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What mathematical formula does Blender use to calculate Bezier paths?

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2 Answers 2

For each segment of the path between two control points, it approximates a cubic Bezier curve:

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where P_0 and P_3 are the control points and P_1 and P_2 are the handles.

enter image description here

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Even though this isn't a question about Blender's code exactly, linking to blenders code for calculating cubic bezier curves may help understanding.

3D curves use an optimized subdivision method: BKE_curve_forward_diff_bezier

2D masks can also use a different (more straightforward but slower) method where you can get any point on along the spline: BKE_mask_point_segment_co

To see how this method works, see wikipedia's descritoion of Higer order curves

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I read that bezier curves commonly are interpolated with Casteljau's algorithm. –  pink vertex Feb 2 '14 at 10:38

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