How to find 3D point on the 3D line with given distance and from given 3D point

Thread starter gbalajimecse
Start date Oct 14, 2009
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3d Line Point

In summary, To find the 3D point on a 3D line with a given distance and a 3D point, you can use the formula x = x1 + t(x2-x1), y = y1 + t(y2-y1), z = z1 + t(z2-z1), where (x1, y1, z1) and (x2, y2, z2) are two points on the line, and t is a scalar value representing the distance along the line from point (x1, y1, z1). You can also use the distance along the line to find multiple 3D points by varying the value of t in the formula. If the given distance is negative

Oct 14, 2009

gbalajimecse

Hi

how to find 3D point(lie on line) on the 3D line with given distance and from given 3D point(this is also lie in line) where the given line equation

Please explain the derivation

Last edited: Oct 14, 2009

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Oct 14, 2009

zhentil

I would parametrize the line and write down the distance equation as a function of t.

1. How do I find the 3D point on a 3D line given a distance and a 3D point?

To find the 3D point on a 3D line with a given distance and a 3D point, you can use the following formula:
x = x1 + t(x2-x1)
y = y1 + t(y2-y1)
z = z1 + t(z2-z1)
where (x1, y1, z1) and (x2, y2, z2) are two points on the line, and t is a scalar value representing the distance along the line from point (x1, y1, z1).

2. Can I use the distance along the line to find multiple 3D points?

Yes, you can use the distance along the line to find multiple 3D points. By varying the value of t in the formula mentioned in the previous answer, you can find multiple points that are a specific distance away from the given point on the 3D line.

3. What happens if the given distance is negative?

If the given distance is negative, it means that the 3D point you are trying to find is in the opposite direction of the line from the given point. In this case, you can use the formula mentioned in the first answer but with a negative value for t.

4. Is it possible to find the 3D point on a 3D line if the given distance is greater than the length of the line?

No, it is not possible to find the 3D point on a 3D line if the given distance is greater than the length of the line. This is because the point you are trying to find would lie beyond the end points of the line and therefore cannot be reached by a distance along the line.

5. Can I find the 3D point on a 3D line without knowing the coordinates of the line's end points?

No, you cannot find the 3D point on a 3D line without knowing the coordinates of the line's end points. The formula mentioned in the first answer requires the coordinates of two points on the line to calculate the coordinates of the desired point. Without this information, it is not possible to find the point on the line.