2004 . 2003 . 2002 . 2001 . 2000 . 1999 . 1998 . 1997 . 1996 . 1995 . 1994 . 1993 . 1992 . 1991 . 1990
MS-CIS-96-01
Berstein Polynomials for Radiative Transfer Computations
Min-Zhi Shao, Norman Badler
In this paper we propose using planar and spherical Berstain
polynomials over angular domain for radiative transfer computations.
In the planar domain, we propose using piecewise Bernstein
basis functions and symmetric Gaussian quadrature formulas
over triangular elements for high quality radiosity solution.
In the spherical domain, we propose using piecewise Bernstein
basis functions over a geodesic triangulation to represent
the radiance function. The representation is intrinsic to the
unit sphere, and may be efficiently stored, evaluated, and
subdivided by the de Casteljau algorithm. The computation of
other fundamental radiometric quantities such as vector irradiance
and reflected radiance may be reduced to the integration of
the piecewise Bernstein basis functions on the unit sphere.
The key result of our work is a simple geometric intergration
algorithm based on adaptive domain subdivision for the Bernstein-Bezier
polynomials over a geodesic triangle on the unit sphere.
MS-CIS-96-02
Spherical Sampling by Archimedes' Theorem
Min-Zhi Shao, Norman Badler
In this paper we present a simple and efficient algorithm
for generating uniformaly distributed samples on the unit sphere
based on an Archimedes' theorem. The implementation is straightforward
and may be easily extended to include stratified sampling for
variance reduction. Applications in image synthesis include
solid angle measurement, irradiance computation, and rendering
equation solution for geometrically complex environments.
MS-CIS-96-05
Effecting Database Transformations Using Morphase
Susan B. Davidson, Anthony Kosky
Database transformations are a frequent problem for data
managers supporting scientific databases, particulary those
connected with the Human Genome Project. The databases involeved
frequently contain complex data structures not typically found
in conventional databases, such as arbitrarily nested records,
sets, variants, and optional fields, as well as object identities
and recursive data structures. Furthermore, programs implementing
the transfomations must be frequently modified since the databases
involved evolve rapidly, as often as 3 to 4 times a year. We
present in this paper a language (WOL) for specifying transformations
between such databases and describe its implementation in a
system called Morphase. Optimization are performed at all stages,
with significant impact on the compilation and execution time
of sample transformations.
MS-CIS-96-06
Consistency Management in the EROS Kernel
Jonathan Shapiro, David J. Farber, Jonathan Smith
EROS is a persistent operating system targeted towards managing
resources with great longevity. The system provides a persistent
single level store supporting two fundamental object types:
nodes and pages. All primary objects, including memory segments
and protection domains, are constructed out of these fundamental
objects, and inherit their persitence. EROS is a pure capability
system: access to objects is provided exclusively through the
invocation of kernal enforced, secure capabilities.
This paper descibes the EROS Abstract Machine and the mechanisms
used to achieve efficient consistency management within the
system. The implementation, including all primary objects,
a low overhead checkpoint/ migration subsystem, and an efficient
interprocess communication mechanism, requires less than 64
Kbytes of supervisor code (prior to size tuning).
MS-CIS-96-08
Connecting Planning and Acting via Object-Specific Reasoning
(Dissertation)
Libby Levison
Instructions from a high level planner are in general too
abstract for a behavioral simulator to execute. In this dissertation
I describe an intermediate reasoning system-the OBJECT-SPECIFIC
REASONER-which bridges the gap between high level task-actions
and action directives of a behavioral system. It decomposes
task-actions and derives parameter values for each action directive,
thus enabling existing high level planners to instruct synthetic
agents with the same task action commands that they currently
produce. The OBJECT-SPECIFIC REASONER's architecture follows
directly from the hypothesis that action representations are
under specified descriptions, and that objects in the same
functional category are manipulated in similar ways. The action
representation and the object representation are combined to
complete the action interpretation, thereby grounding plans
in action. The OBJECT-SPECIFIC REASONER provides evidence that
a small number of object functional categories, organized in
a taxonomy, makes possible a simple and elegant reasoning system
which converts task actions to action directives. To test the
theory behind the Object-Specific Reassoner, I applied the
implementation to three different 3D graphical domains.
