lec12

GR2Advanced Computer GraphicsAGR: 

GR2 Advanced Computer Graphics AGR Lecture 12 Solid Textures Bump Mapping Environment Mapping

Marble Texture: 

Marble Texture

Solid Texture: 

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: 

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 Texture: 

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

Wood Texture: 

Wood Texture

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) ) )

Marble Texture: 

Marble Texture

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’

Bump Mapping: 

Bump Mapping

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 Maths: 

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 Maths: 

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 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

Bump MappingA Bump Map: 

Bump Mapping A Bump Map

Bump MappingResulting Image: 

Bump Mapping Resulting Image

Bump Mapping - Another Example: 

Bump Mapping - Another Example

Bump MappingAnother Example: 

Bump Mapping Another Example

Bump MappingProcedurally Defined Bump Map: 

Bump Mapping Procedurally 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 camera projection of scene on face of cube - environment map

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 eye point environment map

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

Environment Mapping: 

Environment Mapping

Environment Mapping: 

Environment Mapping

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