Titlebook: SAGA – Advances in ShApes, Geometry, and Algebra; Results from the Mar Tor Dokken,Georg Muntingh Book 2014 Springer International Publishin

挡泥板

Sparse Implicitization via Interpolation by interpolation. We implement interpolation by exact or numerical linear algebra following an exact phase which computes a superset of the monomials appearing in the implicit equation. These monomials are then suitably evaluated to build a numeric matrix, ideally of corank 1, whose kernel vector c

Decline

The Intersection Problems of Parametric Curves and Surfaces by Means of Matrix-Based Implicit Represh we will call the matrix implied, establish a bridge between geometry and linear algebra, thus opening the possibility of a more robust digital processing. The contribution of this approach is discussed and illustrated on important issues of geometric modeling and Computer Aided Geometric Design (C

唠叨

冷淡周边

Plane Mixed Discriminants and Toric Jacobiansial, or of a well-constrained system of polynomial equations, which expresses the existence of a multiple root. We describe discriminants in a general context, and focus on exploiting the sparseness of polynomials via the theory of Newton polytopes and sparse (or toric) elimination. We concentrate o

Fortuitous

Topology of the Intersection of Two Parameterized Surfaces, Using Computations in 4D Spaceisotopy with a list of line segments. We certify the exactness of the topology of the curve, up to any specified precision. Our algorithm relies on injectivity criteria and efficient solvers of systems of polynomial equations, generalizing similar studies for curves in 2D and 3D.

flaunt

Rational Bézier Formulas with Quaternion and Clifford Algebra Weightsest non-trivial quaternionic case of bilinear formulas for surface patches is studied in detail. Such formulas reproduce well known biquadratic parametrizations of principal Dupin cyclide patches, and are characterized in general as special Darboux cyclide patches. We also survey the most general ca

武器

Senescent

On the Dimension of Spline Spaces on Triangulationsmial functions (or .) defined on triangular and tetrahedral partitions. Classical splines on planar rectangular grids play an important role in Computer Aided Geometric Design, and splines spaces over arbitrary subdivisions of planar domains are now considered for isogeometric analysis applications.

纵火

Polynomial Interpolation Problems in Projective Spaces and Products of Projective Lines determining the dimension of the vector space of homogeneous or multi-homogeneous polynomials vanishing together with their partial derivatives at a finite set of general points. After translating the problem into the setting of linear systems in projective spaces or products of projective lines, w

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