MS-CIS-96-09
A Query Language and Optimization Techniques for Unstructured
Data Techniques for Unstructured Data
Peter Buneman, Susan Davidson, Gerda Hillebrand, and
Dan Suciu
A new kind of data model has recently emerged in which the
database is not constrained by a conventional schema. Systems
like ACeDB, which has become very popular with biologists,
and the recent Tsimmis proposal for data integration organize
data in tree -like structures whose components can be used
equally well to represent sets and tuples. Such structures
allow great flexibility in data representation.
What query language is appropriate for such structures? Here
we propose a simple language UNQL for querying data organized
as a rooted, edge-labeled graph. In this model, relational
data may be represented as fixed-depth trees, and on such trees
UNQL is equivalent to the relational algebra. The novelty of
UNQL consists in its programming constructs for arbitrarily
deep data and for cyclic structures. While strictly more powerful
than query languages with path expressions like XSQL, UNQL
can still be efficiently evaluated. We describe new optimization
techniques for the deep or ``vertical'' dimension of UNQL queries.
Furthermore, we show that known optimization techniques for
operators on flat relations apply to the ``horizontal'' dimension
of UNQL.
MS-CIS-96-10
A New Look at Bandwidth Latency Tradeoffs
John Shaffer, Jonathan Smith
Concerns about propagation delay have dominated the discussion
of latency, bandwidth and their effect on distributed applications.
In this paper, we argue that the relevant latency measure for
applications is the Applicaiotn Data Unit (ADU) Latency, defined
as the time between the sending of an ADU and its receipt.
Since ADUs are often large, ADU latency is influenced by throughput
as well as propagation delay.
We investigated the effects the effects od ADU latency with
an experimental study of several applications. The applications
used Distributed Shared Memory as an interprocess Comunications
mechanism, constraining the ADUs to page sized units. The applications
were run on an Ethernet, an experimental ATM LAN, and using
ATM on an experimental high-speed WAN. The measured results
were used to normalize results gathered by inserting an experimental
ATM switch output port controller in the network to create
tunable delays.
The results conclusively demonstrate the effect of ADU latency
on distributed application response time. The experiments give
a precise characterization of the effect of varinh bandwidth
and propagation delay on a real system, and suggest promissing
directions for further improving application performance in
future networks.
MS-CIS-96-12
The Power Broker: Intelligent Power Management for Mobile
Computers
Sanjay Udani, Jonathan Smith
Technology has improved processor speed and memory densities
at exponetial rates. Rapid advances in portable computing have
resulted in laptop computers with performance and features
comparable to their desktop counterparts. Battery technology
has failed to keep pace, decreasing the usefulness of mobile
computers and portable wireless devices.
We provide a detailed analysis of power consumption typically
encountered in a networked laptop computer and the power management
methods currently used. We then show how interaction between
independent power consumers results in inefficient use of energy
resources and propose the Power Broker as a means for orchestrating
energy use with the goal of wxtnding battery life. The Power
Broker's resource management algorithms exploit an abundant
resource (CPU power) to conserve one (battery energy).
MS-CIS-96-13
Operating System Support for Protocol Boosters
A. Mallet, J. D. Chung, J. M. Smith
``Protocol Boosters'' are modules inserted into Protocol
graphs. They allow the protocol's behavior to adapt to its
environment. Boosters can mask undesirable properties of links
or subnets in an internetwork. The method permits use of proprietary
protocols and supports endn-to-end optimizations.
We have implemented Protocol Boosters support in the FreeBSD
version of UNIX for Intel architecture machines. Our prototype
embeds boosters in the 4.4 BSD-Lite Internet protocol (IP)
stack. We have measured the performance of two prototype boosters:
an encryption booster (for passage across insecure subnets)
and a compression booster (passage across bacdwidth-impaired
subnets).
Our measurement data suggests that OS support for this method
can be constructed with low performance overhead: execution
of the protocol elements domimates any overhead introduction
by our implementation. We discuss some lessons learned from
implementation.
MS-CIS-96-14
Gigabit Networks
Jonathan Smith
This chapter summarizes what we have learned in the past
decade of research into extremely high throughput networks.
Such networks are colloquially referred to as ``Gigabit Networks''
in reference to the billion bit per second throughput regime
they now operate in. The engineering challenges are in the
integration of fast transmission systems and high-performance
engineering workstations.
