Geometric interpretation of an Edwards curve
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Addition on an elliptic curve in Weierstrass form (over the rationals) is typically depicted with the following figure: (Image CC SA 3.0 https://en.wikipedia.org/wiki/File:ECClines.svg) To add two points, one draws the line that connects these points. The third intersection point is mirrored to get the result of the addition. A curve in Edwards form might look like this: (Image CC SA 3.0 https://commons.wikimedia.org/wiki/File:Edward-curves.svg) However, the classical geometric interpretation for addition on Weierstrass curves does not seem to work on these Edwards curves. Take for example the point $(0,-1)$ . When doubled, this becomes $(0,1)$ , the neutral point, according to the addition law $$(x_1, y_1) + (x_2, y_2) = left(frac{x_1y_2 + x_2y_1}{1-dx_1x_2y_1y_2}, frac{y_1y_2 + x_1x_2}{1-dx_1x_2y_1y