Michael M. Stark

Photographic tone reproduction for digital images

A classic photographic task is the mapping of the potentially high dynamic range of real world luminances to the low dynamic range of the photographic print. This tone reproduction problem is also faced by computer graphics practitioners who map digital images to a low dynamic range print or screen. The work presented in this paper leverages the time-tested techniques of photographic practice to develop a new tone reproduction operator. In particular, we use and extend the techniques developed by Ansel Adams to deal with digital images. The resulting algorithm is simple and produces good results for a wide variety of images.

A physically-based night sky model

This paper presents a physically-based model of the night sky for realistic image synthesis. We model both the direct appearance of the night sky and the illumination coming from the Moon, the stars, the zodiacal light, and the atmosphere. To accurately predict the appearance of night scenes we use physically-based astronomical data, both for position and radiometry. The Moon is simulated as a geometric model illuminated by the Sun, using recently measured elevation and albedo maps, as well as a specialized BRDF. For visible stars, we include the position, magnitude, and temperature of the star, while for the Milky Way and other nebulae we use a processed photograph. Zodiacal light due to scattering in the dust covering the solar system, galactic light, and airglow due to light emission of the atmosphere are simulated from measured data. We couple these components with an accurate simulation of the atmosphere. To demonstrate our model, we show a variety of night scenes rendered with a Monte Carlo ray tracer.

The halfway vector disk for BRDF modeling

We present a mathematical framework for enforcing energy conservation in a bidirectional reflectance distribution function (BRDF) by specifying halfway vector distributions in simple two-dimensional domains. Energy-conserving BRDFs can produce plausible rendered images with accurate reflectance behavior, especially near grazing angles. Using our framework, we create an empirical BRDF that allows easy specification of diffuse, specular, and retroreflective materials. We also present a second BRDF model that is useful for data fitting; although it does not preserve energy, it uses the same halfway vector domain as the first model. We show that this data-fitting BRDF can be used to match measured data extremely well using only a small set of parameters. We believe that this is an improvement over table-based lookups and factored versions of BRDF data.

Direct Ray Tracing of Displacement Mapped Triangles

We present an algorithm for ray tracing displacement maps that requires no additional storage over the base model. Displacement maps are rarely used in ray tracing due to the cost associated with storing and intersecting the displaced geometry. This is unfortunate because displacement maps allow the addition of large amounts of geometric complexity into models. Our method works for models composed of triangles with normals at the vertices. In addition, we discuss a special purpose displacement that creates a smooth surface that interpolates the triangle vertices and normals of a mesh. The combination allows relatively coarse models to be displacement mapped and ray traced effectively.

Exact Illumination in Polygonal Environments using Vertex Tracing

Methods for exact computation of irradiance and form factors associated with polygonal objects have ultimately relied on a formula for a differential area to polygon form factor attributed to Lambert. This paper presents an alternative, an analytical expression based on vertex behavior rather than the edges the polygon. Using this formulation, irradiance values in a scene consisting of partially occluded uniformly emitting polygons can be computed exactly by examining only the set of apparent vertices visible from the point of evaluation without explicit reconstruction of polygon contours. This leads to a fast, low-overhead algorithm for exact illumination computation that involves no explicit polygon clipping and is applicable to direct lighting and to radiosity gathering across surfaces or at isolated points.

Computing exact shadow irradiance using splines

We present a solution to the general problem of characterizing shadows in scenes involving a uniform polygonal area emitter and a polygonal occluder in arbitrary position by manifesting shadow irradiance as a spline function. Studying generalized prism-like constructions generated by the emitter and the occluder in a fourdimensional (shadow) space reveals a simpler intrinsic structure of the shadow as compared to the more complicated 2D projection onto a receiver. A closed form expression for the spline shadow irradiance function is derived by twice applying Stokes’ theorem to reduce an evaluation over a 4D domain to an explicit formula involving only 2D faces on the receiver, derived from the scene geometry. This leads to a straightforward computational algorithm and an interactive implementation. Moreover, this approach can be extended to scenes involving multiple emitters and occluders, as well as curved emitters, occluders, and receivers. Spline functions are constructed from these prism-like objects. We call them generalized polyhedral splines because they extend the classical polyhedral splines to include curved boundaries and a density function. The approach can be applied to more general problems such as some of those occurring in radiosity, and other related topics. CR Categories: I.3.0 [Computer Graphics]: General; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism;

Efficient Construction of Perpendicular Vectors without Branching

This paper presents a novel formula for computing an arbitrary vector perpendicular to a given 3D vector. The formula, as well as the provided C language implementation, are unusual in that they require no conditional branching. The formula involves little arithmetic and is amenable to hardware implementation.

Generation of Stratified Samples for B-Spline Pixel Filtering

B-spline filter kernels have proved useful in many pixel-sampling applications. A cubic B-spline filter kernel, having a width of four pixels, is particularly effective. In distribution ray tracing, pixel filters are evaluated implicitly by having the density of sampling proportional to the filter value. In this work we present a simple method to generate random samples having an underlying B-spline density function. To reduce error it is important to stratify the samples, akin to jittering for uniform sampling. We provide an algebraic and a numerical technique for doing this for B-spline kernels of degree 1, 2, and 3.

Reflected and transmitted irradiance from area sources using vertex tracing

Computing irradiance analytically from polygonal luminaires in polygonal environments has proven effective for direct lighting applications in diffuse radiosity environments. Methods for analytic integration have traditionally used edge-based solutions to the irradiance integral; our previous work presented a vertex-based analytic solution, allowing irradiance to be computed incrementally by ray tracing the apparent vertices of the luminaire. In this work we extend the vertex tracing technique to the analytic computation of irradiance from a polygonal luminaire in other indirect lighting applications: transmission through non-refractive transparent polygons, and reflection off perfectly specular polygons. Furthermore we propose an approximate method for computing transmitted irradiance through refractive polyhedra. The method remains effective in the presence of blockers.

Fast and Stable Conformal Mapping Between a Disc and a Square

Mapping between a square or rectangle to a disc or hemisphere, and vice versa, arises in many areas of computer graphics, including environment and reflection mapping, sampling, and BRDFs to name a few. Different maps have different properties: equal-area maps may be more applicable in sampling, while low-distortion or continuity might be preferable in other applications. Conformal mapping preserves angles and thereby locally preserves shape. Although it has been used for over a century, conformal mapping between a disc and a square involves extensive computation with complex numbers. This paper reviews the construction of a conformal map between the unit disc and the unit square, which is formulated as an elliptic integral, and reviews several computational methods. Efficient algorithms are presented for mapping the disc to the square, and from the square to the disc. An implementation is provided in compact C language source code that runs at speeds comparable to simple trigonometric maps.