1. Texture Mapping +
Texture
Object =
Texture Mapped Object

2. 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. t 1
(s, t): Texture Coordinates
0.0  s  1.0, 0.0  t  1.0 s 1

3. Surface-Texture Transformation
Transform from object space (x, y, z) to texture space (s, t)
Curved surface
Parametric equation P = P(u, v). Usually transform from parametric space (u, v) to texture space (s, t)
Example: Sphere
Parametric equation: z
P = (x, y, z) r  y 
Surface-Texture Transformation x

4. Polygon surface
Specify texture coordinates for each vertex. Then linearly interpolate texture coordinates across projected polygon. y 3 1
Scan line y 4
p(x, y) 5 2 x

5. Texture Mapping Procedure
Projected Pixel Area yd t
Pixel Area
Object Surface s
Pixel Center xd
Device Space
Object Space
Texture Space
Surface-texture transformation

6. Polygon surface with texture coordinates for four corners
Texture Wrapping Methods
Methods to deal with texture coordinates outside [0, 1] range.
(0, 3)
(3, 3)
Texture
(0, 0)
(3, 0)
Polygon surface with texture coordinates for four corners

7. Repeat
Mirrored Repeat
n  s < n  1
s  s  n
n  s < n  1
if (n is even number) s  s  n
if (n is odd number) s  n  1  s

8. Clamp
Border Clamp
if (s < 0) s  0
if (s > 1) s  1
if (s < 0) {s  0; Use border color;}
if (s > 1) {s  1; Use border color;}
Border Color:

9. One-Dimensional and Three-Dimensional Texture
One-Dimensional Texture
(Linear Texture)
Three-Dimensional Texture
(Volume Texture, Solid Texture)
One-dimensional array of data.
Three-dimensional array of data.
Texture coordinate s.
Texture coordinates (s, t, r). r s 1 s t

10. Texture Mapping Examples

11. Texture Filtering Nearest Filtering Linear 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

12. Texture Minification and Magnification
Projected Pixel Area
Projected Pixel Area s s
Minification: Projected pixel area in texture space is larger than a single texel.
Magnification: Projected pixel area in texture space is smaller than a single texel.

13. Projected Pixel Center
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. t
Projected Pixel Center
Nearest Texel Center s
Nearest filtering can result in severe aliasing effects and blocky images.

14. Projected Pixel Center
Linear Filtering (Bilinear Filtering)
Select 22 array of texels that lie nearest to the projected pixel center. The pixel color is linearly interpolated from these texels. t
Projected Pixel Center s
Linear filtering produces better and smooth texture mapped images.

15. Texture array mn (s0, t0+t) (s0+s, t0+t) (s, t) (s0, t0)

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

17. 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.

18. Without Mipmap
With Mipmap

19. 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. yd
Projected Pixel Area t
Pixel Area
Object Surface s xd
View Plane

20. yd
Object Surface
Projected Pixel Area t
Pixel Area s xd
View Plane
Anisotropic Filtering: Use multiple samples in projected pixel area. Different sample patterns are used for different projected pixel area shape.

21. Trilinear Filtering
Anisotropic

23. OpenGL Texture Mapping
OpenGL Texture Mapping Procedures:
Create Texture Object.
Specify Texture Image for Texture Object.
Specify Texture Parameters (Texture Wrapping and Filtering Modes) for Texture Object.
Specify Texture Environment (The way in which texel color is combined with fragment color).
Enable Texture Mapping and Bind Texture Object.
Render Primitives. Specify Texture Coordinates for Each Vertex.

24. 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:
Generate texture object names.
Initially bind texture objects and set texture image data and parameters.
Bind and rebind texture objects for rendering.
Delete texture objects when they are no longer needed.

25. 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.

26. 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 target
textureName: 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.

27. 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.

28. Specify or Replace Texture Image from System Memory
glTexImage*(), glTexSubImage*()
System
Memory
Texture
Memory
Frame
Buffer
Unpack
Pack
Fragment
Operations
Pixel
Storage
Modes
Pixel Transfer
Operations
(Pixel Map)
Rasterization
(Pixel Zoom)

29. Specify or Replace Texture Image from Frame Buffer
glCopyTexImage*(), glCopyTexSubImage*()
System
Memory
Texture
Memory
Frame
Buffer
Unpack
Pack
Fragment
Operations
Pixel
Storage
Modes
Pixel Transfer
Operations
(Pixel Map)
Rasterization
(Pixel Zoom)

30. Two-Dimensional Texture
void glTexImage2D(GLenum target, GLint level, GLint internalFormat,
GLsizei width, GLsizei height, GLint border,
GLenum format, GLenum type, const GLvoid *texels)
Specify a 2D texture image from system memory. The image is set for texture object currently bound to target.
target: 2D texture image target.
level: Mipmap level. Base level is 0.
internalFormat: Internal format for texel data. Indicates how texture image 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.

31. 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
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

32. Internal Format
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
R = Red, G = Green, B = Blue, A = Alpha
L = Luminance, I = Intensity

33. Base Internal Format Internal Format GL_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

34. 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 format
widthin, heightin: Width and height of input image
typein: Pixel data type of input image
datain: Input image data
widthout, heightout: Width and height of output image
typeout: Pixel data type of output image
dataout: Output image data

35. void glCopyTexImage2D(GLenum target, GLint level,
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().

