Results 11 to 20 of about 387,925 (133)
A Generalization of the Klamkin Inequality [PDF]
, 2009 A generalization of a geometric inequality of Klamkin is established by considering the triples of barycentric coordinates of the points from a set which is included in the plane of the fundamental triangle.
Comănescu, Dan, Dragomir, Sever S
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On Transfinite Barycentric Coordinates
, 2006 A general construction of transfinite barycentric coordinates is obtained as a simple and natural generalization of Floater's mean value coordinates [Flo03, JSW05b].
Alexander Belyaev, Belyaev, A.
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The Gergonne point generalized through convex coordinates
International Journal of Mathematics and Mathematical Sciences, 1999 The Gergonne point of a triangle is the point at which the three cevians to the points of tangency between the incircle and the sides of the triangle are concurrent.
J. N. Boyd, P. N. Raychowdhury
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From affine to barycentric coordinates in polytopes [PDF]
, 2023 Each point of a simplex is expressed as a unique convex combination of the vertices. The coefficients in the combination are the barycentric coordinates of the point.
Smith, Jonathan D. H. +2 more
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Spherical Barycentric Coordinates
, 2006 We develop spherical barycentric coordinates. Analogous to classical, planar barycentric coordinates that describe the positions of points in a plane with respect to the vertices of a given planar polygon, spherical barycentric coordinates describe the ...
Seidel, Hans-Peter +2 more
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A convex-valued selection theorem with a non-separable Banach space
Advances in Nonlinear Analysis, 2018 In the spirit of Michael’s selection theorem [6, Theorem 3.1”’], we consider a nonempty convex-valued lower semicontinuous correspondence φ:X→2Y{\varphi:X\to 2^{Y}}.
Gourdel Pascal, Mâagli Nadia
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Second-order finite element discretization of Stokes equations on convex polygonal meshes
Results in Applied MathematicsIn this paper, we construct two finite element discretizations on convex polygonal meshes for the Stokes equations, using the generalized barycentric coordinates (GBCs).
Yanyan Song, Yanqiu Wang, Qiao Xin
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UBVH: Unified Bounding Volume and Scene Geometry Representation for Ray Tracing
Computer Graphics Forum, EarlyView.Abstract Bounding volume hierarchies (BVHs) are currently the most common data structure used to accelerate ray tracing. The existing BVH methods distinguish between the bounding volume representation associated with the interior BVH nodes and the scene geometry representation associated with leaf nodes.
M. Káčerik, J. Bittner
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Real‐Time Conformal Maps and Parameterizations
Computer Graphics Forum, EarlyView.Abstract We present a simple algorithm to conformally map between two simple and bounded planar domains based on the concept of harmonic measure, which is a conformal invariant. With suitable preprocessing, the algorithm is fast enough to compute all possible conformal maps (having three real degrees of freedom) between the two domains in real time in
Q. Chang, C. Gotsman, K. Hormann
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Basis Networks: Learning basis functions for free‐form triangulations
Computer Graphics Forum, EarlyView.Abstract We present a framework for learning compactly supported basis functions that define tangent continuous surfaces based on coarse irregular triangle meshes. The basis functions are represented as MLPs. Smoothness of the basis functions is achieved by using the values of Loop basis functions as the parameterization of the surface.
T. Djuren, M. Alexa
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