MS-CIS-96-15
Event Signaling within Higher Performance Network Systems
Jeffrey D. Chung, C. Brendan S. Traw, Jonathan Smith
The afterburner ATMlink Adapter has allowed us to evaluate
three event-signaling schemes: polling, traditional interrupts
and the clocked interrupts first investigated in our operating
system work in AURORA. The schemes are evaluated in the context
of a single-copy TCP/IP stack. The experimental results indicate
that clocked interrupts can provide throughout comparable with
traditional interrupts for dedicated machines (up to over 144
Mbps, the highest TCP/IP/ATM throughout reported), and better
performance when the machines are loaded with an artificial
workload. Polling, implemeted to be used with an unmodified
netperf measurement tool, was competitive for small TCP/IP
socket buffersizes (32KB). We concluded that clocked interrupts
may be preferable for applications requiring high throughput
on systems with heavy processing workloads, such as servers.
MS-CIS-96-18
Transforming Databases with Recursive Data Structures Dissertation)
Anthony Kosky
This thesis examines the problems of performing structural
transformations on databases involving complex data-structures
and object-identities, and proposes an approach to specifying
and implementing transformations.
We start by looking at various applicationsof such database
transformations, and at some of the more significant work in
these areas. In particular we will look at work on transformations
in the area of database integration, which has been one of
the major motivating areas for this work. We will also look
at various notions of correctness that have been proposed for
database transformations, and show that the utility of such
notions is limited by the dependence of transformations on
certain implicit database constraints. We draw attention to
the limitations of existing work on transformations, and argue
that there is a need for a more general formalism for reasoning
about database transformations and constraints.
We will also argue that, in order to ensure that database
transformations are well-defined and meaningful, it is necessary
to understand the information capacity of the data-models being
transformed. To this end we give a thorough analysis of the
information capacity of data-models supporting object identity,
and will show that this is dependent on the operations supported
by a query language for comparing object identities.
We introduce a declarative language, WOL, based on Horn-clause
logic, for specifying database transformations and constraints.
We also propose a method of implementing transformations specified
in this language, by manipulating their clauses into a normal
form which can then be translated into an underlying database
programming language.
Finally we will present a number of optimizations and techniques
necessary in order to build a practical implementation based
on these proposals, and will discuss the results of some of
the trials that were carried out using a prototype of such
a system.
MS-CIS-96-19
Model-Based Shape and Motion Analysis: Left Ventricle of
a Heart (Dissertation)
Jinah Park
The accurate and clinically useful estimation of the shape,
motion, and deformation of the left ventricle of a heart (LV)
is an important yet open research problem. Recently, computer
vision techniques for reconstructing the 3D shape and motion
of the LV have been developed. The main drawback of these techniques,
however, is that models are formulated in terms of either too
many local parameters that require non-trivial processing to
be useful for close to real time diagnosis, or too few parameters
to offer an adequate approximation to the LV motion.
To address the problem, we present a new class of volumetric
primitives for a compact and accurate LV shape representation
in which model parameters are functions. Lagrangian dynamics
are employed to convert geometric models into dynamic models
that can deform according to the forces manifested in the data
points. It is thus possible to make a precise estimation of
the deformation of the LV shape (endocardial, epicardial and
anywhere in between) with a small number of intuitive parameter
functions.
We believe that the proposed technique has a wide range of
potential applications. In this thesis, we demonstrate the
possibility by applying it to the 3-D LV shape and motion characterization
from magnetic tagging data (MRI-SPAMM). We show that the results
of our experiments with normal and abnormal heart data enable
us to quantitatively verify the physicians' qualitative conception
of the left ventricular wall motion.
MS-CIS-96-21
Adding Structure to Unstructured Data
Peter Buneman, Susan Davidson, Mary Fernandez, and
Dan Suciu
We develop a new schema for unstructured data. Traditional
schemas resemble the type systems of programming languages.
For unstructured data, however, the underlying type may be
much less constrained and hence an alternative way of expressing
constraints on the data is needed. Here, we propose that both
data and schema be represented as edge-labeled graphs. We develop
notions of conformance between a graph database and a graph
schema and show that there is a natural and efficiently computable
ordering on graph schemas. We then examine certain subclasses
of schemas and show that schemas are closed under query applications.
Finally, we discuss how they may be used in query decomposition
and optimization.
MS-CIS-96-22
Adaptive Correlation Tracking of Targets with Changing Scale
Ulf M. Cahn von Seelen, Ruzena Bajcsy
Algorithms for tracking targets imaged through a zoom lens
must accommodate changes in the magnification of the target.
This requirement poses particular problems for correlation
techniques, which usually are not invariant to scale changes.
