A veces, es necesario, sobre todo cuando se programa tener la solución analítica del burbu-centro
It is sometimes necessary, especially when programming have the analytical solution of Bubble-center(véase: http://carreteras-laser-escaner.blogspot.com/2015/07/bubble-center-triangles-burbu-centro-en.html)
It is sometimes necessary, especially when programming have the analytical solution of Bubble-center(véase: http://carreteras-laser-escaner.blogspot.com/2015/07/bubble-center-triangles-burbu-centro-en.html)
El primer paso es tener la curva que contiene los centros a las circunferencias tangentes a otras dos dadas. Cuando resolvamos esta parte nos pondremos a resolver el caso de tres.
The first step is to have the curve containing the centers of the circles tangent to two other given. When we solve this part we will solve the case of three.
The first step is to have the curve containing the centers of the circles tangent to two other given. When we solve this part we will solve the case of three.
Dadas dos circunferencias tangentes:
With two tangent circles:
With two tangent circles:
En este caso, el centro está en los puntos (-3,0) y (5,0) respectivamente.
Para nuestro caso caso general están en los puntos (-a,0) y (b,0).
Un punto que tenga una circunferencia tangente a estas tendrá que cumplir que la distancia al punto de tangencia sea siempre la misma:
In this case, the center is in (-3,0) and (5,0) respectively.
For our case general case are in (-a, 0) and (b, 0).
A point that has a tangent to these will have to meet the distance to the tangent point is always the same:
In this case, the center is in (-3,0) and (5,0) respectively.
For our case general case are in (-a, 0) and (b, 0).
A point that has a tangent to these will have to meet the distance to the tangent point is always the same:
Las condiciones que tiene que cumplir la circunferencia azul de radio "r" son:
The conditions that it must fulfill blue circumference radius "r" are:
The conditions that it must fulfill blue circumference radius "r" are:
distancia (-a,0) al centro circunferencia azul = radio (a) + radio azul (r)
distancia ( b,0) al centro circunferencia azul = radio (b) + radio azul (r)
distance (-a, 0) at the center blue circle radius = (a) + blue radius (r)
distance (b, 0) at the center blue circle radius = (b) + blue radius (r)
distance (b, 0) at the center blue circle radius = (b) + blue radius (r)
((x+a)²+y²)½=r+a NOTA: Obsérvese el signo "+"
((x-b)²+y²)½=r+b
La función solución será:
The solution will be:
The solution will be:
y² = x² ((a+b)²/(a-b)²-1) +x·2b·((a+b)/(a-b)+1)
Es, por tanto, una hipérbola:
It is therefore a hyperbola:
Como toda hipérbola, tiene dos ramas. La segunda rama corresponde a la otra familia de circunferencias tangentes.
Like all hyperbola has two branches. The second branch corresponds to another family of tangent circles.
Like all hyperbola has two branches. The second branch corresponds to another family of tangent circles.
Otra forma de escribir esta ecuación es:
En próximas entregas veremos más propiedades interesantes de esta hipérbolas.
In future deliveries we will see more interesting properties of these hyperbolas.
y² = x²· 4 ab/(a-b)² + x · 4ab·(a-b)
ó
(x-(a-b)/2)²/[(a-b)²/ab] + y²/4=1
ó
y²=x²(e²-1)+x·2b·(e+1)
siendo / with: e²=(a+b)²/(a-b) (eccentricity)
Distancia focal: 2(a+b)²/ab
Distancia vértices: |a-b|/2
In future deliveries we will see more interesting properties of these hyperbolas.
No hay comentarios:
Publicar un comentario