Gs) + GcGs

B = Bf(1 Bs) + BcBs

A = Af

GL_RGBAGL_LUMINANCE_ALPHAGL_INTENSITY

R = Rf(1 Rs) + RcRs

G = Gf(1 Gs) + GcGs

B = Bf(1 Bs) + BcBs

A = AfAs

The fragment color is linearly blended with constant environment color, using texture source color as blending weight.

Specify Texture Coordinates

void glTexCoord2{sifd}(TYPE s, TYPE t)

Specify current texture coordinates. Vertices defined using subsequent glVertex*() commands are assigned current texture coordinates.This command must be used between glBegin( ) and glEnd( ).

void glTexCoord3{sifd}(TYPE s, TYPE t , TYPE r)

void glTexCoord{1234}{sifd}v(TYPE * texcoords)

void glTexCoord4{sifd}(TYPE s, TYPE t , TYPE r , TYPE q)

void glTexCoord1{sifd}(TYPE s)

Texture coordinates

Meaning Applicable texture target

(s) One-dimensional GL_TEXTURE_1D

(s, t) Two-dimensional GL_TEXTURE_2D

(s, t, r) Three-dimensional GL_TEXTURE_3DGL_TEXTURE_CUBE_MAP(s, t, r, q) Homogeneous

Texture Matrix

• Texture matrix is a 44 transformation matrix that is used to transform texture coordinates.

• Texture matrix stack has two entries.

• Use glMatrixMode(GL_TEXTURE) to set current matrix to texture matrix.

• All standard matrix manipulation commands can be applied to texture matrix.

• The default texture matrix is an identity matrix.

Homogeneous Texture Coordinates

q

r

t

s

q

r

t

s

Tq

q

q

M

qrr

qtt

qss

q

q

q

Texture coordinates Homogeneous coordinates

(s) (s, 0, 0, 1)

(s, t) (s, t, 0, 1)

(s, t, r) (s, t, r, 1)

(s, t, r, q) (s, t, r, q)

[MT] is the texture matrix. (s', t', r') are the transformed texture coordinates.Homogenous texture coordinates also undergo perspective division.

Automatic Texture Coordinate Generation

void glTexGen{ifd}(GLenum coord, GLenum pname, TYPE param)void glTexGen{ifd}v(GLenum coord, GLenum pname, TYPE *param)Specify functions for automatic texture coordinate generation.coord: Specify which texture coordinate to use automatic generation.

Valid values are GL_S, GL_T, GL_R, GL_Q

pname param

GL_TEXTURE_GEN_MODE GL_OBJECT_LINEARGL_EYE_LINEARGL_SPHERE_MAPGL_REFLECTION_MAPGL_NORMAL_MAP

GL_OBJECT_PLANE Plane equation coefficients (A, B, C, D)

GL_EYE_PLANE Plane equation coefficients (A, B, C, D)

To enable automatic texture coordinate generation for s-coordinate, use glEnable(GL_TEXTURE_GEN_S).To enable automatic texture coordinate generation for t-coordinate, use glEnable(GL_TEXTURE_GEN_T).To enable automatic texture coordinate generation for r-coordinate, use glEnable(GL_TEXTURE_GEN_R).To enable automatic texture coordinate generation for q-coordinate, use glEnable(GL_TEXTURE_GEN_Q).

Linear Generation Mode (GL_OBJECT_LINEAR, GL_EYE_LINEAR)

GL_OBJECT_LINEAR

Texture coordinate = Ax + By + Cz + Dh(A, B, C, D) are plane equation coefficients specified using GL_OBJECT_PLANE parameter.(x, y, z, h) are vertex coordinates in object space.

GL_EYE_LINEAR

Texture coordinate = A'xe + B'ye + C'ze + D'he

[A' B' C' D']=[A B C D][M]1

(A, B, C, D) are plane equation coefficients specified using GL_EYE_PLANE parameter. [M] is modeview matrix when (A, B, C, D) was specified. (xe, ye, ze, he) are vertex coordinates in eye space.

Sphere Map (GL_SPHERE_MAP)

1. Calculate reflection vector R in eye space.2. Use R to calculate texture coordinates (s, t) for sampling in a sphere

environment map.

Cube Map (GL_REFLECTION_MAP, GL_NORMAL_MAP)

GL_REFLECTION_MAP

1. Calculate reflection vector R in eye space.2. Use R directly as texture coordinates (s, t, r) for sampling in a cube

environment map.

GL_NORMAL_MAP

1. Transform normal vector N from object space to eye space.2. Use transformed N as texture coordinates (s, t, r) for sampling in a

cube environment map.