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GR2 Advanced Computer Graphics AGR. Lecture 12 Solid Textures Bump Mapping Environment Mapping. Marble Texture. Y. object space. V. texture space. U. X. W. Z. Solid Texture. A difficulty with 2D textures is the mapping from the object surface to the texture image

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Gr2 advanced computer graphics agr

GR2Advanced Computer GraphicsAGR

Lecture 12

Solid Textures

Bump Mapping

Environment Mapping



Solid texture

Y

object space

V

texture

space

U

X

W

Z

Solid 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 solid, texturing

    • texture now occupies a volume

    • can imagine object being carved out of the texture volume

Mapping functions trivial: u = x; v = y; w = z


Defining the texture
Defining 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 (w)

    • this is because of the vast amount of storage required if it were defined by data values


Example wood texture

V

texture

space

U

W

Example: 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,

then

texture (u,v,w) = dark

else

texture (u,v,w) = light

looking down:

cross section view


Example wood texture1
Example: 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



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) ) )



Bump mapping
Bump 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 trick

    • surface stays the same

    • but the true normal is perturbed, or jittered, to give the illusion of surface ‘bumps’



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 normal

N’(u) for reflection

model


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)


How it works the maths1
How 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


How it works the maths2
How it Works - The Maths

  • Thus the perturbed surface normal is:

    N’ = P’s x P’t

    or

    N’ = 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


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) = 0

yt (s,t) = 0

zt (s,t) = 1

N = Ps x Pt :

Nx = r cos (s)

Ny = r sin (s)

Nz = 0


Worked example for a cylinder1
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


Bump mapping a bump map
Bump MappingA Bump Map


Bump mapping resulting image
Bump MappingResulting Image



Bump mapping another example1
Bump MappingAnother Example


Bump mapping procedurally defined bump map
Bump MappingProcedurally Defined Bump Map


Environment mapping
Environment 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?


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 map

projection of scene

on face of cube -

environment map

camera


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

environment

map

eye

point


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 mapping

  • Can use sphere rather than cube




Jim blinn
Jim 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


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