R. J. Gardner, Geometric tomography, Encyclopedia of Mathematics and its Applications, vol. 58, Cambridge University Press, Cambridge, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....function f K . In Section 3 we give a simple formula for the curvature function via the projections of K (cf. R] p. 125) All arguments can be generalized to higher dimensions. Let r be a natural number. A real valued function on an open subset U of is said to be of class C (cf. [Ga3], p. 22) if it is r times di#erentiable, that is all partial derivatives of order r exist and are continuous. We denote this class by C (U ) A function f(#) on # is said to be in C ) if its homogeneous extension f( x, y, z) z (R 0 ) We say that a convex body K ....

....r times di#erentiable, that is all partial derivatives of order r exist and are continuous. We denote this class by C (U ) A function f(#) on # is said to be in C ) if its homogeneous extension f( x, y, z) z (R 0 ) We say that a convex body K is of class C (cf. [Ga3], p. 23) if #K is of class C as a submanifold of R . If k 2, we say that K is of class (cf. Ga3] p. 25) if K is of class C and the Gauss curvature of K at each point is positive. Without loss of generality we may assume that e 3 is the axis of revolution. Our main result is the ....

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R. J. Gardner, Geometric tomography. Encyclopedia of Mathematics and its Applications, 58. Cambridge University Press, Cambridge, (1995).

.... 22, 23, 24, 25, 30] When density functions are replaced by geometric objects (for example we have a convex polytope instead of a body with non constant internal density) then geometric information shape, measure, is the detected data, and we arrive to the area of Geometric Tomography [14, 15], a topic recently emerged as a well defined domain of research, which is described by Gardner in [15] as the area of mathematics dealing with the retrieval of information about a geometric object from data about its sections, or projections or both . As an example of how geometry changes the ....

.... polytope instead of a body with non constant internal density) then geometric information shape, measure, is the detected data, and we arrive to the area of Geometric Tomography [14, 15] a topic recently emerged as a well defined domain of research, which is described by Gardner in [15] as the area of mathematics dealing with the retrieval of information about a geometric object from data about its sections, or projections or both . As an example of how geometry changes the situation, let us recall the fact that a planar density distribution is determined by its X rays taken in ....

R. J. Gardner, Geometric Tomography, Encyclopedia of Mathematics and its Applications, vol. 58, Cambridge University Press, New York, 1995.

.... by geometric objects (for example we have a convex polytope instead of a body with non constant internal density) then geometric information shape, measure, is the detected data, and we arrive to the area of Geometric Tomography, a topic that has recently emerged as a well defined domain[2] of research. Computational Geometric Tomography is a natural name for an area grouping results in which the emphasis is on the algorithmic aspect of the problems above. It is illuminating to first distinguish between direct and inverse problems. In direct problems the input is a geometric ....

R. J. Gardner, Geometric Tomography, Encyclopedia of Mathematics and its Applications, vol. 58, Cambridge University Press, New York, 1995.

.... 21, 22, 23, 24, 29] When density functions are replaced by geometric objects (for example we have a convex polytope instead of a body with non constant internal density) then geometric information shape, measure, is the detected data, and we arrive to the area of Geometric Tomography [14, 15], a topic recently emerged as a well defined domain of research, which is described by Gardner in [15] as the area of mathematics dealing with the retrieval of information about a geometric object from data about its sections, or projections or both . As an example of how geometry changes the ....

.... polytope instead of a body with non constant internal density) then geometric information shape, measure, is the detected data, and we arrive to the area of Geometric Tomography [14, 15] a topic recently emerged as a well defined domain of research, which is described by Gardner in [15] as the area of mathematics dealing with the retrieval of information about a geometric object from data about its sections, or projections or both . As an example of how geometry changes the situation, let us recall the fact that a planar density distribution is determined by its X rays taken in ....

R. J. Gardner, Geometric Tomography, Encyclopedia of Mathematics and its Applications, vol. 58, Cambridge University Press, New York, 1995.

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R. J. Gardner, Geometric tomography, Encyclopedia of Mathematics and its Applications, vol. 58, Cambridge University Press, Cambridge, 1995.

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