Tom Duff | Pixar - Academia.edu (original) (raw)

Papers by Tom Duff

The Visual Computer, 2017

Scenes in computer animation can have extreme complexity, especially when high resolution objects... more Scenes in computer animation can have extreme complexity, especially when high resolution objects are placed in the distance and occupy only a few pixels. A useful technique for level-of-detail in these cases is to use a sparse voxel octree containing both hard surfaces and a participating medium consisting of microflakes. In this paper, we discuss three different methods for approximating the distribution of normals of the microflakes, which is needed to compute extinction, inscattering of attenuated direct illumination, and multiple scattering in the participating medium. Specifically, we consider A) k-means approximation with k weighted representatives, B) expansion in spherical harmonics, and C) the distribution of the normals of a specific ellipsoid. We compare their image quality, data size, and computation time.

ACM Transactions on Graphics, 2017

Deep compositing is an important practical tool in creating digital imagery, but there has been l... more Deep compositing is an important practical tool in creating digital imagery, but there has been little theoretical analysis of the underlying mathematical operators. Motivated by finding a simple formulation of the merging operation on OpenEXR -style deep images, we show that the Porter-Duff over function is the operator of a Lie group. In its corresponding Lie algebra, the splitting and mixing functions that OpenEXR deep merging requires have a particularly simple form. Working in the Lie algebra, we present a novel, simple proof of the uniqueness of the mixing function. The Lie group structure has many more applications, including new, correct resampling algorithms for volumetric images with alpha channels, and a deep image compression technique that outperforms that of OpenEXR .

Csys, 1989

proposals, I suggest a small change to the file protection scheme that may be able to interdict m... more proposals, I suggest a small change to the file protection scheme that may be able to interdict many viral attacks without serious effect on the system's functioning and habitability.

ACM SIGGRAPH Computer Graphics, 1992

Recursive subdivision using interval arithmetic allows us to render CSG combinations of implicit ... more Recursive subdivision using interval arithmetic allows us to render CSG combinations of implicit function surfaces with or without anti-aliasing, Related algorithms will solve the collision detection problem for dynamic simulation, and allow us to compute mass. center of gravity, angular moments and other integral properties required for Newtonian dynamics. Our hidden surface algorithms run in 'constant time.' Their running times are nearly independent of the number of primitives in a scene, for scenes in which the visible details are not much smaller than the pixels. The collision detection and integration algorithms are utterly robust-collisions are never missed due 10 numerical error and we can provide guaranteed bounds on the values of integrals.

ACM SIGGRAPH Computer Graphics, 1985

The complexity of anti-aliased 3-D rendering systems can be controlled by using a tool-building a... more The complexity of anti-aliased 3-D rendering systems can be controlled by using a tool-building approach like that of the UNIX™ text-processing tools. Such an approach requires a simple picture representation amenable to anti-aliasing that all rendering programs can produce, a compositing algorithm for that representation and a command language to piece together scenes. This paper advocates a representation that combines Porter and Duff's compositing algebra with a Z-buffer to provide simple anti-aliased 3-D compositing.

ACM SIGGRAPH Computer Graphics, 1979

The appearance of raster-scan renderings of polyhedral approximations to curved surfaces can be e... more The appearance of raster-scan renderings of polyhedral approximations to curved surfaces can be enhanced greatly by shading them in a manner that varies smoothly across each polygon and which matches the correct shade at each vertex. Henri Gouraud and Bui Tuong-Phong have previously described two methods of computing such shading functions. While the computations in Gouraud's method are quite quick to perform, the renderings produced often exhibit pronounced Mach bands, and animated sequences tend to have annoying fluctuations in intensity. Phong's method tries to cure these problems, but is much more expensive computationally. We will show a new, faster method of computing Phong shading, and discuss the relationship of this method to Gouraud shading. We will also exhibit representatives of a class of surfaces for which Phong shading surprisingly produces worse Mach bands than Gouraud shading.

