252 research outputs found
Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification
We present an efficient method for classifying the morphology of the
intersection curve of two quadrics (QSIC) in PR3, 3D real projective space;
here, the term morphology is used in a broad sense to mean the shape,
topological, and algebraic properties of a QSIC, including singularity,
reducibility, the number of connected components, and the degree of each
irreducible component, etc. There are in total 35 different QSIC morphologies
with non-degenerate quadric pencils. For each of these 35 QSIC morphologies,
through a detailed study of the eigenvalue curve and the index function jump we
establish a characterizing algebraic condition expressed in terms of the Segre
characteristics and the signature sequence of a quadric pencil. We show how to
compute a signature sequence with rational arithmetic so as to determine the
morphology of the intersection curve of any two given quadrics. Two immediate
applications of our results are the robust topological classification of QSIC
in computing B-rep surface representation in solid modeling and the derivation
of algebraic conditions for collision detection of quadric primitives
Contact detection between a small ellipsoid and another quadric
[Abstract] We analyze the characteristic polynomial associated to an ellipsoid and another quadric in the context of the contact detection problem. We obtain a necessary and sufficient
condition for an efficient method to detect contact. This condition, named smallness
condition, is a feature on the size and the shape of the quadrics and can be checked
directly from their parameters. Under this hypothesis, contact can be noticed by means
of the expressions in a discriminant system of the characteristic polynomial. Furthermore,
relative positions can be classified through the sign of the coefficients of this polynomial.
As an application of these results, a method to detect contact between a small ellipsoid
and a combination of quadrics is given
Solid rocket booster thermal radiation model, volume 1
A solid rocket booster (SRB) thermal radiation model, capable of defining the influence of the plume flowfield structure on the magnitude and distribution of thermal radiation leaving the plume, was prepared and documented. Radiant heating rates may be calculated for a single SRB plume or for the dual SRB plumes astride the space shuttle. The plumes may be gimbaled in the yaw and pitch planes. Space shuttle surface geometries are simulated with combinations of quadric surfaces. The effect of surface shading is included. The computer program also has the capability to calculate view factors between the SRB plumes and space shuttle surfaces as well as surface-to-surface view factors
Fixing All Moduli in a Simple F-Theory Compactification
We discuss a simple example of an F-theory compactification on a Calabi-Yau
fourfold where background fluxes, together with nonperturbative effects from
Euclidean D3 instantons and gauge dynamics on D7 branes, allow us to fix all
closed and open string moduli. We explicitly check that the known higher order
corrections to the potential, which we neglect in our leading approximation,
only shift the results by a small amount. In our exploration of the model, we
encounter interesting new phenomena, including examples of transitions where D7
branes absorb O3 planes, while changing topology to preserve the net D3 charge.Comment: 68 pages, 19 figures; v2: references adde
Accessibility for Line-Cutting in Freeform Surfaces
Manufacturing techniques such as hot-wire cutting, wire-EDM, wire-saw cutting, and flank CNC machining all belong to a class of processes called line-cutting where the cutting tool moves tangentially along the reference geometry. From a geometric point of view, line-cutting brings a unique set of challenges in guaranteeing that the process is collision-free. In this work, given a set of cut-paths on a freeform geometry as the input, we propose a conservative algorithm for finding collision-free tangential cutting directions. These directions, if they exist, are guaranteed to be globally accessible for fabricating the geometry by line-cutting. We then demonstrate how this information can be used to generate globally collision-free cut-paths. We apply our algorithm to freeform models of varying complexity.RYC-2017-2264
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