CSE 410 Computer Graphics Sessional
Virtual Realism
TEXTURE MAPPING
The Quest for Visual Realism
Why Texture Map?
So far we have done flat shading and Gouraud/Phong shadingNot good to represent everything in real world
What are some of our other options?Represent everything with tiny polygons
Geometry would get complicated very quickly
Apply textures across the polygonsThis allows for less geometry but the image
looks almost as good
Basic Concept
Textures are almost always rectangular array of pixels called texels (texture elements)
• Pasting an image onto a model• An image is mapped onto the 2D domain of a 3D model
Texture Coordinates
A texture is usually addressed by two numbers (s, t)s and t takes values in [0,1]
A vertex can be associated with a point on the texture by giving it one of these texture coordinatesglTexCoord*(s,t);glVertex*(x,y,z);
s
t
[0,0] [1, 0]
[0, 1]
Example Texture Map
Types of TexturesBitmap textures
Bitmapped representation of imagesRepresented by an array
Color3 texture(float s, float t){ Return txtr[(int)(s*c),(int)(t*r)]
}
Procedural texturesDefined by a mathematical function
In either case, we have a ‘texture function’texture(s,t)
Texture Mapping Problem
Texture space World space Screen space
(sx,sy)=Tws(Ttw (s*,t*))
Mapping Textures on Flat Surfaces
• Associate points on texture with points on the polygonal face– OpenGL uses the function glTexCoord*()
• sets the current texture coordinates
Rendering Textures on Flat Surfaces
Similar to Gouraud shadingConsider the current scan line ys
For each xs, compute the correct position P on the face
From that, obtain the correct texture coordinate (s,t)
xright
ys
ytop
ybott
xleft
(s0,t0)
(s3,t3)
(s1,t1)
(s2,t2)
xs
CaveatLinear interpolation does not work always!This is because…
Equal steps across a projected space do not corresponds to equal steps across the 3D space
Visualizing the Problem
Notice that uniform steps on the image plane do not correspond to uniform steps along the edge.
An Example
Proper Interpolation
If we move in equal steps across Ls on the screen, how should we step across texels along Lt in texture space?
Texture space Eye space Screen space
Proper InterpolationR(g) = lerp(A,B,g) r(f)=lerp(a,b,f), a = (a1, a2, a3, a4) or ( a1/a4, a2/a4, a3/a4)r1(f) = lerp(a1/a4, b1/b4, f)
A
B
R(g)M a
br(f)
• R(g) = lerp(A,B,g) • In homogenous coordinate [R(g),1]t
• = [lerp(A,B,g),1]t
• After perspective transformation M([lerp(A,B,g),1]t)• = lerp( M(A,1)t , M(B,1)t , g )• =[ lerp( a1, b1, g ) , lerp( a2, b2, g) , lerp(a3, b3, g) , lerp( a4, b4, g) ]• r1(f ) = lerp(a1,b1,g)/lerp(a4,b4,g)
Proper Interpolationr1(f) = lerp(a1/a4, b1/b4, f)r1(f ) = lerp(a1,b1,g)/lerp(a4,b4,g)
g = f / lerp((b4/a4), 1, f)
R(g) = A(1-g) + Bg= lerp(A1/a4, B1/b4, f) / lerp( 1/a4, 1/b4, f)
Proper Interpolation
a cooresponds to A which maps to texture (Sa, Ta)b corresponds to B which maps to texture ( Sb, Tb)
left = lerp(a,b,f)sleft(y) =lerp(SA/a4, SB/b4, f) / lerp( 1/a4, 1/b4, f)
Similar for tleft(y) and right pixelSimilar hyperbolic interpolation for intermediate pixels
a
b
a’
b’
yleft
right
Texture Maps and Visual Realism
Three different visual effects:1. Glowing objects
– Intensity is set equal to the texture value: I = texture(s,t)– Object appears to emit light or glow– Color can be added by considering the red, green and
blue components separately
2. Modulate reflection coefficients– Make texture appear to be painted on the surface– Change the reflection coefficients at each point by:
3. Bump mapping– Model the roughness of the surface
fsspddaa phongIlambertIItsI )(,texture
Bump Mapping
Bump Mapping Use texture map to perturb surface normal
Use texture array to set a function which perturbs surface normal Apply illumination model using perturbed normal
Bump Mapping
vuvuvuPvuP ,m,texture,, • The ‘perturbed’ surface becomes:
• One approximation to new normal m´(u,v) is:
vuvuvu ,d,m,m
where d is: vuuv PPvu texturemtexturem,d
Bump Mapping
vuvuvuPvuP ,m,texture,,
• The ‘perturbed’ surface becomes:
• To find the new normal m´(u,v)– Find two vectors tangent to the bumpy surface, then m´(u,v) is their
cross product– The two vectors follow from the partial derivatives of the P´(u,v)
equation wrt u,v
Wrapping Texture on Curved SurfacesWrap a label around a cylinder
• Wrap a label onto a sphere
References
Hill 8.5.1 – 8.5.3, 8.5.5