Xyz coordinate from distance

2018-06-30 10:33:41

如果我在xyz平面上有3个点，我知道他们和他们两个的坐标之间的距离什么是可以让我找到最后点的坐标的方程？

You have two fixed points A and B with distance l between them.

You have a third point C with only known distances to A and B as a and b respectively.

You find the angle γ=angle(ACB) using the cosine rule

γ = ACOS( (a^2+b^2-l^2)/(2*a*b) )

Now you find the distance h of point C to the line AB

h = a*b*SIN(γ)/l

Lastly you find the other two angles of the triangle. The angle α has vertex A and angle β has vertex B.

α = ASIN(h/a)
β = ASIN(h/b)

You can find the coordinates of C using the distance & angle formulas you have in polar coordinates.

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