1、 首先，我们来绘制一个二焦点曲面——椭球面：Manipulate[ContourPlot3D[ Norm[{x, y, z} - {1, 0, 0}] + Norm[{x, y, z} - {-1, 0, 0}] == a, {x, -a, a}, {y, -a, a｝， {z, -a, a}, Boxed -> False, Axes -> False], {a, 2, 3}]
2、 再来绘制一个三焦点曲面。 先定义几个点：{P, Q, R巳呀屋饔, S, T} = {{0, 1, 0}, {1, 0, 0}, {0, 0, 1}, {1, 1, 0}, {0, 0荑樊综鲶, 0}};X = {x, y, z}; 再作图，以P、Q、R为焦点：b = 2;Manipulate[ContourPlot3D[ Total[Norm /@ {X - P， X - Q, X - R}] == a, {x, -b, b}, {y, -b, b}, {z, -b, b}, Boxed -> False, Axes -> False], {a, 2.5, 5}]
3、 特别的，要关注一下a在2.79附近的图形：b = 1;ContourPlot3D[Total[Norm /@ {X - P, X - Q, X - R}] == 2.79, {x, -b, b}, {y, -b, b}, {z, -b, b}， Boxed -> False, Axes -> False]
4、 仍旧是三焦点曲面：ContourPlot3D[Sqrt[(x - 1)^2 + (y - 1)^2 + z^2] + Sqrt[x^2 + y^2 + z^2] + Sqrt[x^2 + (y - 1)^2 + z^2] == 2, {x, 0, 0.6}, {y, 0.4, 1｝, {z, -0.3, 0.3}] 你能看出三个焦点的坐标吗？
5、 尝试着把三个焦点转化为Locator，结果是失败的！ 如下，二维空间里的三焦点曲线代码可以运行：Manipul锾攒揉敫ate[xy = {x, y};Show[ContourPlot[ Norm[xy - a] + Norm[xy - b] + Norm[xy - c] == p, {x, -3， 3}, {y, -3, 3}], Graphics[Line[{a, b, c, a}], PlotRange -> 3]], {{a, {0, 0}}, Locator, Appearance -> "A"}, {{b, {0, 1}}, Locator, Appearance -> "B"}, {{c, {1, 1}}, Locator, Appearance -> "C"},Dynamic[a], Dynamic[b], Dynamic[c], {p, 2, 10}] 然而照搬到三维空间里，就不适用了！
6、 这里是三维空间情形的代码：Manipulate[xyz = 辘腋粪梯{x, y, z};Show[ContourPlot3D[ Norm[xyz - a] + Norm[xyz - b] + Norm[xyz - c] == p, {x, -3, 3}, {y, -3, 3}, {z, -3, 3}]],{{a, {0, 0, 1}}, Locator, Appearance -> "A"},{{b, {0, 1, 0}}, Locator, Appearance -> "B"},{{c, {1, 0, 0}}, Locator, Appearance -> "C"},Dynamic[a], Dynamic[b], Dynamic[c], {p, 2, 10}] 此时，如果只拖动滑块p，看不出异常！ 但是，如果拖动三个定位器的位置，运行结果就崩溃了！
