Sandbox

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Banking to 45 degrees

Assume a linear coordinate system.

Let <math>A</math> be the aspect ratio (the viewport's vertical length divided by the horizontal length), which we must find by iteratively approximating:

<math>\frac{\sum_{i=1}^n{\arctan \left(A \frac{\bar v_i}{\bar h_i}\right)\sqrt{\bar h_i^2+A^2\bar v_i^2}}}{\sum_{i=1}^n\sqrt{\bar h_i^2+A^2\bar v_i^2}}=45^\circ</math>;

where <math>\bar v_i=\frac{\ddot v_i}{\ddot v}</math>, with <math>\ddot v_i</math> being the vertical length of the <math>i^{th}</math> line segment and <math>\ddot v</math> being the span (absolute value of "stop-start") of the whole Y axis. Both of these later values are in world coordinates.

(<math>h</math> terms are similar, but are for the horizontal component.)