36. void glTexSubImage2D(GLenum target, GLint level,
GLint xoff, GLint yoff, GLsizei width, GLsizei height,
GLenum format, GLenum type, const GLvoid *texels)
Replace a subimage of a 2D texture with image data from system memory.
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.
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().

37. width
Sub-Image
height
xoff
yoff
Texture Image

38. 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.

39. One-Dimensional Texture
glTexImage1D(), glTexSubImage1D()
glCopyTexImage1D(), glCopyTexSubImage1D()
gluBuild1DMipmaps()
Three-Dimensional Texture
glTexImage3D(), glTexSubImage3D()
glCopyTexImage3D(), glCopyTexSubImage3D()
gluBuild3DMipmaps()

40. 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_2D
GL_TEXTURE_3D
GL_TEXTURE_CUBE_MAP
pname: Texture parameter name
param: Texture parameter value

41. Texture parameter name Values
GL_TEXTURE_BORDER_COLOR
(R, G, B, A)
GL_TEXTURE_MAG_FILTER
GL_NEAREST
GL_LINEAR
GL_TEXTURE_MIN_FILTER
GL_NEAREST_MIPMAP_NEAREST
GL_NEAREST_MIPMAP_LINEAR
GL_LINEAR_MIPMAP_NEAREST
GL_LINEAR_MIPMAP_LINEAR
GL_TEXTURE_WRAP_S
GL_TEXTURE_WRAP_T
GL_TEXTURE_WRAP_R
GL_REPEAT
GL_MIRRORED_REPEAT
GL_CLAMP
GL_CLAMP_TO_EDGE
GL_CLAMP_TO_EDGE was added in OpenGL 1.2.
GL_MIRRORED_REPEAT was added in OpenGL 1.4.

42. 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

43. 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 mipmap
Nearest filtering between mipmaps
GL_NEAREST_MIPMAP_LINEAR
Linear filtering between mipmaps
GL_LINEAR_MIPMAP_NEAREST
Linear filtering within each mipmap
GL_LINEAR_MIPMAP_LINEAR

44. 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, 22 texel array wraps to the opposite edge of the texture.
GL_MIRRORED_REPEAT
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 22 texel array for linear filtering.
GL_CLAMP_TO_EDGE
Border color is always ignored.
Texels at or near the edge are used.

45. 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_DECAL
GL_BLEND
GL_TEXTURE_ENV_COLOR
Constant environment color
(Rc, Gc, Bc, Ac)

46. 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)

47. Replace Mode
The texture source color components replace corresponding fragment color components.
Base Internal Format
GL_REPLACE
GL_ALPHA
R = Rf, G = Gf , B = Bf
A = As
GL_RGB
GL_LUMINANCE
R = Rs, G = Gs , B = Bs
A = Af
GL_RGBA
GL_LUMINANCE_ALPHA
GL_INTENSITY

48. Modulation Mode (default mode)
The texture source color components multiply corresponding fragment color components.
Base Internal Format
GL_MODULATE
GL_ALPHA
R = Rf, G = Gf , B = Bf
A = AfAs
GL_RGB
GL_LUMINANCE
R = RfRs, G = GfGs , B = BfBs
A = Af
GL_RGBA
GL_LUMINANCE_ALPHA
GL_INTENSITY

49. Decal Mode
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.
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
GL_ALPHA
GL_LUMINANCE
GL_LUMINANCE_ALPHA
GL_INTENSITY
undefined

50. Blending Mode
The fragment color is linearly blended with constant environment color, using texture source color as blending weight.
Base Internal Format
GL_BLEND
GL_ALPHA
R = Rf, G = Gf , B = Bf
A = AfAs
GL_RGB
GL_LUMINANCE
R = Rf(1  Rs) + RcRs
G = Gf(1  Gs) + GcGs
B = Bf(1  Bs) + BcBs
A = Af
GL_RGBA
GL_LUMINANCE_ALPHA
GL_INTENSITY

51. Specify Texture Coordinates
void glTexCoord1{sifd}(TYPE s)
void glTexCoord2{sifd}(TYPE s, TYPE t)
void glTexCoord3{sifd}(TYPE s, TYPE t , TYPE r)
void glTexCoord4{sifd}(TYPE s, TYPE t , TYPE r , TYPE q)
void glTexCoord{1234}{sifd}v(TYPE * texcoords)
Specify current texture coordinates. Vertices defined using subsequent glVertex*() commands are assigned current texture coordinates.
This command must be used between glBegin( ) and glEnd( ).
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_3D
GL_TEXTURE_CUBE_MAP
(s, t, r, q)
Homogeneous

52. Texture Matrix
Texture matrix is a 44 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.

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

54. 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_LINEAR
GL_EYE_LINEAR
GL_SPHERE_MAP
GL_REFLECTION_MAP
GL_NORMAL_MAP
GL_OBJECT_PLANE
Plane equation coefficients (A, B, C, D)
GL_EYE_PLANE

55. 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).

56. Linear Generation Mode (GL_OBJECT_LINEAR, GL_EYE_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.

57. Sphere Map (GL_SPHERE_MAP)
Calculate reflection vector R in eye space.
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
Calculate reflection vector R in eye space.
Use R directly as texture coordinates (s, t, r) for sampling in a cube environment map.
GL_NORMAL_MAP
Transform normal vector N from object space to eye space.
Use transformed N as texture coordinates (s, t, r) for sampling in a cube environment map.