Virtual Realism TEXTURE MAPPING

The Quest for Visual Realism

Why Texture Map? So far we have done flat shading and Gouraud/Phong shading Not 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 polygons This 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 coordinates glTexCoord*(s,t); glVertex*(x,y,z); s t [0,0] [1, 0] [0, 1]

Example Texture Map

Types of Textures Bitmap textures Bitmapped representation of images Represented by an array Color3 texture(float s, float t){ Return txtr[(int)(s*c),(int)(t*r)] } Procedural textures Defined by a mathematical function In either case, we have a ‘texture function’ texture(s,t)

Texture Mapping Problem Texture spaceWorld spaceScreen space (sx,sy)=T ws (T tw (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 shading Consider the current scan line y s For each x s, compute the correct position P on the face From that, obtain the correct texture coordinate (s,t) x right ysys y top y bott x left (s 0,t 0 ) (s 3,t 3 ) (s 1,t 1 ) (s 2,t 2 ) xsxs

Caveat Linear 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 L s on the screen, how should we step across texels along L t in texture space? Texture spaceEye spaceScreen space

Proper Interpolation R(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 b r(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 Interpolation r1(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) s left(y) =lerp(S A /a4, S B /b4, f) / lerp( 1/a4, 1/b4, f) Similar for t left(y) and right pixel Similar hyperbolic interpolation for intermediate pixels a b a’ b’ y left 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

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 The ‘perturbed’ surface becomes: One approximation to new normal m´(u,v) is: where d is:

Bump Mapping 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 Surfaces Wrap a label around a cylinder Wrap a label onto a sphere

References Hill – 8.5.3, 8.5.5