Kurt W. Fleischer

Elastically deformable models

The theory of elasticity describes deformable materials such as rubber, cloth, paper, and flexible metals. We employ elasticity theory to construct differential equations that model the behavior of non-rigid curves, surfaces, and solids as a function of time. Elastically deformable models are active: they respond in a natural way to applied forces, constraints, ambient media, and impenetrable obstacles. The models are fundamentally dynamic and realistic animation is created by numerically solving their underlying differential equations. Thus, the description of shape and the description of motion are unified.

Computer-generated watercolor

A watercolor model based on an ordered set of translucent glazes, which are created independently usinig a shallow water fluid simulation. A Kubelka-Munk compositing model is used for simulating the optical effect of the superimposed glazes. The computer generated watercolor model is used as part of an interactive watercolor paint system, or as a method for automatic image “watercolorization.”

Modeling inelastic deformation: viscolelasticity, plasticity, fracture

We continue our development of physically-based models for animating nonrigid objects in simulated physical environments. Our prior work treats the special case of objects that undergo perfectly elastic deformations. Real materials, however, exhibit a rich variety of inelastic phenomena. For instance, objects may restore themselves to their natural shapes slowly, or perhaps only partially upon removal of forces that cause deformation. Moreover, the deformation may depend on the history of applied forces. The present paper proposes inelastically deformable models for use in computer graphics animation. These dynamic models tractably simulate three canonical inelastic behaviors---viscoelasticity, plasticity, and fracture. Viscous and plastic processes within the models evolve a reference component, which describes the natural shape, according to yield and creep relationships that depend on applied force and/or instantaneous deformation. Simple fracture mechanics result from internal processes that introduce local discontinuities as a function of the instantaneous deformations measured through the model. We apply our inelastically deformable models to achieve novel computer graphics effects.

Energy constraints on parameterized models

A simple but general approach to imposing and solving geometric constraints on parameterized models is introduced, applicable to animation as well as model construction. Constraints are expressed as energy functions, and the energy gradient followed through the models parameter space. Intuitively, energy constraints behave like forces that pull and parametrically deform the parts of the model into place. A wide variety of geometric constraints are amenable to this formulation, and may be used to influence arbitrary model parameters. A catalogue of basic constraints is presented, and results are shown.

Cellular texture generation

We propose an approach for modeling surface details such as scales, feathers, or thorns. These types of cellular textures require a representation with more detail than texture-mapping but are inconvenient to model with hand-crafted geometry. We generate patterns of geometric elements using a biologically-motivated cellular development simulation together with a constraint to keep the cells on a surface. The surface may be defined by an implicit function, a volume dataset, or a polygonal mesh. Our simulation combines and extends previous work in developmental models and constrained particle systems.

Interval methods for multi-point collisions between time-dependent curved surfaces

We present an efficient and robust algorithm for finding points of collision between time-dependent parametric and implicit surfaces. The algorithm detects simultaneous collisions at multiple points of contact. When the regions of contact form curves or surfaces, it returns a finite set of points uniformly distributed over each contact region. Collisions can be computed for a very general class of surfaces: those for which inclusion functions can be constructed. Included in this set are the familiar kinds of surfaces and time behaviors encountered in computer graphics. We use a new interval approach for constrained minimization to detect collisions, and a tangency condition to reduce the dimensionality of the search space. These approaches make interval methods practical for multi-point collisions between complex surfaces. An interval Newton method based on the solution of the interval linear equation is used to speed convergence to the collision time and location. This method is more efficient than the Krawczyk‐Moore iteration used previously in computer graphics.

Stylizing animation by example

Skilled artists, using traditional media or modern computer painting tools, can create a variety of expressive styles that are very appealing in still images, but have been unsuitable for animation. The key difficulty is that existing techniques lack adequate temporal coherence to animate these styles effectively. Here we augment the range of practical animation styles by extending the guided texture synthesis method of Image Analogies [Hertzmann et al. 2001] to create temporally coherent animation sequences. To make the method art directable, we allow artists to paint portions of keyframes that are used as constraints. The in-betweens calculated by our method maintain stylistic continuity and yet change no more than necessary over time.

Heating and melting deformable models

We develop physically-based graphics models of non-rigid objects capable of heat conduction, thermoelasticity, melting and fluid-like behaviour in the molten state. These deformable models feature non-rigid dynamics governed by Lagrangian equations of motion and conductive heat transfer governed by the heat equation for non-homogeneous, non-isotropic media. In its solid state, the discretized model is an assembly of hexahedral finite elements in which thermoelastic units interconnect particles situated in a lattice. The stiffness of a thermoelastic unit decreases as its temperature increases, and the unit fuses when its temperature exceeds the melting point. The molten state of the model involves a molecular dynamics simulation in which ‘fluid’ particles that have broken free from the lattice interact through long-range attraction forces and short-range repulsion forces. We present a physically-based animation of a thermoelastic model in a simulated physical world populated by hot constraint surfaces.

Accurate polygon scan conversion using half-open intervals

Publisher Summary This chapter describes a simple, efficient polygon scan-conversion algorithm that allows a mesh of polygons to be scan-converted, one polygon at a time, without drawing any pixel twice and without leaving any holes. The algorithm uses a slightly modified Bresenham algorithm to scan-convert the polygon edges and uses half-open intervals to disambiguate the pixels lying on edges shared by adjacent polygons. The chapter presents a scan-line algorithm for triangles; however, the technique is readily extended to arbitrary simple polygons. A scan conversion algorithm that paints pixels whose centers are mapped to a given polygon P will be able to render all the polygons of a polygonal mesh, one at a time, without leaving any holes or duplicating any pixels. For efficiency, EdgeScan is computed incrementally using a Bresenham-like algorithm. The EdgeSetup routine initializes a structure that contains the increments, and the EdgeScan routine uses those increments to compute the intersection of the edge with each scan line. A necessary consequence of painting only those pixels whose centers map to a polygon is that the algorithm may draw disconnected sets of pixels for very thin polygons and draws no pixels at all for polygons that are degenerate—such as line segments or single points.

Pure phase-encoded MRI and classification of solids

Here, the authors combine a pure phase-encoded magnetic resonance imaging (MRI) method with a new tissue-classification technique to make geometric models of a human tooth. They demonstrate the feasibility of three-dimensional imaging of solids using a conventional 11.7-T NMR spectrometer. In solid-state imaging, confounding line-broadening effects are typically eliminated using coherent averaging methods. Instead, the authors circumvent them by detecting the proton signal at a fixed phase-encode time following the radio-frequency excitation. By a judicious choice of the phase-encode time in the MRI protocol, the authors differentiate enamel and dentine sufficiently to successfully apply a new classification algorithm. This tissue-classification algorithm identifies the distribution of different material types, such as enamel and dentine, in volumetric data. In this algorithm, the authors treat a voxel as a volume, not as a single point, and assume that each voxel may contain more than one material. They use the distribution of MR image intensities within each voxel-sized volume to estimate the relative proportion of each material using a probabilistic approach. This combined approach, involving MRI and data classification, is directly applicable to bone imaging and hard-tissue contrast-based modeling of biological solids.