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How do materials and shaders work in graphics programming?

I stumbled upon a few videos about shaders and materials from The Cherno and my understanding is that materials are this sort of input that a shader takes to calculate an output instead of hard coding values into the shader so basically shaders become more flexible since you can control what their output is with a material.

I’m not sure if this is 100% accurate, but it makes sense so if this is true would you have multiple types of materials for different shaders? For example, shadows I believe require at least a shadow and depth shader so would I have a shadow material? Same for skinning/skeleton animations or are materials only for controlling how an object reacts to light?

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