10.1 si31_2001 si31 advanced computer graphics agr lecture 10 solid textures bump mapping...
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10.1si31_2001
SI31Advanced Computer
GraphicsAGR
SI31Advanced Computer
GraphicsAGR
Lecture 10Solid TexturesBump Mapping
Environment Mapping
10.2si31_2001
Marble TextureMarble Texture
10.3si31_2001
Solid TextureSolid Texture
A difficulty with 2D textures is the mapping from the object surface to the texture image– ie constructing fu(x,y,z) and fv(x,y,z)
This is avoided in 3D, or solidsolid, texturing– texture now occupies a volume– can imagine object being carved out of
the texture volumeU
V
W
texturespace X
Y
Z
object space
Mapping functions trivial: u = x; v = y; w = z
10.4si31_2001
Defining the TextureDefining the Texture
The texture volume itself is usually defined procedurally– ie as a function that can be
evaluated, such as:
texture (u, v, w) = sin (u) sin (v) sin texture (u, v, w) = sin (u) sin (v) sin (w) (w)
– this is because of the vast amount of storage required if it were defined by data values
10.5si31_2001
Example: Wood TextureExample: Wood Texture
Wood grain texture can be modelled by a set of concentric cylinders – cylinders coloured dark, gaps
between adjacent cylinders coloured light
radius r = sqrt(u*u + w*w)
if radius r = r1, r2, r3,
thentexture (u,v,w) = darkelsetexture (u,v,w) = light
looking down:cross section view
U
V
W
texturespace
10.6si31_2001
Example: Wood TextureExample: Wood Texture
It is a bit more interesting to apply a sinusoidal perturbation– radius:= radius + 2 * sin( 20*) , with
0<<2 .. and a twist along the axis of the
cylinder– radius:= radius + 2 * sin( 20* + v/150
) This gives a realistic wood texture
effect
10.7si31_2001
Wood TextureWood Texture
10.8si31_2001
How to do Marble?How to do Marble?
First create noise function (in 1D):– noise [i] = random numbers on lattice
of points Next create turbulence:
– turbulence (x) = noise(x) + 0.5*noise(2x) + 0.25*noise(4x) + …
Marble created by:– basic pattern:
• marble (x) = marble_colour (sin (x) )
– with turbulence:• marble (x) = marble_colour (sin (x + turbulence
(x) ) )
10.9si31_2001
Marble TextureMarble Texture
10.10si31_2001
Using Turbulence for Flame Simulation
Using Turbulence for Flame Simulation
Flame in 2D region [-b,b] x [0,h] can be modelled as:
– flame(x,y) = (1-y/h) * flame_col(abs(x/b))
flame_col has max intensity at 0, min at 1
Adding turbulence factor to flame_col gives more realistic effect:
– flame(x,y) = (1-y/h) * flame_col(abs(x/b)+turb(x))
10.11si31_2001
Animating the TurbulenceAnimating the Turbulence
The noise function, and hence the turbulence function, can be made time-dependent
10.12si31_2001
Bump MappingBump Mapping
This is another texturing technique Aims to simulate a dimpled or
wrinkled surface– for example, surface of an orange
Like Gouraud and Phong shading, it is a tricktrick– surface stays the same– but the true normal is perturbed, or
jittered, to give the illusion of surface ‘bumps’
10.13si31_2001
Bump MappingBump Mapping
10.14si31_2001
How Does It Work?How Does It Work?
Looking at it in 1D:
original surface P(u)
bump map b(u)
add b(u) to P(u)in surface normal direction, N(u)
new surface normalN’(u) for reflectionmodel
10.15si31_2001
How It Works - The Maths!How It Works - The Maths!
