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Descrizione delle misure lineari ed angolari

Rappresentazione scalare dei tracciati condilari

Descrizione delle distanze e delle direzioni

Di seguito sono riportate le distanze calcolate tra i punti rispetto al punto di partenza (punto 1) considerato il unto di riferimento essendo la mandibola in una posizione di Massima Intercuspidazione e le relative direzioni nello spazio, utilizzando le coordinate corrette per gli assi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X} (antero-posteriore) e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y} (latero-mediale).

Calcolo della distanza tra i punti

Coordinate

Punto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1L} : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (59.0, -58.3) }
Punto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2L} : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (59.0, -92.3). }

Formula della distanza euclidea La distanza tra due punti è calcolata come: $d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}$

Calcolo dettagliato

Differenze lungo gli assi:

$x_{2}-x_{1}=59.0-59.0=0$ Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_2 - y_1 = -92.3 - (-58.3) = -92.3 + 58.3 = -34.0}

Quadrati delle differenze:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_2 - x_1)^2 = 0^2 = 0} $(y_{2}-y_{1})^{2}=(-34.0)^{2}=1156.0$ *Somma dei quadrati: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_2 - x_1)^2 + (y_2 - y_1)^2 = 0 + 1156.0 = 1156.0}

Radice quadrata:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d = \sqrt{1156.0} = 34.0 \, \text{pixel}}

Conversione in millimetri:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d = 34.0 \, \text{pixel} \times 0.1 \, \text{mm/pixel} = 3.40 \, \text{mm}}

Conclusione La distanza corretta tra il punto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1L} e il punto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2L} è: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d = 34.0 \, \text{pixel} = 3.40 \, \text{mm}}

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Punto 3L

Coordinate: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (46.3, -169.5). } Calcolo della distanza rispetto a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1L} : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d= \sqrt{(46.3 - 59.0)^2 + (-169.5 - (-58.3))^2} = \sqrt{(-12.7)^2 + (-111.2)^2} = \sqrt{161.29 + 12346.24} \approx \sqrt{12507.53} \approx 111.9 \, \text{pixel} }

Distanza in millimetri: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 111.9 \, \text{pixel} \times 0.1 \, \text{mm/pixel} = 11.19 \, \text{mm} }

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Punto 4L

Coordinate: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (44.1, -207.7)} Calcolo della distanza rispetto a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1L} : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d = \sqrt{(44.1 - 59.0)^2 + (-207.7 - (-58.3))^2} = \sqrt{(-14.9)^2 + (-149.4)^2} = \sqrt{222.01 + 22320.36} \approx \sqrt{22542.37} \approx 150.1 \, \text{pixel} }

Distanza in millimetri: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 150.1 \, \text{pixel} \times 0.1 \, \text{mm/pixel} = 15.01 \, \text{mm} }

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Punto 5L

Coordinate: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (38.4, -136.2)} Calcolo della distanza rispetto a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1L} : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d= \sqrt{(38.4 - 59.0)^2 + (-136.2 - (-58.3))^2} = \sqrt{(-20.6)^2 + (-77.9)^2} = \sqrt{424.36 + 6062.41} \approx \sqrt{6486.77} \approx 80.5 \, \text{pixel} }

Distanza in millimetri: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 80.5 \, \text{pixel} \times 0.1 \, \text{mm/pixel} = 8.05 \, \text{mm} }

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Punto 6L

Coordinate: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (36.4, -48.2)} Calcolo della distanza rispetto a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1L} : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d = \sqrt{(36.4 - 59.0)^2 + (-48.2 - (-58.3))^2} = \sqrt{(-22.6)^2 + (10.1)^2} = \sqrt{510.76 + 102.01} \approx \sqrt{612.77} \approx 24.75 \, \text{pixel} }

Distanza in millimetri: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 24.75 \, \text{pixel} \times 0.1 \, \text{mm/pixel} = 2.48 \, \text{mm} }

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Punto 7L

Coordinate: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (44.0, -34.9) } Calcolo della distanza rispetto a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1L} : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d = \sqrt{(44.0 - 59.0)^2 + (-34.9 - (-58.3))^2} = \sqrt{(-15.0)^2 + (23.4)^2} = \sqrt{225.0 + 547.56} \approx \sqrt{772.56} \approx 27.79 \, \text{pixel} }

Distanza in millimetri: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 27.79 \, \text{pixel} \times 0.1 \, \text{mm/pixel} = 2.78 \, \text{mm} }

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Punto 8L

Coordinate: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (52.9, -48.0)} Calcolo della distanza rispetto a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1L} : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d= \sqrt{(52.9 - 59.0)^2 + (-48.0 - (-58.3))^2} = \sqrt{(-6.1)^2 + (10.3)^2} = \sqrt{37.21 + 106.09} \approx \sqrt{143.3} \approx 11.97 \, \text{pixel} }

Distanza in millimetri: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 11.97 \, \text{pixel} \times 0.1 \, \text{mm/pixel} = 1.20 \, \text{mm} }

e così via per le altre zone di misurazione. L'obiettivo dell'analisi è determinare l'angolo tra due movimenti all'interno di un sistema articolare, in particolare nell'area di studio della cinematica masticatoria. La comprensione di questi angoli ci consente di: Valutare la dinamica mandibolare: Calcolare gli angoli tra i segmenti mandibolari può fornire informazioni essenziali su come la mandibola si sposta durante il movimento, aiutando a descrivere i pattern del movimento articolare. Modellare la biomeccanica del sistema masticatorio: Gli angoli tra i punti permettono di costruire modelli accurati che simulano il comportamento meccanico del sistema mandibolare, utilizzabili in applicazioni cliniche per diagnosi e trattamenti. Confrontare con angoli standard: Gli angoli misurati possono essere confrontati con valori normali o patologici per identificare eventuali alterazioni nei movimenti mandibolari che potrebbero indicare disturbi dell'articolazione temporomandibolare (ATM). Questo calcolo è fondamentale per fornire una descrizione matematica precisa della cinetica mandibolare e per migliorare la modellazione biomeccanica di strutture orofacciali, cruciali per la diagnosi e l'intervento clinico.

A questo punto non ci resta altro da fare che rappresentare e simulare la posizione spaziale dei punti dinamici marcati dalla figura, quantificandone lo spostamento lineare ed angolare.