An adaptive correlation method has been developed that selectively
updates the correlation template in response to scale changes
in an image sequence. The algorithm estimates a subset of the
parameters of the affine transformation between the template
and the matched image patch and updates the template only when
the scaling exceeds given bounds. The selective template update
enables correlation to track targets at varying scale while
decreasing the risk of template drift.
MS-CIS-96-25
An Easy Case of Sorting by Reversals
Nicholas Tran
We show that sorting by reversals can be performed in polynomial
time when the number of breakpoints is twice the distance.
MS-CIS-96-26
Pipeline Rendering: Interaction and Realism Through Hardware-Based
Multi-Pass Rendering (Dissertation)
Paul Joseph Diefenbach
While large investments are made in sophisticated graphics
hardware, most realistic rendering is still performed off-line
using ray trace or radiosity systems. A coordinated use of
hardware-provided bitplanes and rendering pipelines can however,
approximate ray trace quality illumination effects in a user-interactive
environment, as well as provide the tools necessary for a user
to declutter such a complex scene. A variety of common ray
trace and radiosity illumination effects are presented using
multi-pass rendering in a pipeline architecture. We provide
recursive refelections through the use of secondary viewpoints,
and present a method for using a homogeneous 2-D projective
image mapping to extend this method for refractive transparent
surfaces. This paper then introduces the Dual Z-buffer, or
DZ-buffer, an evolutionary hardware extension which, along
with current frame-buffer functions such as stencil planes
and accumulation buffers, provides the hardware platform to
render non-refractive transparent surfaces in a back-to- front
or front-to-back order. We extend the traditional use of shadow
volumes to provide reflected and refracted shadows as well
as specular light reclassification. The shadow and lighting
effects are then incorporated into our recursive viewpoint
paradigm. Global direct illumination is provided through a
shadow blending technique. Hardware surface illumination is
fit to a physically-based BRDF to provide a better local direct
model, and the framework permits incorporation of a radiosity
solution for indirect illumination as well. Additionally, we
incorporate material properties including translucency, light
scattering, and non-uniform transmittance to provide a general
framework for creating realistic renderings. The DZ-buffer
also provides decluttering facilities such as transparency
and clipping. This permits selective scene viewing through
arbitrary view-dependent and non- planar clipping and transparency
surfaces in real-time. The combination of these techniques
provide for understandable, realistic scene rendering at typical
rates 5-50 times that of a comperable ray trace images. In
addition, the pixel-parallel nature of these methods leads
to exploration of further hardware rendering engine extensions
which can exploit this coherence.
MS-CIS-96-27
A Lexical Theory of Quantification in Ambiguous Query Interpretation
(Dissertation)
Jong Cheol Park
Although the connection between natural language syntax and
semantics has received serious attention in both linguistics
and computational linguistics for the last several decades,
it does not appear that it has yet been entirely satisfactorily
identified. The present dissertation focuses on quantifier
scope ambiguity in an attempt to identify such a connection.
We show that there are some readings that are incorrectly allowed
by the theories and that other readings that are available
are allowed for the wrong reason.
First, we distinguish referential NP interpretations from
quantificational NP interpretations. Most traditional theories
of scope do not, and they are shown to significantly overgenerate
readings and/or miss a crucial generalization regarding quantificationally
available readings. We present a hypothesis based on the notion
of surface constituency to predict quantificationlly available
readings. The hypothesis is tested on core English constructions,
including transitive verbs, dative alternation (ditransitive)
verbs, attitude verbs, complex NPs containing prepositional
phrases, possessives, and subject or non-subject Wh-relatives
(also with pied-piping), and varoius coordinate structures.
We argue that the scopings allowed under the hypothesis are
the ones that are available.
We then present a competence theory of quantifier scope,
couched in a combinatory categorial grammar framework. The
theory defines the connection between syntax and semantics
in a precise way, utilizing the dual quantifier representation.
We show theoretical predications on the core English constructions,
and verify that the theoretical predications are consistent
with the predications made by the hypothesis and that there
are further reasonable theoretically predicted readings.
Finally, we describe an implementation of the theory in Prolog.
The implemented system takes English sentences as ambiguous
queries (regarding scope), generates logical forms that are
associated with them, and evaluates those logical forms with
respect to a predefined datebase of facts. The system also
works as a proof-checker of the theory.
