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.

This paper describes the various artistic effects of watercolor and shows how they can be simulated automatically. Our watercolor model is based on an ordered set of translucent glazes, which are created independently using a shallow-water fluid simulation. We use a Kubelka-Munk compositing model for simulating the optical effect of the superimposed glazes. We demonstrate how computergenerated watercolor can be used in three different applications: as part of an interactive watercolor paint system, as a method for automatic image "watercolorization," and as a mechanism for nonphotorealistic rendering of three-dimensional scenes.

No abstract

Abstract-We present a new algorithm for identifying the distribution of different material types in volumetric datasets such as those produced with Magnetic Resonance Imaging (MRI) or Computed Tomography (CT). Because we allow for mixtures of materials and treat voxels as regions, our technique reduces errors that other classification techniques can create along boundaries between materials and is particularly useful for creating accurate geometric models and renderings from volume data. It also has the potential to make volume measurements more accurately and classifies noisy, low-resolution data well.There are two unusual aspects to our approach. First, we assume that, due to partial-volume effects, or blurring, voxels can contain more than one material, e.g., both muscle and fat; we compute the relative proportion of each material in the voxels. Second, we incorporate information from neighboring voxels into the classification process by reconstructing a continuous function, x, from the samples and then looking at the distribution of values that x takes on within the region of a voxel. This distribution of values is represented by a histogram taken over the region of the voxel; the mixture of materials that those values measure is identified within the voxel using a probabilistic Bayesian approach that matches the histogram by finding the mixture of materials within each voxel most likely to have created the histogram. The size of regions that we classify is chosen to match the spacing of the samples because the spacing is intrinsically related to the minimum feature size that the reconstructed continuous function can represent.

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.