eulerAPE: Drawing Area-Proportional 3-Venn Diagrams Using Ellipses
At every iteration of the optimization algorithm, the (A) centre, (B) semi-axes and (C) angle of rotation of every ellipse are respectively modified by parameters pγ, pαβ and pθ in search for other solutions. (A) The grey points indicate the new centres that are obtained when one or both coordinates of the centre of an ellipse (solid black) are increasing or decreasing by pγ. (B) A label +pαβ means that that semi-axis was increased by the pαβ percentage, while -pαβ means that that semi-axis was decreased by the pαβ percentage. The dashed ellipses indicate how an ellipse (solid black) is changed when: (top, left) only the semi-major axis is increased or decreased by pαβ; (top, right) only the semi-minor is increased or decreased by pαβ; (bottom, left) the semi-axes are both increased or both decreased by pαβ; (bottom, right) one of the semi-axes is increased and the other is decreased by pαβ. (C) The dashed ellipses indicate how an ellipse (solid black) is changed when its angle of rotation is increased or decreased by pθ.