Localizing a point in a circle by 2 points on the circumference

In summary, the conversation is about finding the proper formulas and/or Matlab code to locate a point within a circle given 2 points on the circumference. The points will be acquired by an image panel that rotates about a fixed axis. The challenge is that the image panels are flat and tangent to the circle at their center. The desired outcome is to measure the offset of a small spherical object from the center of the panel at 2 different positions on the circumference, extend a vector normal to the image panel from the object's position, and find the point where the two vectors intersect (the position of the object within the circle). The individual is seeking insights or tips on how to approach this problem, and mentions using polar or cartesian coordinates and wondering if
  • #1
fenpark15
4
0
I'm looking to find the proper formulas and/or Matlab code to localize a point within a circle given 2 points on the circumference. The points will be acquired by an image panel that rotates about a fixed axis. The hitch is that I am using flat image panels that are tangent to the circle at their center. I would like to measure the offset of a small spherical object from the center of the panel at 2 different positions on the circumference, extend a vector normal to the image panel from where that object appears on the images, and locate the point where the two vectors intersect (the position of the object within the circle). How can I go about doing this? Your help is much appreciated!
 

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  • #2
Let me rephrase this request. I'm not looking for anyone to do it for me, I'm just looking for insights or tips. I know that I will need to go about creating a vector or line segment to represent the panel, construct a normal vector from the surface of the panel at a specified point (perhaps by solving to make the dot product=0?), and do the math to find the intersection of 2 such vectors. I'm still looking at a blank page for my methods and I'm wondering if I should tackle this using polar or cartesian coordinates, wondering how to map the position and orientation of the panel to the circle and/or its center, and if there's any nice Matlab function that might take care of more than 1 step at a time for me. Known parameters are the position of the panel, its angle (always tangent to the circle from its center) and the radius to the center.
 

Related to Localizing a point in a circle by 2 points on the circumference

What is "localizing a point in a circle by 2 points on the circumference"?

Localizing a point in a circle by 2 points on the circumference refers to the process of finding the exact location of a point on a circle by using the coordinates of two points on its circumference.

Why is it important to localize a point in a circle?

Localizing a point in a circle is important in many fields such as navigation, geometry, and engineering. It allows us to determine the position of objects or landmarks on a circular path, which is useful for measuring distances, angles, and creating accurate maps.

How do you localize a point in a circle by 2 points on the circumference?

To localize a point in a circle, we use the concept of trigonometry and the Pythagorean theorem. By measuring the distance between the two points on the circumference and the radius of the circle, we can calculate the coordinates of the point using the sine, cosine, and tangent functions.

Can you localize a point in a circle with only one point on the circumference?

No, it is not possible to localize a point in a circle with only one point on the circumference. Two points are required to determine the exact location of a point on a circle.

Are there any real-world applications of localizing a point in a circle by 2 points on the circumference?

Yes, there are many real-world applications of localizing a point in a circle. For example, it is used in GPS systems to determine the location of a receiver based on the coordinates of satellites on the circumference of the Earth. It is also used in surveying and cartography to create accurate maps.

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