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MDC-ELLIPSOIDs.test.002

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MDC-ELLIPSOIDs.test.001

Confocal Quadrics 2 - intersect Same as Confocal Quadrics 2 - but also showing the intersection with the XY-plane, which generates a system of confocal conics. For more information, films, and interactive material, see

Quadrics Booth - SC02 Supercomputing Conference - Baltimore View of the Quadrics Booth at SC02

Confocal Quadrics 2 A triply orthogonal system of surfaces. Through each point in space there passes three surfaces from this system and they are mutually orthogonal. For more information, films, and interactive material, see

Rational Plane Curves Given a curve C={f=0} of degree d in complex projective 2-space, one may ask, if C admits a parametization, ie if there is a rational map from projective 1-space to C with dense image. C minus the singularities of C is a 1-dimensional complex manifold, ie a real surface. As a topological space it is homeomorphic to a compact oriented surface minus finitely many points. Compact oriented surfaces are topologically classified by their genus g, the number of handles one has to attach to a sphere to obtain the given surface. Necessary and sufficient for a curve to admit a parametrization is the condition g=0. If rp is the multiplicity of C at p and C has rp different tangents at p, then g is (d-1)*(d-2)/2 minus the sum of rp*(rp-1)/2 for all points p of C. If the equation f has rational coefficients, a parametization with rational coefficients can be given, up to a field extension of degree 2, which may be necessary if d is even. In the example shown the curve C (drawn in red) is given by a polynomial of degree 5 and has 3 double points and one triple point, so the formula above reads g = 4*3/2-1-1-1-3 = 0, hence C admits a parametrization. The theorem of Bezout implies, that the curve C of degree 5 intersects a quadric in 5*2 = 10 points, counted with multiplicities. Hence the system of all quadrics (shown in green) through the singular points of C has 5*2-3-2-2-2 = 1 moving point of intersection with C. Elimination gives the coordinates of this point in terms of the ...

Super Toroids Height Maps An example of the blShapeAPI to show its power and simplicity

Alenia HPC Centre 1 minute video on the installation of the HPC Centre in Pomigliano, 9 HP racks and 11 Bull racks, with a Quadrics full bandwidth 256 way network based on QsNetII.

MDC-ELLIPSOIDs.test.003

ConfocalQuadrics-Intersect-XY Confocal quadrics intersecting the XY-plane in a set of confocal conics. For more information, films, and interactive material, see

Amiga animations: upstairs Collision detection test created in Real3D. Character consisting of animated quadrics (spheres, cones, cylinders).

Diagonalizing a quadric 3 Showing the singularities of (Q - lambda Id). For more information, films, and interactive material, see

Diagonalizing a quadric 2 Showing the singularities of (Q - lambda Id). For more information, films, and interactive material, see

Diagonalizing a quadric 4 Showing the singularities of (Q - lambda Id). For more information, films, and interactive material, see

SuperQuadrics [Demo 2] Demostració dels estiraments dels superquadrics

Manicone The video is a description of our work "Manicone" - a Java application displaying a humanoid form in four spatial dimensions. website: /art/manicone

One-sheeted Hyperboloid as a line surface, generated by the intersection of two moving planes. For more information, films, and interactive material, see

Old Amiga/ Real3D animation: Fuse Simulation created in Amiga / Real3D. Cubes, spheres and cones acting under the influence of gravity force field (created in 1994).

LUKE BOW - Believe It (But You Don't)

MDC-ELLIPSOIDs.test.006

Diagonalizing a quadric 1 Showing the singularities of (Q - lambda Id). For more information, films, and interactive material, see

Superquadrics The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Superquadrics are generalizations of quadrics (which are ellipsoids, hyperboloids of one or two sheets, and paraboloids) using the exponents epsilon1, epsilon2 assuming non-integer values. All such surfaces involve the use of a combination of trig... Contributed by: Robert Kragler

Ellipsoid - Principal Net Showing the lines of curvature on a non-rotationally symmetric ellipsoid and the singularities at the umbilical points. The principal net appears as the intersection with the ellipsoid of its confocal family of quadrics. For more information, films, and interactive material, see

ConfocalQuadrics A certain 1-parameter family of quadrics. For more information, films, and interactive material, see

Rational Points on an Elliptic Curve The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. On an elliptic curve, if a line through two rational points P and Q intersects the curve again at R, then R is another rational point. This property is fundamental in number theory. Contributed by: Ed Pegg Jr

LeMieux Installation at PSC

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