Published Papers

Papers/Publications are listed under the categories

        Freeware
        Character Animation
        Implicit and Skeletal Modeling
        Implicit Surface Polygonization
        Convolution Surfaces
        Transformations and Geometry
        Miscellaneous Offline Papers
        PhD Dissertation
        Masters Thesis

Barycentric Quad Rasterization
    (2022) Journal of Computer Graphics Techniques

Public Domain Polygonizer
    (1994) original, written in C

Character Animation

Medial-Based Vertex Deformation, Symposium on Computer Animation, 2002

Vertex deformation is a popular technique to animate an erstwhile static object. It is difficult, however, to deform those vertices near multiple limbs of the controlling stick-figure skeleton while maintaining a natural-appearing surface.

By applying convolution to the medial axis/surface of the object, the weights associated with vertex deformation can be computed automatically. Fewer undesired artifacts are evidenced in the animated surface.

Implicit and Skeletal Modeling

Implicit Surfaces Bibliography

Implicit Surfaces

A reference article on implicit surfaces in the Encyclopedia of Computer Science and Technology (ã 2001 Marcel Dekker, Inc., NY).

Skeletal Methods of Shape Manipulation (with Chek Lim), Shape Modeling Int'l '99, 1999 (invited paper)

The geometric skeleton is derived from a static object using an implicit ‘directions’ method; an IK-skeleton is derived from and used to manipulate the geometric skeleton. The model may be reconstructed from the modified skeleton using implicit distance and convolution methods.

Interactive Techniques for Implicit Modeling (with Brian Wyvill), Symp. on Interactive 3D Computer Graphics, 1990

Recent research has demonstrated the usefulness of implicit surfaces for modeling geometric objects. The interactive design of such surfaces has not, however, received the same attention as has the design of parametric surfaces. Principally this is due to the difficulty of controlling the shape of implicit surfaces while displaying the changes quickly enough for use within an interactive design environment. This paper describes progress towards interactive control of implicit surfaces and introduces new techniques useful to the designer. missing figures 4 and 5.

Techniques for Implicit Modeling (1.7M), Xerox PARC Technical Report P89-00106, 1989

Abstract: Computer graphics has traditionally favored the parametric surface over the implicit surface because the parametric is easier to render. Implicit representations, however, have natural advantages in surface design, particularly in their ability to concisely express constraints that a surface must obey. This paper discusses this advantage, emphasizing the use of distance as a constraint.

Implicit Surface Polygonization

Polygonization of Implicit Surfaces (331K) Computer Aided Geometric Design, 1988

This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface or track it. A piecewise polygonal representation is derived from the octree.

The technique is insensitive to the complexity of the implicit function, allowing the designer great latitude. With a polygonal representation of the surface available, certain computational economies result. In particular, the roots to the function need not be solved each time the surface is rendered.

An Implicit Surface Polygonizer (634K) Graphics Gems IV, 1994

An algorithm for the polygonization of implicit surfaces is described and an implementation in C is provided. The discussion reviews implicit surface polygonization, and compares various methods.

An Evaluation of Implicit Surface Tilers (98K) (with Paul Ning), Computer Graphics and Applications, 1993

In recent years, numerous techniques have been developed for the polygonization of implicit surfaces. This article reviews the principal algorithms and provides a framework for identifying their conceptual similarities as well as their practical differences. Particular attention is devoted to the much discussed problem of topological ambiguity, with solutions analyzed according to their consistency and correctness. Included in this evaluation are implementation suggestions for various application requirements. missing figures 8 and 9.

Polygonization of Non-Manifold Implicit Surfaces (228K) (with Keith Ferguson), SIGGRAPH, 1995

A method is presented to broaden implicit surface modeling. The implicit surfaces usually employed in computer graphics are two dimensional manifolds because they are defined by real-valued functions that impose a binary regionalization of space (i.e., an inside and an outside). When tiled, these surfaces yield edges of degree two. The new method allows the definition of implicit surfaces with boundaries (i.e., edges of degree one) and intersections (i.e., edges of degree three or more). These non-manifold implicit surfaces are defined by a multiple regionalization of space. The definition includes a list of those pairs of regions whose separating surface is of interest.

