Image synthesis and OpenGL: textures

1. Textures for what?
2. Parametrization
3. Mapping functions
4. Texture modes
5. Filtering
   
6. Sources
   

Textures for what?

Parametrization

• Correspondence between fragment and texture
• Unfold the 3D surface in 2D
• Parametrization
• compute a texture coordinate per vertex
• the rasterization/interpolation is automatically done from vertex to fragment shader
• fetch texture using uv coordinates in the fragment shader
• Texture space: \( \left[ 0,1 \right] \)
  

1D textures

2D textures

3D textures

Mapping functions

Flat mapping

Cylindrical mapping

Spherical mapping

Cube mapping

Parametric mapping

UV mapping

• Possibility to compute many kinds of uv-coordinates
• via automatic algorithms (difficult problem)
• via designers
  
• Possibility to deform textures
• by non-linearly varying texture coordinates

Texture modes

• GL_CLAMP: use a user defined border value
• GL_CLAMP_TO_EDGE: use the texture border value
• GL_REPEAT: use fractional part of texture coordinates
• GL_MIRRORED_REPEAT: use (possibly reversed) fractional part of texture coordinates

• Also use transformation matrices for offsets, scales, rotation, etc.
  

GL_CLAMP (deprecated)	GL_CLAMP_TO_EDGE
GL_REPEAT	GL_MIRRORED_REPEAT

Filtering

Problem

• Which color do we apply if one texel is projected on several fragments (magnification - GL_TEXTURE_MAG_FILTER)?
• Which color do we apply if several texels are projected on one fragments (minification - GL_TEXTURE_MIN_FILTER)?

Options

• GL_NEAREST: nearest texel from the uv coordinate
• GL_LINEAR: bilinear interpolation. Slower but better.
  

GL_NEAREST / GL_NEAREST	GL_LINEAR / GL_LINEAR
Images from Jerome Jouvie

• Bilinear interpolation
• weighted sum of 4 texels
• \( R_1 = z(1,1)+(z(2,1)-z(1,1))\frac{x-x_1}{x_2-x_1} \)
• \( R_2 = z(1,2)+(z(2,2)-z(1,2))\frac{x-x_1}{x_2-x_1} \)
• \( z = R_1+(R_2-R_1)\frac{y-y_1}{y_2-y_1} \)

Mipmapping

• Pyramid of textures at different resolutions
  
• using glGenerateMipmap()
• Automatic choice by OpenGL depending on filtering options

level 0 1:1	level 1 4:1	level 2 16:1	level 3 64:1	level 4 256:1	level 5 1024:1

• Options (only for minification - GL_TEXTURE_MIN_FILTER)
  
• GL_NEAREST_MIPMAP_NEAREST: nearest texel in the nearest mipmap level
  
• GL_LINEAR_MIPMAP_NEAREST: bilinear interpolation in the nearest mipmap level
• GL_NEAREST_MIPMAP_LINEAR: nearest texel linearly interpolated from the 2 closest mipmap levels
• GL_LINEAR_MIPMAP_LINEAR: bilinear interpolation, interpolated from the 2 closest mipmap levels (trilinear interpolation)
  

GL_NEAREST / GL_NEAREST	GL_LINEAR / GL_LINEAR	GL_LINEAR / GL_LINEAR_MIPMAP_LINEAR
Images from Jerome Jouvie

Sources

• J. Baril, F. Berthaut, N. Mellado
• Xavier Granier
• Mathias Paulin