Any 3D surface can be described in terms of 2 parameters– eg cylinder of fixed radius r is defined by
parameters (s,t)
x=rcos(s); y=rsin(s); z=t Thus a point P on surface can be written
P(s,t) where s,t are the parameters The vectors:
Ps = dP(s,t)/ds and Pt = dP(s,t)/dt
are tangential to the surface at (s,t)
10.16si31_2001
How it Works - The MathsHow it Works - The Maths
Thus the normal at (s,t) is:N = Ps x Pt
Now add a bump map to surface in direction of N:
P’(s,t) = P(s,t) + b(s,t)N To get the new normal we need to
calculate P’s and P’t
P’s = Ps + bsN + bNs
approx P’s = Ps + bsN - because b small
P’t similar– P’t = Pt + btN
10.17si31_2001
How it Works - The MathsHow it Works - The Maths
Thus the perturbed surface normal is:N’ = P’s x P’t
orN’ = Ps x Pt + bt(Ps x N) + bs(N x Pt) + bsbt(N x N)
But since– Ps x Pt = N and N x N = 0, this simplifies to:
N’ = N + D
– where D = bt(Ps x N) + bs(N x Pt)
= bs(N x Pt) - bt(N x Ps )
= A - B
10.18si31_2001
Worked Example for a Cylinder
Worked Example for a Cylinder
P has co-ordinates:
Thus:
and then
x (s,t) = r cos (s)y (s,t) = r sin (s)z (s,t) = t
Ps : xs (s,t) = -r sin (s)ys (s,t) = r cos (s)zs (s,t) = 0
Pt : xt (s,t) = 0yt (s,t) = 0zt (s,t) = 1
N = Ps x Pt : Nx = r cos (s)Ny = r sin (s)Nz = 0
10.19si31_2001
Worked Example for a Cylinder
Worked Example for a Cylinder
Then: D = bt(Ps x N) + bs(N x Pt) becomes:
and perturbed normal N’ = N + D is:
D : bt *0 + bs*r sin (s) = bs*r sin (s)bt *0 - bs*r cos (s) = - bs*r cos (s)bt*(-r2) + bs*0 = - bt*(r2)
N’ : r cos (s) + bs*r sin (s)r sin (s) - bs*r cos (s)-bt*r2
10.20si31_2001
Bump MappingA Bump Map
Bump MappingA Bump Map
10.21si31_2001
Bump MappingResulting ImageBump Mapping
Resulting Image
10.22si31_2001
Bump Mapping - Another Example
Bump Mapping - Another Example
10.23si31_2001
Bump MappingAnother ExampleBump Mapping
Another Example
10.24si31_2001
Bump MappingProcedurally Defined Bump
Map
Bump MappingProcedurally Defined Bump
Map
10.25si31_2001
Environment MappingEnvironment Mapping
This is another famous piece of trickery in computer graphics
Look at a highly reflective surface– what do you see?– does the Phong reflection model predict
this? Phong reflection is a local illumination
model– does not convey inter-object reflection– global illumination methods such as ray
tracing and radiosity provide this .. but can we cheat?
10.26si31_2001
Environment Mapping - Recipe
Environment Mapping - Recipe
Place a large cube around the scene with a camera at the centre
Project six camera views onto faces of cube - known as an environment mapenvironment map
camera
projection of sceneon face of cube -environment map
10.27si31_2001
Environment Mapping - Rendering
Environment Mapping - Rendering
When rendering a shiny object, calculate the reflected viewing direction (called R earlier)
This points to a colour on the surrounding cube which we can use as a texture when rendering
eyepoint
environmentmap
10.28si31_2001
Environment Mapping Example
Environment Mapping Example
The six views from the teapot
Environment Mapped Teapot
10.29si31_2001
Environment Mapping - Limitations
Environment Mapping - Limitations
Obviously this gives far from perfect results - but it is much quicker than the true global illumination methods (ray tracing and radiosity)
It can be improved by multiple environment maps (why?) - one per key object
Also known as reflection mappingreflection mapping Can use sphere rather than cube
10.30si31_2001
Jim BlinnJim Blinn
Both bump mapping and environment mapping concepts are due to Jim Blinn
Pioneer figure in computer graphics
www.research.microsoft.com/~blinn
www.siggraph.org/s98/conference/keynote/slides.html
10.31si31_2001
AcknowledgementsAcknowledgements
Thanks again to Alan Watt for many of the images
Flame simulation movie from Josef Pelikan, Charles University Prague
Environment mapping examples from Mizutani and Reindel, Japan
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