Also presented is an implementation that converts a non-manifold implicit surface definition into a collection of polygons. Although following conventional implicit surface polygonization, there are significant differences that are described in detail. Several example surfaces are defined and polygonized.

Triangulation of Implicitly Defined Mid-Surfaces, International Meshing Roundtable, 2013

Coping surfaces of a thin-wall object are used for insidedness but ignored for footpoints, yielding the mid-surface, not the medial axis. Three distinct contour-followers are employed. After a brief, manual tagging of the coping surfaces, the method is automatic. It computes a triangulation to arbitrary precision and appears robust for complex, thin-wall objects.

Convolution Surfaces

Convolution Surfaces (26K) (with Ken Shoemake), SIGGRAPH, 1991

Smoothly blended articulated models are often difficult to construct using current techniques. Our solution in this paper is to extend the surfaces introduced by Blinn [Blinn 1982] by using three-dimensional convolution with skeletons composed of polygons or curves. The resulting convolution surfaces permit fluid topology changes, seamless part joins, and efficient implementation.
(missing several figures)

Hand Crafting (98K) (extended abstract), Proc. Western Canadian Graphics Workshop, 1992

In [Bloomenthal and Shoemake] convolution surfaces, an implicit modeling technique based upon three dimensional convolution, was applied to skeletal primitives (see [Bloomenthal and Wyvill]) to simulate a human arm. We present here the use of skeletal primitives and convolution surfaces for the modeling of a human hand. We begin with a review of the arm model, which consists of five `muscles,' blended together and each represented by a planar polygon.

Bulge Elimination for Convolution Surfaces (296K) Computer Graphics Forum, 1997

The relationship between surface bulges and several implicit blend techniques, particularly those based on convolution of a skeleton, is discussed. An examination of branching skeletons reveals that for two and three-dimensional skeletons, the surface will be bulge-free if skeletal elements are sufficiently large with respect to the convolution kernel.

Transformations and Geometry

Homogeneous Coordinates (93K) (with Jon Rokne) The Visual Computer, 1994

Abstract: Homogeneous coordinates have a natural application to Computer Graphics; they form a basis for the projective geometry used extensively to project a three-dimensional scene onto a two-dimensional image plane. They also unify the treatment of common graphical transformations and operations. The graphical use of homogeneous coordinates is due to [Roberts, 1965], and an early review is presented by [Ahuja, 1968]. Today, homogeneous coordinates are presented in numerous computer graphics texts (such as [Foley, Newman, Rogers, Qiulin and Davies]); [Newman], in particular, provides an appendix of homogeneous techniques. [Riesenfeld] provides an excellent introduction to homogeneous coordinates and their algebraic, geometric and topological significance to Computer Graphics. [Bez] further discusses their algebraic and topological properties, and [Blinn77, Blinn78] develop additional applications for Computer Graphics.

Our aim here is to provide an intuitive yet theoretically based discussion that assembles the key features of homogeneous coordinates and their applications to Computer Graphics. These applications include affine transformations, perspective projection, line intersections, clipping, and rational curves and surfaces. For the sake of clarity in accompanying illustrations, we confine our development to two dimensions and then use the intuition gained to present the application of homogeneous coordinates to three dimensions. None of the material presented here is new; rather, we have tried to collect in one place diverse but related methods.

Calculation of Reference Frames along a Space Curve (51K) in Graphics Gems, Academic Press, 1990 in Graphics Gems, Academic Press, 1990 in Graphics Gems, Academic Press, 1990

Abstract: Three-dimensional space curves can represent the path of an object or the boundary of a surface patch. They can also participate in various free-form geometric constructions. For example, the generalized cylinder (a cylinder with arbitrary cross-sections along a central, space curve axis) is used in Computer Graphics to good effect. Establishing reference frames for the cross-sections of a generalized cylinder, or for any other geometric use, is the subject of this article.

