This paper presents a method for generating a region with a lot of randomly distributed ellipsoids. Using the parametric expression of an ellipsoid, the criterion for determining if a spatial point is in the interior or exterior of the ellipsoid is established. Then the computation of the distance between a point and the ellipsoid is converted into finding the solution to an optimization problem, which can be efficiently approximated by the searching method. Based on these facts, the proposed method is able to make the distance between generated ellipsoids very small and then successfully improve the content of ellipsoids grains in the region. Numerical results show that the proposed method can generate simulation of specimens in which the content of ellipsoids is higher than 55% according to four-graded aggregates, 50% according to three-graded aggregates, and 45% according to two-graded aggregates, respectively, in relatively short time.

For getting the parametric equation of random polygon, by the basic extension factor to stretch the round, there generates polygon of meeting the required conditions. Such algorithm overcomes the disadvantage in the generation of polygon from round under control of a single parameter and the complication of mathematical background. Firstly, a detailed introduction is given to the basic extension factor and the selection of relevant coefficient, and then the errors of such algorithm are analyzed. And the experimental result shows that the mathematical background of such method is relatively easy, the parameters are easy to control and constitute, and the generation of arbitrary polygon is available with high precision. Such the parametric equation of random polygon and method can be used in relevant fields such as geometric modeling, CAD/CAM, and computer graphics.