Lecture 8 - Texture Mapping

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CSC 830 Computer GraphicsLecture 6 Texture more
Course Note Credit Some of slides are extracted
from the course notes of prof. Mathieu Desburn
(USC) and prof. Han-Wei Shen (Ohio State
University).
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Announcements

• Term Project Proposal Due April 14th (next
  class)
• Assignment 4 Shading 5 texture

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Can you do this
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Texture Mapping

• Surfaces in the wild are very complex
• Cannot model all the fine variations
• We need to find ways to add surface detail
• How?

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Texture Mapping

• Particles and fractals
• gave us lots of detail information
• not easy to model
• mathematically and computationally challenging

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Texture Mapping

• Of course, one can model the exact micro-geometry
  material property to control the look and feel
  of a surface
• But, it may get extremely costly
• So, graphics use a more practical approach
  texture mapping

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Texture Mapping

• Solution - (its really a cheat!!)
• How?

MAP surface detail from a predefined
multi-dimensional table (texture) to a simple
polygon
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Slide Courtesy of Leonard McMillan Jovan
Popovic, MIT
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OpenGL functions - demo

• During initialization read in or create the
  texture image and place it into the OpenGL state.
• glTexImage2D (GL_TEXTURE_2D, 0, GL_RGB,
  imageWidth, imageHeight, 0, GL_RGB,
  GL_UNSIGNED_BYTE, imageData)
• Before rendering your textured object, enable
  texture mapping and tell the system to use this
  particular texture.
• glBindTexture (GL_TEXTURE_2D, 13)

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OpenGL functions

• During rendering, give the cartesian coordinates
  and the texture coordinates for each vertex.
• glBegin (GL_QUADS)
• glTexCoord2f (0.0, 0.0)
• glVertex3f (0.0, 0.0, 0.0)
• glTexCoord2f (1.0, 0.0)
• glVertex3f (10.0, 0.0, 0.0)
• glTexCoord2f (1.0, 1.0)
• glVertex3f (10.0, 10.0, 0.0)
• glTexCoord2f (0.0, 1.0)
• glVertex3f (0.0, 10.0, 0.0)
• glEnd ()

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What happens when outside the 0-1 range?

• (u,v) should be in the range of 01
• What happens when you request (1.5 2.3)?
• Tile repeat (OGL) the integer part of the value
  is dropped, and the image repeats itself across
  the surface
• Mirror the image repeats itself but is mirrored
  (flipped) on every other repetition
• Clamp to edge value outside of the range are
  clamped to this range
• Clamp to border all those outside are rendered
  with a separately defined color of the border

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Methods for modifying surface

• After a texture value is retrieved (may be
  further transformed), the resulting values are
  used to modify one or more surface attributes
• Called combine functions or texture blending
  operations
• Replace replace surface color with texture color
• Decal replace surface color with texture color,
  blend the color with underlying color with an
  alpha texture value, but the alpha component in
  the framebuffer is not modified
• Modulate multiply the surface color by the
  texture color (shaded textured surface)

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Okay, then how can you implement?
Slide Courtesy of Leonard McMillan Jovan
Popovic, MIT
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Texture and Texel

• Each pixel in a texture map is called a Texel
• Each Texel is associated with a (u,v) 2D texture
  coordinate
• The range of u, v is 0.0,1.0 due to
  normalization

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(u,v) tuple

• For any (u,v) in the range of (0-1, 0-1)
  multiplied by texture image width and height, we
  can find the corresponding value in the texture
  map

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How do we get F(u,v)?

• We are given a discrete set of values
• Fi,j for i0,,N, j0,,M
• Nearest neighbor
• F(u,v) F round(Nu), round(Mv)
• Linear Interpolation
• i floor(Nu), j floor(Mv)
• interpolate from Fi,j, Fi1,j, Fi,j1,
  Fi1,j
• Filtering in general !

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Interpolation
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Filtering Textures
Texture
Image
Texture gt Image
Image gt Texture
Footprint changes from pixel to pixel no single
filter
Resampling theory Magnification Interpolation Mi
nification Averaging
We would like a constant cost per pixel
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Mip Mapping Williams
MIP Multim In Parvo Many things in a small
place
d
R
R
G
B
v
G
B
u
Trilinear interpolation
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Mip Mapping - Example

• Courtesy of John hart

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Was it working correctly?
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Perspective Correction
No perspective Correction
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Probably the most common form of perspective
texturing is done via a divide by Z. Its a very
simple algorithm. Instead of interpolate U and
V, we instead interpolate U/Z and V/Z. 1/Z is
also interpolated. At each pixel, we take our
texture co-ords, and divide them by Z. Hang on,
you're thinking - if we divide by the same
number twice (Z) don't we get back to where we
started - like a double reciprocal? Well, sort
of. Z is also interpolated, so we're not
dividing by the same Z twice. We then take the
new U and V values, index into our texture map,
and plot the pixel. Pseudo-code might be su
Screen-U U/Z sv Screen-V V/Z sz
Screen-Z 1/Z for xstartx to endx u su /
sz v sv / sz PutPixel(x, y,
texturevu) su deltasu sv deltasv
sz deltasz end Very simple, and
very slow.
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Are correct_s correct_t integer?
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Useful links (Google perspective correct
texture)

