10. Texture mapping

Brock University
COSC 3P98 Computer Graphics
Instructor: Brian J. Ross

Texture mapping

• using lighting with flat or blended shading renders objects with smooth but constant or blended colour
• most objects have texture: minute details on surfaces
• a number of ways to do this in graphics:
  • a) surface-detail polygons
    • add more polygons of different colours and shapes to give surface detail
    • not realistic for fine detail: too many polygons!
  • b) texture maps: define a texture image, and then "wrap" it around object
  • c) procedural textures: compute the colour of each point on the surface of the object
  • d) bump maps: define a function which varies the geometry of points on the surface when lighting is being computed
    • lighting effects will yield bumpy surface
    • i) surface normal manipulation: normals altered according to bump map, but geometry stays the same
    • ii) surface deformation: actual surface geom is altered

Texture maps

• texture maps: somewhat like a pixmap, except:
  • (i) there isn't a 1:1 correspondence between map entries and pixels;
  • (ii) it is applied to objects in a variety of ways
• texture maps may be drawn, scanned, photographed, generated mathematically (fractals), sampled from a video image...
• typical maps: leathery skin, granite, bricks, spaceships...
• texture map resides in its own 2D coordinate space ("texture space", often (u,v) coords)
• simply means you can talk about texture coords without confusing them with your model coordinate space
• texel: one texture map element
• combined with lighting equations, texture mapping can yield impressive photorealism

Mapping 2D textures

• different geometric mappings (texture projections) possible

• simple one: planar
  • map texture to a plane
  • position the plane with respect to the object, such that it covers the entire object; for example, position it on (x, y) plane.
  • For each surface point P (x,y,z) on model, use it's (x,y) to access colour at texture map position (x, y) --> use that colour at P
    • Effect: the texture runs straight through the entire object from one side to the other.
  • interpolate fractional coordinates on the texture map
  • Can scale the texture onto object by shrinking or expanding its pixmap size.

• cylindrical projection: a texture cylinder encloses the scene
  • first need to map your rectangular bitmap to this cylinder
  • any point on cylinder can be computed by:
    • (r cos A, r sin A, hz)
    • 0 < A < 2*pi
    • 0 < z < 1
  • then texmap coordinates mapped to cylinder via: (u, v) = (A / (2*pi), z)
    • 0 <= u, v <= 1
  • This maps texture to a cylinder. If you have a non-cylindrical object, you can enclose it within the cylinder.
    Then you can use various strategies to associate surface points with the cylinder.

• parametric mapping: the model has a coordinate space defined on it
  • coordinate system generated when model initialized
  • deformed along with model surface during model editing
  • texture coordinates will map around model surface directly; there is a 1 to 1 mapping between texture and all points on the model surface
  • permits precise interactive painting on model (eg. Bodypaint 3D: screendump.)

OpenGL: Texture maps

• OpenGL has a powerful texture mapping utility that has a number of user-specifiable parameters
• Very complex and comprehensive! We'll only touch on its basic capabilities.
• Scheme:
  • Specify the texture.
    • 2d or 1d image; resolution
  • Indicate how texture is to be applied to each pixel.
    • decals, blending with lighting, ...
  • Enable texture mapping.
  • Draw the scene, supplying both texture and geometric coordinates.
    • mapping texture to polygons; how to treat boundaries (wrapping,...)

OpenGL: specifying texture

glTexImage2D(GL_TEXTURE_2D, GLint level, GLint components, GLsizei width, GLsizei height, GLint border, GLenum format, GLenum type, const GLvoid *pixels)

• level - resolution; if 1 resolution, set to 0 (recommended)
• components - number of components, from 1 to 4
  • determines which channels blend with material colours
• width, height - # texels wide, high in image table
  • Note that size must be a power of 2 (64, 128, ...)
• border - width of border (usually 0)
• format, type - information on image format
• pixels - texture image
• image formats: a number of predefined image formats are recognized (see documentation)
  • the glPixelStorei command permits setting formatting conventions for drawing and reading image bitmaps in OpenGL

OpenGL: more texture control commands

glTexEnv{if}{v}(GL_TEXTURE_ENV, GLenum pname, TYPE param);

• defines how textures are applied; e.g.
• if param=GL_REPLACE, then texture's colour is used for polygon's colour
• param=GL_DECAL, then texture's colour is blended with polygon using ALPHA channel
• param= GL_MODULATE, then texture multiplied with other colour
• etc.

glTexParameter{if}{v}(GL_TEXTURE_2D, GLenum pname, TYPE param);

• controls if texture repeats, clamps (last texel used wraps across remainder of poly), how texture magnify or minimize, etc

OpenGL: assigning texture coordinates

• (a) manually: use glTexCoord2*(vertices)
  • for each vertex of polygon, you also supply position it maps to in texture table
  • then texture is linearly interpolated through the polygon when its drawn
  • eg.

glBegin(GL_POLYGON);
   glTexCoord2f(0.0, 0.0); glVertex3f(1.0, -1.0, 0.0);
   glTexCoord2f(0.0, 3.0); glVertex3f(1.0, 1.0, 0.0);
   glTexCoord2f(3.0, 3.0); glVertex3f(2.41, 1.0, -1.41);
   glTexCoord2f(3.0, 0.0); glVertex3f(2.41, -1.0, -1.41);
glEnd();

• (b) Automatic texture coordinate generation: glTexGen( );
  • Can be used to create FX such as mirror reflection.

