I want to display the complete website within the WebGL in Unity. I have tried Awesomium plugin but it doesn't work in WebGL. Please tell me is there any way to display the webpage.
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There is currently no plugin that renders a website and supports WebGL.
I conclude two things from this. A, you have to do it yourself, get ready to research website rendering, suitable libraries for Mono maybe and probably a lot more.
And B, it won't be easy or even possible to do it (with acceptable performance). Rendering webpages is a feature many people want but plugins doing that mostly only support one platform (only windows or only android, etc.).