Shadow mapping with arbitrary number of meshes and lights

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I am developing a 3D engine with WebGL and I am trying to implement shadows. My logic is as follow:

The first time that scene is rendered I loop over all meshes and create and compile the shader program (vertex and fragment shader). I only have one shader program per mesh, so, when the shader is created I need to know the lights that has the scene, the mesh's material and other considerations.

Once the shader is created I attached it to the mesh object and render the object. In the next iteration the shader is not created (because it was created previously).

I heard about shadow mapping. In order to implement it I need to render to texture and compute the distance between the light and the current fragment and this for each light source. So if I have 2 lights I need to do this process twice and then pass those textures to the shader that render the scene.

The problem is that I can create 100 ligths if I want and I would need to render 100 textures and pass it to the shader that render the scene, but OpenGL and WebGL has a limited unit textures, so I couldn't bind all textures to render the complete scene.

How can I implement shadow mapping with an arbitrary number of lights?

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