The Visual Computer, 2017

Scenes in computer animation can have extreme complexity, especially when high resolution objects... more Scenes in computer animation can have extreme complexity, especially when high resolution objects are placed in the distance and occupy only a few pixels. A useful technique for level-of-detail in these cases is to use a sparse voxel octree containing both hard surfaces and a participating medium consisting of microflakes. In this paper, we discuss three different methods for approximating the distribution of normals of the microflakes, which is needed to compute extinction, inscattering of attenuated direct illumination, and multiple scattering in the participating medium. Specifically, we consider A) k-means approximation with k weighted representatives, B) expansion in spherical harmonics, and C) the distribution of the normals of a specific ellipsoid. We compare their image quality, data size, and computation time.

ACM Transactions on Graphics, 2017

Deep compositing is an important practical tool in creating digital imagery, but there has been l... more Deep compositing is an important practical tool in creating digital imagery, but there has been little theoretical analysis of the underlying mathematical operators. Motivated by finding a simple formulation of the merging operation on OpenEXR -style deep images, we show that the Porter-Duff over function is the operator of a Lie group. In its corresponding Lie algebra, the splitting and mixing functions that OpenEXR deep merging requires have a particularly simple form. Working in the Lie algebra, we present a novel, simple proof of the uniqueness of the mixing function. The Lie group structure has many more applications, including new, correct resampling algorithms for volumetric images with alpha channels, and a deep image compression technique that outperforms that of OpenEXR .

Csys, 1989

proposals, I suggest a small change to the file protection scheme that may be able to interdict m... more proposals, I suggest a small change to the file protection scheme that may be able to interdict many viral attacks without serious effect on the system's functioning and habitability.

ACM SIGGRAPH Computer Graphics, 1992

Recursive subdivision using interval arithmetic allows us to render CSG combinations of implicit ... more Recursive subdivision using interval arithmetic allows us to render CSG combinations of implicit function surfaces with or without anti-aliasing, Related algorithms will solve the collision detection problem for dynamic simulation, and allow us to compute mass. center of gravity, angular moments and other integral properties required for Newtonian dynamics. Our hidden surface algorithms run in 'constant time.' Their running times are nearly independent of the number of primitives in a scene, for scenes in which the visible details are not much smaller than the pixels. The collision detection and integration algorithms are utterly robust-collisions are never missed due 10 numerical error and we can provide guaranteed bounds on the values of integrals.

ACM SIGGRAPH Computer Graphics, 1985

The complexity of anti-aliased 3-D rendering systems can be controlled by using a tool-building a... more The complexity of anti-aliased 3-D rendering systems can be controlled by using a tool-building approach like that of the UNIX™ text-processing tools. Such an approach requires a simple picture representation amenable to anti-aliasing that all rendering programs can produce, a compositing algorithm for that representation and a command language to piece together scenes. This paper advocates a representation that combines Porter and Duff's compositing algebra with a Z-buffer to provide simple anti-aliased 3-D compositing.

ACM SIGGRAPH Computer Graphics, 1979

The appearance of raster-scan renderings of polyhedral approximations to curved surfaces can be e... more The appearance of raster-scan renderings of polyhedral approximations to curved surfaces can be enhanced greatly by shading them in a manner that varies smoothly across each polygon and which matches the correct shade at each vertex. Henri Gouraud and Bui Tuong-Phong have previously described two methods of computing such shading functions. While the computations in Gouraud's method are quite quick to perform, the renderings produced often exhibit pronounced Mach bands, and animated sequences tend to have annoying fluctuations in intensity. Phong's method tries to cure these problems, but is much more expensive computationally. We will show a new, faster method of computing Phong shading, and discuss the relationship of this method to Gouraud shading. We will also exhibit representatives of a class of surfaces for which Phong shading surprisingly produces worse Mach bands than Gouraud shading.