# OpenGL glPolygonOffset

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Does anyone know where I can find more information behind the math in OpenGL's glPolygonOffset routine? I have a 3D engine I use for mobile devices and I want to reproduce this function in my own code. Thanks. Here's the info about glPolygonOffset: http://www.opengl.org/resources/faq/technical/polygonoffset.htm#0020
Quote:
 Polygon offset allows the application to specify a depth offset with two parameters, factor and units. factor scales the maximum Z slope, with respect to X or Y of the polygon, and units scales the minimum resolvable depth buffer value. The results are summed to produce the depth offset. This offset is applied in screen space, typically with positive Z pointing into the screen.

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The math behind glPolygonOffset is in the OpenGL spec in section 3.5.5 Depth Offset, starting on page 112 (page 126 of the pdf).

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Thanks! That's exactly what I was looking for.

I'm having some trouble with the equation (3.9). Do you know what the w subscript refers to when it talks about a point on the triangle (x,y,z) in the equation? It sounds like from the document that it's just a value from an arbitrary point, but the partial derivative of a number is always 0, so I'm not sure how to evaluate the equation.

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The w subscript just means that the x, y, and z coordinates are the window-space coordinates of a point inside the triangle. That is, they're the coordinates you get after the viewport transformation is applied to normalized device coordinates.

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Thanks Eric. That helped a lot. How do you find the point inside the triangle? Also, does the del symbol in the equation (3.9) mean partial derivative or does it mean something else?

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Yes, those are partial derivatives. Since the triangle is planar, these derivatives are the same everywhere in the triangle, so you could just use ratios of differences between values at different vertices of the triangle for the derivatives.

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