MS-CIS-96-28
Quantifier Scope, Lexical Semantics, and Surface Structure
Constituency
Jong C. Park
We present a novel conjecture concerning the scope ambiguities
that arise in sentences including multiple non-referential
quantifiers. We claim that many existing theories of the phenomenon
fail to correctly limit the set of readings that such sentences
engender by failing to distinguish between referential and
non-referential quantifiers. Once the distinction is correctly
drawn, we show that surface syntax can be made, via an extended
notion of surface constituency, to identify the set of available
differently-scoped readings for such sentences. We examine
various English constructions to show that the scopings predicted
by the conjecture are the only ones that are available to human
language understanders. We show how to incorporate this conjecture
into a theory of quantifier scope, by couching it in a unification-
based Combinatory Categorial Grammer framework and implementing
it in SICStus Prolog. Finally, we compare the proposal with
related approaches to quantifier scope ambiguity.
MS-CIS-96-29
Kinematic Control of Human Postures for Task Simulation
Xinmin Zhao
Kinematic control of human postures for task simulation is
important in human factor analysis, simulation and training.
It is a challenge to control the postures of a synthesized
human figure in real-time on today's graphics workstations
because the human body is highly articulated. In addition,
we need to consider many spatial restrictions imposed on the
human body while performing a task.
In this study, we simplfy the human posture control problem
by decoupling the degrees of freedom (dof) in the human body.
Based on the several decoupling schemes, we develop an analytical
human posture control algorithm. This analytical algorithm
has a number of advantages over existing methods. It eliminates
the local minima problem, it is efficient enough to control
whole human body postures in real-time, and it provides more
effective and convenient control over redundant degrees of
freedom. The limitation of this algorithm is that it cannot
handle over-constrained problems or general constraint functions.
To overcome this limitation, we transform the human posture
control problem from a 40 variable joint space to a 4 to 9
redundancy parameter space. We then apply nonlinear optimization
techniques on the transformed problem. Because the search space
is reduced, this new numerical algorithm is more likely to
find a solution than existing methods which apply optimization
techniques directly in the joint space.
The contribtions of this thesis include a decoupling approach
for simplifying the human posture control problem, an analytical
human posture control algorithm based on this decoupling approach,
and a numerical human posture control algorithm in redundancy
parameter space. These two new algorithms are more efficient
and effective than existing methods, and they also give the
user control to select the desired solution. Moreover, the
analytical algorithm can control postures of a few 92 dof human
figures at 30 Hz.
MS-CIS-96-31
The Machine-Assisted Proof ofProgramming Language Properties
(Dissertation)
Myra VanInwegen
The goals of the project described in this thesis are twofold.
First, we wanted to demostrate that if a programming language
has a semantics that is complete and rigorous (mathematical),
but not too complex, then substantial theorems can be proved
about it. Second, we wanted to assess the utility of using
an automated theorem prover to aid in such proofs. We chose
SML as the language about which to prove theorems: it has a
published semantics that is complete and rigorous, and while
not exactly simple, is comprehensible. We encoded the semantics
of Core SML into the theorem prover HOL (creating new definitional
packages for HOL in the process). We proved important theorems
about evaluation and about the type system. We also proved
the type preservation theorem, which relates evaluation and
typing, for a good portion of the language. We were not able
to complete the proof of type preservation because it is not
true: we found counterexamples. These proofs demonstrate that
a good semantics will allow the proof of programming language
properties and allow the identification of trouble spots in
the language. The use of HOL had its plusses and minuses. One
the whole the benefits greatly outweigh the drawbacks, enough
so that we believe that these theorems could not been proved
in amount of time taken by this project had we not used automated
help.
MS-CIS-96-32
Creating efficient fail-stop cryptographic protocols
Angelos D. Keromytis, Jonathan M. Smith
Fail-stop cryptographic protocols are characterized by the
property that they terminate when an active attack is detected,
rather than releasing information valuable to the attacker.
Since such a construction forces attacks (other than denial-of-service)
to be passive, the protocol designer's concerns can be restricted
to passive attacks and malicious insiders. A significant advantage
of such protocols is that by stopping and not attempting to
recover, proofs about protocol behavior and security properties
are greatly simplified.
This paper presents a generic method of converting any existing
(cryptographic) protocol into a fail-stop one, or designing
new protocols to be fail-stop. Our technique uses cryptographic
hashes to validate sequences of messages by reflecting message
dependencies in the hash values. An informal proof of correctness
is given. We apply it to an early version of Netscape's Secure
Socket Layer (SSL) cryptographic protocol. We also suggest
a possible application to TCP streams as a high-preformance
alternative to the per-packet authentication of IPSEC.
