Adaptive forward differencing for rendering curves and surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
A geometric characterization of parametric cubic curves
ACM Transactions on Graphics (TOG)
Computer graphics (2nd ed. in C): principles and practice
Computer graphics (2nd ed. in C): principles and practice
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
High-quality curve rendering using line sampled visibility
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
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We present two related algorithms for flattening (generating polyline approximations for) curves associated with planar cubic Bezier segments. One flattens the path curve, and the other flattens the left and right offset curves. The algorithm for flattening path curves yields an average of 67% of the vertices generated by recursive subdivision, while maintaining flatness to within 4% of the specified value, and runs 37% faster. The algorithm for flattening offset curves generates 70% of the vertices as the methods based on recursive subdivision, such that 94% of all subsegments fall within 20% of the flatness criterion. This latter code runs as fast as recursive subdivision.