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Fig. 2 | Progress in Orthodontics

Fig. 2

From: The inflection point: a torque reference for lingual bracket positioning on the palatal surface curvature of the maxillary central incisor

Fig. 2

a Image shows crown’s long axis (L) and its perpendicular at 2 mm (red line), point P1 (intersection of red line with PSC) and the visually estimated location of inflection point. b Tracing of the first and second cubic poly-Bezier curves. c First cubic poly-Bezier extends from its initial anchor point P1 to its terminal anchor point P4, which in this case is located 2.1 mm cervical to the estimated visual position of inflection point. P2 and P3 are respectively the second and third control points of the first cubic poly-Bezier. Tracing of second cubic poly-Bezier extends from its initial anchor point P4 to its terminal anchor point P7 which was placed cervical and labial to palatal CEJ. The second control point (P5) of the second cubic poly-Bezier was positioned so both lengths and slopes of P3P4 and P4P5 are equal. P6 is the third control point of second cubic poly-Bezier. d Origin (P1) and x–y axes of the poly-Bezier curves. e Tangents to PSC are calculated at intersections of 0.5-mm increment lines with first and second cubic poly-Bezier curves. f Two examples of the tangents to PSC and their respective torque angles at [P1 + 3.5] and [P1 + 7]. The torque angle value is negative on [P1 + 3.5] and positive at [P1 + 7]

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