2d array to calculate height for player in heightmap?

I'm trying to work out how to do so my player position takes into the account of the floor so if I generate a floor that is hilly when I walk I won't walk through the heel. The problem is that I'm not sure how to do it.

I can do basic collision detection for walls. However, this isn't collision detection. I need the add the height of the terrain to the player.

So as you see the terrain is really a grid with 4 points making a face. So I can get the 4 points and work out. I can probably work this out on myself, but I was wondering if I should store say the heigh at (x,z) in a 2d array or do I just work out the height again everytime I move?

It just I use simplexnoise and I worry that this will be expensive to do every turn.

 import java.util.ArrayList;

    public class VoxelLevel 
    {
    Mesh mesh;
    Material material;
    Transform transform;
    Shader shader;

    VoxelLevel(String textureName)
    {
        material = new Material(new Texture(textureName));
        transform = new Transform();

        shader = BasicShader.getInstance();

        generateLevel();

    }

    private void generateLevel() 
    {
        ArrayList<Vertex> vertices = new ArrayList<Vertex>();
        ArrayList<Integer> indices = new ArrayList<Integer>();

        int sizeX = 10;
        int sizeZ = 10;
        int freq = 25;

        for(int x=-300; x<300; x+= sizeX)
        {
            for(int z=-300; z<300; z+=sizeZ)
            {
                indices.add(vertices.size()+0);
                indices.add(vertices.size()+3);
                indices.add(vertices.size()+2);
                indices.add(vertices.size()+0);
                indices.add(vertices.size()+1);
                indices.add(vertices.size()+3);


                vertices.add(new Vertex(new Vector3f(x,50+25*(float)(SimplexNoise.noise(x/freq, z/freq) + 0.25 * SimplexNoise.noise(2*x/freq, 2*z/freq)),z), new Vector2f(0.75f,0.75f)));
                vertices.add(new Vertex(new Vector3f(x+sizeX,50+25*(float)(SimplexNoise.noise((x+sizeX)/freq, z/freq) + 0.25 * SimplexNoise.noise(2*(x+sizeX)/freq, 2*z/freq)),z), new Vector2f(0.75f,1.0f)));
                vertices.add(new Vertex(new Vector3f(x,50+25*(float)(SimplexNoise.noise(x/freq, (z+sizeZ)/freq)+ 0.25 * SimplexNoise.noise(2*x/freq, 2*(z+sizeZ)/freq)), z+sizeZ), new Vector2f(1.0f,0.75f)));
                vertices.add(new Vertex(new Vector3f(x+sizeX,50+25*(float)(SimplexNoise.noise((x+sizeX)/freq, (z+sizeZ)/freq)+ 0.25 * SimplexNoise.noise(2*(x+sizeX)/freq, 2*(z+sizeZ)/freq)),z+sizeZ), new Vector2f(1.0f,1.0f)));
            }
        }

        Vertex[] vertArray = new Vertex[vertices.size()];
        Integer[] intArray = new Integer[indices.size()];

        vertices.toArray(vertArray);
        indices.toArray(intArray);

        mesh = new Mesh(vertArray, Util.toIntArray(intArray));
    }

    public void input()
    {

    }

    public void update()
    {
        //SimplexNoise.noise(0.25, 0.25);
        //SimplexNoise.noise(0.35, 0.65);
        //SimplexNoise.noise(0.254, 0.225);
        //SimplexNoise.noise(0.254, 0.215);
    }

    public void render()
    {
        shader.bind();
        shader.updateUniforms(transform.getTransformation(), transform.getProjectedTransformation(), material);
        mesh.draw();
    }

}