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--- en:crowncoordinatesystem [2022/04/01 07:28] – onyxadmin
+++ en:crowncoordinatesystem [2024/04/01 09:23] (current) – [Preface] onyxadmin
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 ====== Crown Coordinate System ======
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-To numerically describe tooth movements in all OnyxCeph³™ modules in an uniform manner, a crown specific coordinate system is used. The definition for points, axes and movements is based on the terms traditionally used for this purpose in dentistry. Note that for anatomical reasons, the crown coordinate system is a non-Carthesian coordinate system.
+===== Preface=====
+The verbal description of tooth movements has always been based on the anatomical conditions of tooth anchoring in the jaw. Different reference systems are used for individual movement components. For example, rotations are understood as rotations around the root axis, while inclination and angulation refer to the alignment of the clinical crown axis (FACC) in relation to the occlusal plane of the jaw. The situation is similar for the displacement components: here, occlusal movements are interpreted along the root axis while transversal movement components are understood in the mesial-distal direction or perpendicular to it.\\
+The digital planning of tooth movements requires to formulate the anatomically non-orthogonal tooth coordinate system in a mathematically consistent manner in order to be able to clearly describe tooth positions and their changes numerically. \\
+The mathematically consistent modeling of tooth movements used in all OnyxCeph³(tm) modules is described below.\\
+\\
+===== Crown coordinates=====
+The definitions for points, axes and movements are based on the terms traditionally used for this purpose in dentistry. For anatomical reasons, this is a non-Cartesian (oblique-angled) coordinate system.\\
 {{:crowncoordinates_en.png?600&direct|Crown Coordinate System}}\\
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 //Note:// The measurement of angulation is always performed with reference to an arch plane that is aligned with the midpoint and endpoints of the arch curve and whose position and alignment can be adjusted by the user to the skeletal conditions in the jaw.\\
+===== Tooth Displacements =====
+  * Displacements along root axis are measured positive in apical direction
+  * Displacements along m/d axis are measured positive in mesial direction
+  * Displacements along vestibular axis are measured positive in vestibular direction
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