Complex Features on a Surface. CITS4241 Visualisation Lectures 22 & 23. Texture mapping techniques. Texture mapping techniques

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1 Complex Features on a Surface CITS4241 Visualisation Lectures 22 & 23 Texture Mapping Rendering all surfaces as blocks of colour Not very realistic result! Even with shading Many objects have detailed surface features Grain on wood Ripples on water Construct many polygons? One for each micro "feature"? Explosion in polygon numbers! Long rendering times Texture Mapping Realistic results Reasonable computation times CITS Lectures 22 & 23 2 Texture mapping techniques We restrict ourselves to the class of texture mapping techniques which are mappings R 3 R 2 Basic idea: Given a 2D image (or texture pattern), find the mapping that maps this texture onto a 3D object (x, y, z) mapping (u, v) Texture mapping techniques There are 3 general categories of these techniques: 1. General texture mapping Pasting of a 2D texture pattern onto an object 2. View dependent mapping Known colloquially as chrome mapping a cheap form of environment mapping Environment surrounding an object is pasted on to it Pattern seen will be dependent on viewing angle 3. Bump mapping Creates apparent alterations to geometry of object surface Can simulate ripples or rough textured materials such as leather CITS Lectures 22 & 23 3 CITS Lectures 22 &

2 Differences among these techniques In general texture mapping: A flat texture pattern is pasted onto an object in 3D Object s surface geometry is unchanged Pattern at a point is independent of viewing direction of observer Texture now becomes part of the object database When a texture mapped sphere rotates about its centre, the texture moves with it In chrome or environment mapping: Similar to general texture mapping, but pattern seen at a point is dependent on viewing direction of observer E.g. Reflecting the surrounding environment in a shiny object Object's geometry unchanged Flat texture pattern When an environment mapped sphere rotates, the texture map is not changed Differences among these techniques In bump mapping: Object s surface geometry is unchanged, but surface may appear dimpled or wrinkled Trick the reflection model, I.e. surface normals are perturbed with a bump map giving local variations to surface Simulating 3D micro-structure on the surface Wrinkles Ripples CITS Lectures 22 & 23 5 CITS Lectures 22 & 23 6 Done in Matrox hardware All of the three mapping approaches are displayed ripple texture of water is environment mapped bump mapping Example 1 This version is without bump mapping Example 2 CITS Lectures 22 & 23 7 CITS Lectures 22 &

3 General texture mapping For all the texture mapping techniques in the 3 categories, the texture projection function must be determined Mapping a 2D texture onto an analytically defined object, e.g. a sphere or cylinder, is easy as the projection function can be determined analytically E.g. A cylinder of radius r and height h in parametric coordinates (θ, z) is: (r cos(θ), r sin(θ), hz) where 0 <= θ < 2π and 0 <= z <= 1. The texture projection function is then (u, v) = f(θ, z) = (θ θ / 2π, z) for (u, v) elements in the unit square E.g. Mapping a texture pattern onto a sphere is similar, except that needs to avoid regions near the poles Distortion? See the book by Kellaway General texture mapping (cont.) Mapping a 2D texture onto an arbitrary polygonal is more we need to derive a projection function in some ad hoc manner A common approach for mapping onto a polygon consists of two steps: 1. Determine a projection function, f, for mapping the vertices of the polygon onto the (u, v) coordinates in the texture pattern, I.e. find f such that (u, v) = f(x, y, z) 2. Derive a method whereby the renderer can associate texture values internal to the polygon ( see later) using the information obtained from Step 1. CITS Lectures 22 & 23 9 CITS Lectures 22 & Practical mapping The objects onto which we wish to paste a texture are not, in general, cylinder or spherical we need to look for strategies that enable us to use a cylindrical or spherical mapping. There are two strategies: 1. If the object approximates a cylinder or sphere then first, paste the pattern onto the approximating object, then apply the necessary transformation to shape the approximating object to the final object Eg. Mapping texture onto a banana (see Plate 8 of Watt and Watt) the second strategy 2. If the object does not fall in the above class then we can use a two-staged mapping process: i. The first stage is known as the S-mapping Find a mapping from the 2D texture space to a simple 3D intermediate surface, e.g. cylinder: T (u,v) T (x i, y i, z i ) One can imagine that this might be a useful step to create a texture pattern that can completely surround the actual object ii. The second stage is known as the O-mapping Find a mapping from the 3D texture pattern onto the actual object surface, I.e. T (x i, y i, z i ) O(x, y, z) We can see that strategy 2 is not dissimilar to strategy 1 CITS Lectures 22 & CITS Lectures 22 &

