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Visible-to-camera points of a 3d model

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Hello guys, I have a 3d object in terms of points and triangles and a camera. I want to get the points that are visible to the camera. I had an idea which is: I take every point of the model one by one and, together with the position of the camera, construct a line. Then I check this line with every triangle of the model. If there is intersection with at least one triangle, then the point is not visible to the camera, else it lies on the visible-to-camera surface of the model. I think that it is right, does anybody has any objection? Is there any other better way? I think that the above solution will be slow. I am sure that this problem is already solved in game programming so there may be optimized solutions. I heard something about z-buffering or ray-tracing but I don't know what they are exactly about. Thank you for any suggestions

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