• Rotating cube with light and texture and screen cap. Note that you could load your own bitmap into the checkerboard texture!
• example program and screen cap: generates its own texture map algorithmically, rather than reading an image

Procedural textures

• 2D textures
  • advantage: literally any picture that can be scanned or painted can be used as a texture
  • disadvantage: difficult to wrap 2d textures around 3D objects
    • stretch marks
    • seams
    • repeated patterns ("tiling")

• procedural textures: (algorithmic textures, 3D textures)
  • texture is computed by a function/program
  • T(x,y,z) is a function over point coord (x,y,z), and returns a colour to render that point
    • Parameters can also include surface characteristics such as height, slope,...
  • think of T(x,y,z) as an infinite function in 3D
  • each renderable point of an object intersects the T(x,y,z) volume; where it intersects it determines its colour/texture
  • if you translate the 3D texture along with the object, the object texture will remain static; otherwise, it will transform when it moves wrt coordinate space

• advantages of 3D textures:
  • continuous in (x,y,z) space; means that texture features wrap around minute folds in objects
    • no seams, stretch marks
    • eg. wood grains will naturally encompass object --> solid texturing
  • infinite variations
  • can obtain very realistic, natural textures: wood, marble, terrain, ...
  • can be animated for special effects: animate the texture equation parameters
    • Example 1.
    • Example 2.
    • Example 3.
    • Example 4.
  • often work hand-in-hand with procedural modeling

• disadvantages of 3D textures:
  • not necessarily easy to create a mathematical model of a desired effect
  • can be computationally expensive

• example 3: noise
  • use a finite lattice of random numbers; numbers denote colours (shades)
  • mod (x,y,z) coordinate into the lattice, and interpolate its colour based on lattice values
  • if you use a spline interpolation, realistic stone effects result
  • can also add turbulence (good for marble)
    • turbulence(x) = sum {i=0 to k} (noise((2^i) x) / 2^i
    • as i increases, its contribution from noise increases, and hence it is scaled by 2^i
    • this has fractal properties: the turbulence has the same general shape no matter how precisely you draw it
  • of course, you also apply lighting effects on top of this (and other example 3d textures)
  • Famous example of using noise to emulate natural textures (minerals, clouds,...): Perlin noise by Ken Perlin (Academy Award winner!)
    (Dr Perlin's home page @ NYU).
  • Here's Eric Sneek's implementation result: Picture

Complex 3D textures: Daz3D Bryce

• Current version is Bryce 7 Pro ($22 US)
• Bryce's realistic (and not-so-realistic) materials make use of:
  • lighting effects
  • 2D texture mapping
  • 3D algorithmic textures
  • mixing of multiple textures
  • other procedural effects (fuzziness, alpha-channels,...)
• 3D textures use model geometry within equations
  • slope or altitude of a mountain can effect textures (snow, rock stratification)
  • shows how modeling and texturing work together
• Impressive cloud FX.

Example Bryce images: One Two. Three. Four.

Complex editor features (Bryce 1)

• an interactive GUI interface that manipulates 3D texture equation parameters

(from Bryce 1.0 user manual)

• Step 1: Noise: basic source of texture
  • type: various algorithmic generation schemes (random, fractal, ...)
  • dimensions: 1D, 2D, 3D, ...
  • frequency: density along # dimensions assigned above
  • orientation: direction of noise
  • octaves: complexity parameter - a cyclic measurement
  • modulation: means for combining octaves
• Step 2: Filter: post-processing of noise signal
  • clipping, smoothing, ...
  • usually, parameter a controls intensity of filter, b adjusts height
• Step 3: Output type
  • value (alpha channel - transparency), colour, normal (bump map)
  • or a combination of the three
• Step 4: can assign 3 components using steps 1 thru 3, and combine them
  • various parameters for blending them together

  Complex texture editor (Bryce 2)

References

• Advanced Animation and Rendering Techniques, A. Watt and M. Watt, Addison-Wesley 1992, ISBN 0-201-54412-1.
• OpenGL Programming Guide, OpenGL ARB, Addison-Wesley 1993, ISBN 0-201-63274-8. (chapter 9)
• The KPT Bryce Book, S. Kitchens, Addison-Wesley 1995, ISBN 0-201-48355-6.
• Real World Bryce 2: the art of digital landscape, S. Kitchens, 1997, ISBN 0-201-694190

COSC 3P98 Computer Graphics
Brock University
Dept of Computer Science
Copyright © 2023 Brian J. Ross (Except noted figures).
http://www.cosc.brocku.ca/Offerings/3P98/course/lectures/texture/
Last updated: November 22, 2023