Point and Circle intersection in 3 D

In summary, the conversation discusses the confusion of finding the intersection point between a line and a circle in 3D space. The speaker knows how to find it in 2D, but is unsure of how to approach it in 3D. They mention having a point and a circle, but it is unclear what role the point plays in the problem. It is noted that the line and circle may not necessarily intersect in 3D or 2D space.
  • #1
Adee
1
0
Hi
I need some support regarding a problem.
I know the poistion of a point in 3D let say (sp,yp,zp) and I know the circle with Center (xc,yc,zc) having radius rc. My question is how to find the intersection point of the circle and a line in 3D.
I know that we can find the POI in 2 D by solving equation of line and circle but in 3 D its confusing for me ?


Regards
Adee
 
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  • #2
Adee said:
Hi
I need some support regarding a problem.
I know the poistion of a point in 3D let say (sp,yp,zp) and I know the circle with Center (xc,yc,zc) having radius rc. My question is how to find the intersection point of the circle and a line in 3D.
I know that we can find the POI in 2 D by solving equation of line and circle but in 3 D its confusing for me ?


Regards
Adee
Your question is very confusing. You say that you are given a point and a circle. What line are you talking about? What does the given point have to do with this problem?
 
  • #3
do have the exact question?

that doesn't make a heap of senese...

that said if you have a line & a circle in a 3D space, they don't necessarily have to intersect (nor in 2D either)
 

FAQ: Point and Circle intersection in 3 D

How do you determine if a point and a circle intersect in 3D?

In order to determine if a point and a circle intersect in 3D, you first need to know the coordinates of the point and the center of the circle. Then, you can calculate the distance between the point and the center of the circle. If the distance is less than or equal to the radius of the circle, then the point and circle intersect.

What is the formula for calculating the distance between a point and a circle in 3D?

The formula for calculating the distance between a point and a circle in 3D is:
distance = √((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
where (x1, y1, z1) are the coordinates of the point and (x2, y2, z2) are the coordinates of the center of the circle.

Can a point intersect with a circle at more than one point?

No, in 3D space, a point can only intersect with a circle at one point. This is because a circle is a two-dimensional shape, and a point only has one dimension. Therefore, the two can only intersect at a single point.

What are some real-world applications of point and circle intersection in 3D?

Point and circle intersection in 3D has various applications in fields such as computer graphics, computer vision, and robotics. For example, it can be used to determine if a specific point lies within the range of a robot's sensors, or to calculate the position of objects in a 3D scene in computer graphics.

Are there any limitations to using the distance formula to determine point and circle intersection in 3D?

One limitation of using the distance formula to determine point and circle intersection in 3D is that it assumes the circle is a perfect, symmetrical shape. In reality, circles can be imperfect and distorted, leading to potentially inaccurate results. Additionally, the distance formula does not take into account any obstacles or barriers that may exist between the point and the circle, which could also affect the intersection. Other methods, such as ray tracing, may be more suitable in these cases.

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