Kuan-Loong Yong, Seth Green, Patti McLain CS348B Image Synthesis Final Project Writeup [edited] Smoke ----- Our group modelled smoke as a volumetric object specified completely by a space-density function and an gas illumination model. The ray-marching algorithm involves approximating an integral that accummulates color and opacity along the ray [1]. We used Blinn's [2] formulation of the Henyey-Greenstein phase formula to compute the brightness of a smoke particle. In order to speed up the computation, we do not compute for ray-object intersections when tracing light rays from a smoke particle to the light sources. This has little effect on the believability of the smoke object since it is so amorphous anyway. Note, however, that the smoke does cast convincing shadows on other surfaces. To get the right look for the smoke, we used a cone distorted by a simple (1 - exp(kx)) function to suggest the effect of smoke clinging onto the surface of the cigarette before dissipating upwards, which corresponds rather closely to our observations. To give the cone a puffy smoke-like appearance, we peturbed the cone by a 3D turbulence function. The amount of turbulence is proportional to the square of the height of the smoke particle. The density of the smoke drops off linearly radially, and as a function of the square root of the height vertically. Although we chose these functions arbitrarily, the result is very convincing. Given this framework, animating the smoke becomes an extremely straightforward task. By simply displacing the 3D turbulence function downwards as a function of time, we create the illusion of rising smoke. Water ----- We introduced an automatic means of generating radial waves with interpolated surface normals in our ray tracer. At run-time, the program reads in a description of the wave surface and generates a huge polyset, replete with an octree structure and per-vertex normals, on the fly. The height of the waves vary sinusiodally with the distance from the wave origin; their amplitude drops off linearly with increasing radial distance. To add a touch of irregularity, we added a small amount of low-frequency FBm noise to the wave function. The water waves are also fully animatable. The program simply regenerates a whole new polyset and discards the previous one whenever time progresses. Caustics -------- We formulated an efficient way of simulating reflection caustics due to undulating height fields by hybridizing Watt's backward beam tracing technique [3] with well-known techniques in the field of two-pass texture mapping [4]. Using Watt's caustic polygon approach, we rasterize polygons onto an intermediate bounding cylinder surrounding the object we wish to throw caustics on. We form each caustic polygon by tracing rays from the light source to each vertex of a triangle on the polygonal mesh, reflecting those rays off (each vertex of the triangle must have its own normal for this approach to be effective), and rasterizing the caustic triangle formed by those rays when they intersect the intermediate cylinder. Rasterization occurs on a special texture map which we term a "caustic map" that the program can easily index into given the cylindrical coordinates of the point of intersection. The brightness of each caustic triangle is uniform, and is simply a function of the dot product between the the averaged normal of the triangle and the ray direction to the light source, and the ratio of the area of the actual polygon to that of the caustic polygon. Please refer to [3] for a detailed discussion of this computation. For speed and simplicity, we do not compute for ray-object intersections when casting caustic polygons on the intermediate surface. The second stage involves treating the caustic map as an ambient color map, and projecting it optimally onto the underlying polyset mesh. A simple radial projection fails miserably when the object is highly non-cylindrical because of excessive distortion. We present a better approach: Given a point on the polyset object, we find the further intersection of the ray originating from that point and having a direction parallel to the surface normal with the bounding cylinder (the ray can intersect the cylinder at most twice), after discarding all vector components parallel to the axis of the cylinder. This is essentially a 2D problem involving the intersection of a line with a circle. The program does the caustic map lookup based on that point of intersection. The ambient color returned from the lookup is scaled by the dot product of the surface normal with the axis of the bounding cylinder before the shader adds that to the surface color computed from the regular phong illumination model. This additional step is necessary to attenuate caustics on surfaces that point in the direction of the axis of the cylinder. Notice in our renderings that caustics do not appear on flat, horizontal surfaces pointing away from the water surface. Our mapping technique works remarkably well on surfaces which are not highly cylindrical, as evidenced by our rendering of the cat polymesh. We also noticed that, in order to get sufficient detail in the caustics, it is necessary to subdivide the height field much more finely for computing caustics than for actually rendering the height field itself. Our ray tracer accomplishes this by storing two copies of each height field in memory -- an ultra-high resolution mesh for creating caustic polygons, and a lower resolution one used by the regular ray tracing pipeline. *************************************************************** Cigarette Tip ------------- The tip of the cigarette is modeled as a large number of small flat polygons to simulate the flecks of charred tobacco that are produced by a burning cigarette. Before being lit a cigarette tip contains about 10-50 pieces of tobacco arranged in a somewhat spiral pattern. After burning the tobacco breaks up into 100-1000 small flecks. Near the center of the cigarette the charred tobacco is black, and on the outer edge it is colored white from the burnt wrapping paper. The tip of the cigarette was modeled in Matlab and exported as an inventor format file to be read by Composer. The tip is modeled as a dense number of concentric rings which were then split into equicircumferential slices. The vertices of each slice are perturbed by a Gaussian noise function and a scaling function to give the end of the tip a rounded appearance. Each vertex is given a diffuse color based on it�s distance from the center. ***************************************************************** Distribution Ray Tracing ________________________ The semi-diffuse reflections are based on the Gregory Ward anisotropic reflection model [1]. The specular part Ward's model is used, the diffuse portion of the reflection implements the Whitted model. The diffuse portion of the Ward model is equivalent to the Whitted model. The Ward model uses an elliptical gaussian function for the specular component. To generate the secondary rays using importance sampling, directions with the highest contribution have a higher probability of being sampled. Therefore, the sample rays are also generated from a gaussian distribution, around the mirror direction, and equal weighting is used for each of the rays. Multiple rays are only spawned at the first reflection, since the return from spawning multiple rays at each intersection is not computationally efficient, and the contribution is lessened after each reflection. Translucence is modeled similarly, the distribution is isotropic about the refracted direction. The contribution of rays are weighed equally. This gives the appearance of a mottled transparent medium. Penumbra- To generate penumbrae lights were modeled as axis-aligned boxes. This was computationally efficient, and does provide softened shadows. To model lighting in an environment to evaluate different lighting selections, a more faithful approach to modeling the light extent should be made. Shadow rays were uniformly generated that intersect the box. All rays provided equal contribution to the shadowing. Camera Animation ________________ The animation of the camera is computed by providing 3 camera data sets from composer. The animation uses the 3 sets of data as control points for a quadradic Bezier curve. Therefore, the first and last points are interpolated with the intermediate point providing the control. *************************************************************** References ---------- [1] Kajiya and Kay 1989 Ray Tracing Volume Densities SIGGRAPH 89, vol 18, pp 165-174 [2] Blinn, James 1982 Light Reflection Functions for Simulation of Clouds and Dusty Surfaces. SIGGRAPH 82, vol 16, pp 21-29 [3] Watt, Alan and Mark Watt 1992 Advanced Animation and Rendering Techniques ACM Press, pp 253-256 [4] Bier, E. A. 1986 Two part texture mapping IEEE Computer Graphics and Applications, Sep 1986, 6(9), pp 40-53 [5] Peitgen and Saupe 1988 The Science of Fractal Images Springer-Verlag, pp 100-101 [6] Ward, Gregory Measuring and Modeling Anisotropic Reflection Computer Graphics 26, 2, July 1992