• http//www.whisqu.se/per/docs/graphics16.htm
• http//p205.ezboard.com/fyabasicprogrammingfrm20.s
  howMessage?topicID20.topic (Perspective
  correction with Z-buffering)
• http//csdl2.computer.org/persagen/DLAbsToc.jsp?re
  sourcePath/dl/proceedings/toccomp/proceedings/c
  giv/2005/2392/00/2392toc.xmlDOI10.1109/CGIV.2005
  .58 (Perspective Correct Normal Vectors for Phong
  Shading )
• http//easyweb.easynet.co.uk/mrmeanie/tmap/tmap.h
  tm

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Procedural Texture

• Periodic

Checkerboard Scale s 10 If (u s) 20 (v
s)20 texture(u,v) 0 // black Else texture
(u,v) 1 // white
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Slide Courtesy of Leonard McMillan Jovan
Popovic, MIT
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Slide Courtesy of Leonard McMillan Jovan
Popovic, MIT
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t
Slide Courtesy of Leonard McMillan Jovan
Popovic, MIT
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Slide Courtesy of Leonard McMillan Jovan
Popovic, MIT
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Environment Maps

• Use texture to represent reflected color
• Texture indexed by reflection vector
• Approximation works when objects are far away
  from the reflective object

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Environment Maps

• Using a spherical environment map

Spatially variant resolution
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Environment Maps

• Using a cubical environment map

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Environment Mapping

• Environment mapping produces reflections on shiny
  objects
• Texture is transferred in the direction of the
  reflected ray from the environment map onto the
  object
• Reflected ray R2(NV)N-V
• What is in the map?

Environment Map
Viewer
Reflected ray
Object
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Approximations Made

• The map should contain a view of the world with
  the point of interest on the object as the eye
• We cant store a separate map for each point, so
  one map is used with the eye at the center of the
  object
• Introduces distortions in the reflection, but the
  eye doesnt notice
• Distortions are minimized for a small object in a
  large room
• The object will not reflect itself
• The mapping can be computed at each pixel, or
  only at the vertices

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Environment Maps

• The environment map may take one of several
  forms
• Cubic mapping
• Spherical mapping (two variants)
• Parabolic mapping
• Describes the shape of the surface on which the
  map resides
• Determines how the map is generated and how it is
  indexed
• What are some of the issues in choosing the map?

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Example
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Refraction Maps

• Use texture to represent refraction

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Opacity Maps

• Use texture to represent opacity

Useful for billboarding
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Illumination Maps

• Use texture to represent illumination footprint

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Illumination Maps

• Quake light maps

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Bump Mapping

• Use texture to perturb normals
• - creates a bump-like effect

original surface
bump map
modified surface
Does not change silhouette edges
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Bump Mapping

• Many textures are the result of small
  perturbations in the surface geometry
• Modeling these changes would result in an
  explosion in the number of geometric primitives.
• Bump mapping attempts to alter the lighting
  across a polygon to provide the illusion of
  texture.

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Bump Mapping

• This modifies the surface normals.

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Bump Mapping
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Bump Mapping
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Bump Mapping

• Consider the lighting for a modeled surface.

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Bump Mapping

• We can model this as deviations from some base
  surface.
• The questionis then how thesedeviations change
  thelighting.

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Bump Mapping

• Step 1 Putting everything into the same
  coordinate frame as B(u,v).
• x(u,v), y(u,v), z(u,v) this is given for
  parametric surfaces, but easy to derive for other
  analytical surfaces.
• Or O(u,v)

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Bump Mapping

• Define the tangent plane to the surface at a
  point (u,v) by using the two vectors Ou and Ov.
• The normal is then given by
• N Ou ? Ov

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Bump Mapping

• The new surface positions are then given by
• O(u,v) O(u,v) B(u,v) N
• Where, N N / N
• Differentiating leads to
• Ou Ou Bu N B (N)u ? Ou Ou Bu N
• Ov Ov Bv N B (N)v ? Ov Ov Bv N
• If B is small.

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Bump Mapping

• This leads to a new normal
• N(u,v) Ou ? Ov - Bu(N ? Ov) Bv(N ? Ou)
• Bu Bv(N ? N)
• N - Bu(N ? Ov) Bv(N ? Ou)
• N D

D
N
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Bump Mapping

• For efficiency, can store Bu and Bv in a
  2-component texture map.
• The cross products are geometry terms only.
• N will of course need to be normalized after the
  calculation and before lighting.
• This floating point square root and division
  makes it difficult to embed into hardware.

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Displacement Mapping

• Use texture to displace the surface geometry

Bump mapping only affects the normals, Displacemen
t mapping changes the entire surface (including
the silhouette)
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3D Textures

• Use a 3D mapping

Usually stored procedurally
Can simulate an object carved from a material
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3D Textures - Noise

• Pseudo-random
• Bandlimited
• few high or low frequencies
• Controllable

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3D Textures - Noise

• Create a nD integer-aligned lattice of random
  numbers
• For any nDPoint p, noise is defined as

noise(nDPoint p) Find 2 neighbors of p
Linearly interpolate neighbors table values
Return interpolated value
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Turbulence

• Noise with self-similarity

Add together many octaves of noise
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Turbulence
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Animating Turbulence

• Use an extra dimension as time

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Slide Courtesy of Leonard McMillan Jovan
Popovic, MIT
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Slide Courtesy of Leonard McMillan Jovan
Popovic, MIT
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Slide Courtesy of Leonard McMillan Jovan
Popovic, MIT