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I'm new to graphics and want to implement algorithms like dda,scan-line, clipping,etc. I'm confused which library to use. OpenGl, graphics in turbo c,or any other. Please suggest.

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If you're completely new to graphics programming I would start with Processing. It's based on Java and JOGL but comes with a whole bunch of drawing commands built in, and its own basic IDE. It's very good for prototyping algorithms and getting quick visual feedback without having to write a ton of boilerplate code, and it insulates you from the underlying API (OpenGL in this case). Presumably you're not going for high performance, since the algorithms you mention are efficiently implemented in hardware, and you just want to familiarize yourself with how they work? If so it's a great place to start.

Once you've got the hang of Processing you can move over to OpenFrameworks, which is very similar but in C++, with the option to 'drill down' and call the underlying OpenGL commands directly. From there, the sky's the limit. :-)

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