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Questions concerning terrain heightmaps

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I'm curious as to how one calculates position coordinates for the terrain; specifically the height coordinates. My understanding of Terrain generation with height maps is iterating through the heightmap and retrieving pixel data. The pixel data, depending on its greyscale color (white or black), will determine its height. However, I'm unsure of the practical implementation of this, specifically the equation used to convert pixel data to new height coordinates. In addition to the Y coordinates, how do I determine the values in the X and Z plane. Do I just pick a range of values (ex. [-30, 30]) in X and Z? Lastly, I'm sure indices will have to be used in order to make an efficient program. My prior experience with Index is manually entering values for simple geometric shapes (Cubes and triangles). This seems more involved than before. I was wondering if there exists an algorithm that handles indices when dealing with terrain.

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