The modified protocols require small increases in message
size and the number of cryptographic operations relative to
the initial non-fail-stop protocols.
MS-CIS-96-33
Testing Real-Time Constraints (Dissertation)
Duncan Clarke
The verification of timing properties of real-time system
models by traditional approaches that depend on the exploration
of the entire system state space is impractical for large systems.
In contrast, testing allows the search for violations of a
property to be narrowed to a relatively small portion of the
overall state space, based on assumptions regarding the structure
of an implementation.
In a computer systems engineering context the primary advantages
of testing over traditional state-space exploration approaches
are two-fold. First, testing offers the possibility of model
validation without state space explosion. Second, the tests
themselves are produced as an artifact of model validation.
Thus, the same tests that validated the model can be used to
validate the hardware or software implementation that is created
from it.
We present a framework for testing timing constraints of
real-time systems. These tests are based on specifications
of minimum and maximum allowable delays between input/output
events in the execution of a system. We present specification
and test languages and their formal semantics, and formalize
a new hierarchy of test coverage criteria for domain testing
of real-time properties. Based on these test coverage critera,
techniques for automatically deriving optimized test suites
are presented. Our testing framework and optimization techniques
are illustrated with examples and a substantial case study.
MS-CIS-96-34
Protocol Boosters
D. C. Feldmeier, A. J. Mcauley, and J. M. Smith
MS-CIS-96-35
A Secure and Reliable Bootstrap Architecture
William A. Arbaugh, David J. Farber, and Jonathan M.
Smith
In a computer system, the integrity of lower layers is treated
as axiomatic by higher layers. Under the presumption that the
hardware comprising the machine (the lowest layer) is valid,
integrity of a layer can be guaranteed if and only if: (1)
the integrity of the lower layers is checked, and (2) transitions
to higher layers occur only after integrity checks on them
are complete. The resulting integrity ``chain'' inductively
guarantees system integrity.
When these conditions are not met, as they typically are
not in the bootstrapping (initialization) of a computer system,
no integrity guarantees can be made. Yet, these guarantees
are increasingly important to diverse applications such as
Internet commerce, intrusion detection systems, and ``active
networks.'' In this paper, we describe the AEGIS architecture
for initializing a computer system. It validates integrity
at each layer transition in the bootstrap process. AEGIS also
includes a recovery process for integrity check failures, and
we show how this results in robust systems. We discuss our
prototype implementation for the IBM personal computer (PC)
architecture, and show that the cost of such system protection
is surprisingly small.
MS-CIS-96-36
Computational Methods for Realistic Image Synthesis (Dissertation)
Min-Zhi Shao
In this thesis, we investigate the computational methods
for both diffuse and general reflections in realistic image
synthesis and propose two new approaches: the overrelaxation
solution and the Bernstein polynomial solution.
One of the major concerns with the radiosity method is its
expensive computing time and memory requirements. In this thesis,
we analyze the convergence behavior of the progressive refinement
radiosity method and propose two overrelaxation algorithms:
the gathering and shooting solution and the positive overshooting
solution. We modify the conventional shooting method to make
the optimal use of the visibility information computed in each
iteration. Based on a concise record of the history of the
unshot light energy distribution, a solid convergence speed-up
is achieved.
Though a great effort has been made to extend the radiosity method
to accommodate general non-diffuse reflection, the current algorithms
are still quite limited to simple environment settings. In this
thesis, we propose using the piecewise spherical Bernstein basis
functions over a geodesic triangulation to represent the radiance
function. The representation is intrinsic to the unit sphere,
and can be efficiently stored, evaluated, and subdivided by the
numerically stable de Casteljau algorithm. We demonstrate that
the computation of other fundamental radiometric quantities such
as vector irradiance and reflected radiance can be reduced to
the integration of the piecewise spherical Bernstein basis functions.
A novel geometric integration algorithm based on adaptive domain
subdivision is presented for the Bernstein- Bezier polynomials
over a geodesic triangle on the unit sphere.
MS-CIS-96-37
Worlds of Change: Counterfactual Reasoning and Causation
(Dissertation)
Charles L. Ortiz, Jr.
The development of a commonsense theory of causation has
often been pursued along a number of, somewhat orthogonal,
directions. The work contained herein examines the role that
counterfactual reasoning can play within such a theory. The
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