How to interpolate 3D plane by a three-dimensional facenormal and random pointclouds?

ptCloud = pointCloud(3*rand(1000,3,'single')); %create 1000 random points in a 1x1x1 box Vertex=[0,0,0]; %vertex coordinate Fn=[1,1,1] %Fn means a specified face normal Now I want to interpolate a plane which satisfies two conditions: 1.Its face-normal must be the same as Fn ; 2.The interpolated plane contains the largest number of the random pointclouds; What should I do?Thank you!