4 the second strategy (cont.) There are 4 intermediate surfaces that are commonly used for the second strategy: 1. Plane at any orientation 2. The curved surface of a cylinder 3. The faces of a cube, and 4. The surface of a sphere Which intermediate surface to use? Depends on the geometric form of the object onto which you want to map texture O-mapping 1: Intersection of reflected view ray with intermediate surface T CITS Lectures 22 & CITS Lectures 22 & O-mapping 2: Intersection of surface normal at (x, y, z) with T O-mapping 3: Intersection of the line through (x, y, z) and the object centroid with T CITS Lectures 22 & CITS Lectures 22 &

5 O-mapping 4: Intersection of the line through (x, y, z) to T whose orientation is given by the normal at (x i, y i, z i ) Mapping interior points We mentioned earlier that, given the projection mapping, f, for texture coordinates at vertices of a polygon, the renderer needs to associate texture values internal to the polygon. The question is: how does the renderer produce the textures for the interior polygon points? The most obvious solution: apply an interpolation technique this is analogous to Phong shading. Problems? Yes Edge interpolation in perspective case is always prone to inconsistency Interior interpolation is ill-defined for polygons of more than 4 vertices CITS Lectures 22 & CITS Lectures 22 & Mapping interior points (cont.) There are two better solutions: Solution 1: suitable for applications where the projection function is known Projection function is taken along as polygon is clipped by the renderer Vertices of the pixel-clipped polygon are then transformed back into the space in which the projection function is invoked (usually the object space) and Projection function is applied to the transformed clipped coordinates Mapping interior points (cont.) There are two better solutions: Solution 2: suitable for applications where the projection function is not known First, need to assume that texture coordinates vary linearly across the plane of the polygon subdivision of polygon into smaller polygons may be required Next, let the variation of the u-coordinates be defined as u = T. (x x 0 ) + u 0 Vector of length 3 scalar T is the direction along which u varies most rapidly. T, which is the gradient operation of f, is referred to as the texture vector u 0 is the value of u at x 0 CITS Lectures 22 & CITS Lectures 22 &

6 That is, f f f T = f = x y z The problem then reduces to: Compute T from a given sequence of quadruples (x 0, u 0 ), (x 1, u 1 ), Ł Mapping interior points (cont.) Obtain T by solving the simultaneous equations: u a = T. (x a - x 0 ) + u 0 Obtain x a and x b from the u b = T. (x b - x 0 ) + u 0 T. n = 0 n is the normal to the plane of the polygon sequence of quadruples. Ensure that x a is far way from x 0, and x b is far away from both x a and x 0. Also, x 0, x a, and x b should not be collinear or nearly so. CITS Lectures 22 & Bump mapping A brief introduction Aim: To make a surface appear wrinkled or dimpled without having to geometrically vary the surface of object Bump mapping is proposed by Blinn Basic idea: Angularly perturb the surface normals according to some desired bump model, I.e. we trick the local reflection model Computation details are a bit complicated CITS Lectures 22 & Environment mapping Case study: Images where detailed reflections of the environment can be seen in a highly reflective object Classic - lunar landscape reflected off the visor of an Apollo astronaut. Creating this reflection detail by ray tracing would be computationally prohibitive. Environment mapping produces these reflections more cheaply, with an acceptable loss of accuracy See Plates 16 and 18 of Watt and Watt Environment mapping (cont.) Object surrounded by a closed 3D surface onto which the environment is projected Reflected rays are traced from the object, hits the 3D surface, and then index into the environment map The environment map is an image of the environment as seen from the object of interest in its centre of space Enables pre-computation of a 3D environment as a 2D projection onto a surface References: Watt and Watt, Section 6.1, pages ; Sections , pages CITS Lectures 22 & CITS Lectures 22 &