Modeling the Mighty Maple (3.8M), Proceedings of SIGGRAPH, 1985

Abstract: A method is presented for representing botanical trees, given three-dimensional points and connections. Limbs are modeled as generalized cylinders whose axes are space curves that interpolate the points. A free-form surface connects branching limbs. ``Blobby'' techniques are used to model the tree trunk as a series of non-circular cross sections. Bark is simulated with a bump map digitized from real world bark; leaves are textures mapped onto simple surfaces.

 

Miscellaneous

Graphics Remembrances, IEEE Annals of the History of Computing, 1998

A collection of essays by eleven computer graphics pioneers

Edge Inference with Applications to Anti-Aliasing, Proceedings SIGGRAPH, 1983

Abstract: An edge, when point-sampled for display by a raster device and not aligned with a display axis, appears as a staircase. This common aliasing artifact often occurs in computer images generated by two- and three-dimensional algorithms. The precise edge information often is no longer available but, from the set of vertical and horizontal segments which form the staircase, an approximation to the original edge with a precision beyond that of the raster may be inferred. This constitutes a smoothing of the staircase edge.

Among other applications, the inferred edges may be used to re-shade the pixels they intersect, thereby anti-aliasing the inferred edges. The anti-aliased inferred edges prove a more attractive approximation to the real edges than their aliased counterparts.

Introductory Computer Graphics, University of California course notes, 1990

A set of notes developed for a course taught at UCSC.

Nature at New York Tech, Computer Graphics and Applications, May, 1986

Abstract: Since 1974 the Computer Graphics Lab at the New York Institute of Technology has been a home to artistic expression as well as scientific development. The myriad images created over the years reflect the wide-ranging interests of the lab's researchers and animators. Although gleaming globes and robot romances are still popular at New York Tech, considerable activity also has been devoted to representing natural phenomena.

Tree, The Treasure of Computer Graphics, Kodansha Publishing, Tokyo, 1998

An invited essay on Nature and computer graphics.

A Representation for Botanical Trees using Density Distributions, 1st Int'l Conf. on Engineering and Computer Graphics, 1984

Abstract: Presented is a method for representing botanical trees given three-dimensional data consisting of a points list and a connectivity list. The data are interpolated by three-dimensional space curves described with b-splines. Points along the curves serve as centers of density functions from which are derived planar contours. The collection of contours is polygonized to produce a surface representing a tree. The resulting model has a natural appearance.

Frame Buffer System Selection (with Russell Fish), University of Utah technical report, 1979

In the late seventies, the University of Utah Computer Graphics Lab faced a crisis: their sole frame buffer was returned to Evans and Sutherland for renovation; the department was framebuffer-less, but not penniless. Read about the exciting events that lead to the acquisition of a new frame buffer.

 

PhD Dissertation

Skeletal Design of Natural Form, University of Calgary, 1995

Abstract: An edge, when point-sampled for display by a raster device and not aligned with a display axis, appears as a staircase. This common aliasing artifact often occurs in computer images generated by two- and three-dimensional algorithms. The precise edge information often is no longer available but, from the set of vertical and horizontal segments which form the staircase, an approximation to the original edge with a precision beyond that of the raster may be inferred. This constitutes a smoothing of the staircase edge.

Among other applications, the inferred edges may be used to re-shade the pixels they intersect, thereby anti-aliasing the inferred edges. The anti-aliased inferred edges prove a more attractive approximation to the real edges than their aliased counterparts.

 

Masters Thesis

Reconstruction of Three-Dimensional Surfaces from Two-Dimensional Projections, University of Utah, 1981

This thesis introduced a technique to reconstruct three-dimensional shapes from photographs; this was one of the first demonstrations of `photometric stereo.'