Fran (Functional Reactive Animation) is a collection of data types and functions for composing richly interactive, multimedia animations. The key ideas in Fran are its notions of behaviors and events. Behaviors are time-varying, reactive values, while events are sets of arbitrarily complex conditions, carrying possibly rich information. Most traditional values can be treated as behaviors, and when images are thus treated, they become animations. Although these notions are captured as data types rather than a programming language, we provide them with a denotational semantics, including a proper treatment of real time, to guide reasoning and implementation. A method to e#ectively and efficiently perform event detection using interval analysis is also described, which relies on the partial information structure on the domain of event times. Fran has been implemented in Hugs, yielding surprisingly good performance for an interpreter-based system. Several examples are given, including the ability to describe physical phenomena involving gravity, springs, velocity, acceleration, etc. using ordinary di#erential equations.

Solid objects in the real world do not pass through each other when they collide. Enforcing this property of "solidness" is important in many interactive graphics applications; for example, solidness makes virtual reality more believable, and solidness is essential for the correctness of vehicle simulators. These applications use a collision-detection algorithm to enforce the solidness of objects. Unfortunately, previous collision-detection algorithms do not adequately address the needs of interactive applications. To work in these applications, a collision-detection algorithm must run at real-time rates, even when many objects can collide, and it must tolerate objects whose motion is specified "on the fly" by a user. This dissertation describes a new collision-detection algorithm that meets these criteria through approximation and graceful degradation, elements of time-critical computing. The algorithm is not only fast but also interruptible, allowing an application to trade accuracy ...

In this paper we present a framework for minimum distance computations that allows efficient solution of minimum distance queries on a variety of surface representations, including sculptured surfaces. The framework depends on geometric reasoning rather than numerical methods and can be implemented straightforwardly. We demonstrate performance that compares favorably to other polygonal methods and is faster than reported results for other methods on sculptured surfaces. 1 Introduction We introduce a framework for minimum distance calculations that applies well to both polygonal and parametric model representations (Figure 1). The resulting methods scale well with problem size, have time-critical properties, and are interactive for large polygonal models and sculptured surfaces. In robotics, minimum distance queries have been used in path planning [2], path modification [25], and collision avoidance [15]. In computer graphics, minimum distance computations have played roles in physical...

We describe a new method for numeric computations, which we call affine arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track of rounding and truncation errors for each computed value. However, by taking into account correlations between operands and sub-formulas, AA is able to provide much tighter bounds for the computed quantities, with errors that are approximately quadratic in the uncertainty of the input variables. We also describe two applications of AA to computer graphics problems, where this feature is particularly valuable: namely, ray tracing and the construction of octrees for implicit surfaces.

We introduce a new method of creating smooth implicit surfaces of arbitrary manifold topology. These surfaces are described by specifying locations in 3D through which the surface should pass, and also identifying locations that are interior or exterior to the surface. A 3D implicit function is created from these constraints using a variational scattered data interpolation approach. We call the iso-surface of this function a variational implicit surface. Like other implicit surface descriptions, these surfaces can be used for CSG and interference detection, may be interactively manipulated, are readily approximated by polygonal tilings, and are easy to ray trace. A key strength is that variational implicit surfaces allow the direct specification of both the location of points on the surface and surface normals. These are two important manipulation techniques that are difficult to achieve using other implicit surface representations such as sums of spherical or ellipsoidal Gaussian functions ("blobbies"). We show that these properties make variational implicit surfaces particularly attractive for interactive sculpting using the particle sampling technique introduced by Witkin and Heckbert in [30]. Our formulation also yields a simple method for converting a polygonal model to a smooth implicit model.

Sphere tracing is a new technique for rendering implicit surfaces using geometric distance. Distance-based models are common in computer-aided geometric design and in the modeling of articulated figures. Given a function returning the distance to an object, sphere tracing marches along the ray toward its first intersection in steps guaranteed not to penetrate the implicit surface. Sphere tracing is particularly adept at rendering pathological surfaces. Creased and rough implicit surfaces are defined by functions with discontinuous or undefined derivatives. Current root finding techniques such as L-G surfaces and interval analysis require periodic evaluation of the derivative, and their behavior is dependent on the behavior of the derivative. Sphere tracing requires only a bound on the magnitude of the derivative, robustly avoiding problems Manuscript, July 1994. Recommended for publication: The Visual Computer. 5-70 where the derivative jumps or vanishes. This robustness and scope ...

This paper introduces a fast continuous collision detection technique for polyhedral rigid bodies. As opposed to most collision detection techniques, the computation of the first contact time between two objects is inherently part of the algorithm. The method can thus robustly prevent objects interpenetrations or collisions misses, even when objects are thin or have large velocities. The method is valid for general objects (polygon soups), handles multiple moving objects and acyclic articulated bodies, and is efficient in low and high coherency situations. Moreover, the method can be used to speed up existent continuous collision detection methods for parametric or implicit rigid surfaces. The collision detection algorithms have been successfully coupled to a real-time dynamics simulator. Various experiments are conducted that show the method’s ability to produce high-quality interaction (precise objects positioning for example) between models up to tens of thousands of triangles, which couldn’t have been performed with previous continuous methods. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Animation- Virtual Reality 1.

This paper presents a method for modeling the surface of an object from a sequence of range maps. Our method is based on a volumetric approach that produces a compact surface without boundary. It provides robustness through the use of interval analysis techniques and computational efficiency through hierarchical processing using octrees. 1.

An environment for general research into and prototyping of algorithms for reliable constrained and unconstrained global nonlinear optimization and reliable enclosure of all roots of nonlinear systems of equations, with or without inequality constraints, is being developed. This environment should be portable, easy to learn, use, and maintain, and sufficiently fast for some production work. The motivation, design principles, uses, and capabilities for this environment are outlined. The environment includes an interval data type, a symbolic form of automatic differentiation to obtain an internal representation for functions, a special technique to allow conditional branches with operator overloading and interval computations, and generic routines to give interval and non-interval function and derivative information. Some of these generic routines use a special version of the backward mode of automatic differentiation. The package also includes dynamic data structures for exhaustive sear...

Analytic visibility algorithms, for example methods which compute a subdivided mesh to represent shadows, are notoriously unrobust and hard to use in practice. We present a new method based on a generalized definition of extremal stabbing lines, which are the extremities of shadow boundaries. We treat scenes containing multiple edges or vertices in degenerate configurations, (e.g., collinear or coplanar). We introduce a robust ɛ method to determine whether each generalized extremal stabbing line is blocked, or is touched by these scene elements, and thus added to the line's generators. We develop robust blocker predicates for polygons which are smaller than ɛ. For larger ɛ values, small shadow features merge and eventually disappear. We can thus robustly connect generalized extremal stabbing lines in degenerate scenes to form shadow boundaries. We show that our approach is consistent, and that shadow boundary connectivity is preserved when features merge. We have implemented our algorithm, and show that we can robustly compute analytic shadow boundaries to the precision of our chosen ɛ threshold for non-trivial models, containing numerous degeneracies.