Distance between a point and a triangular plane segment

In summary, to determine the distance between a point and a plane segment, you can assume the plane is infinite and find the distance. Then, determine if the closest point in the plane is within the triangle and if not, use Pythagoras to calculate the distance between the original point and the triangle. Another method suggested is to minimize (pa + qb + rc)^2 for p+q+r = 1 and p, q, and r being non-negative, which can be done in MATLAB.
  • #1
lemonCBI
2
0
I need to determine the distance between a point and a plane segment. I have 1 point in space and 3 points which form a triangula plane segment. I know the 3 points are not colinear and the 4th point is not coplanar with the others. I want to calculate the distance between the point and the triangular plane segment described by the other 3 points.

My initial idea is to assume the plane is infinite and find the distance. I would then determine if the closest point in the plane lay within the triangle (but was not sure how I was going to do that). If it was then I was done. If not, then I would find which of the 3 line segements of the triangle lay closest to the point in the plane and use Pythagoras to figure out the distance between my original point in space and the triangle.

Any advice about this or any other method would be greatly appreciated. Also, I am performing these calculations in MATLAB so any suggestion on how to optimize my code would be very helpful as well. Thanks!
 
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  • #2
hi lemonCBI! :smile:

if you're doing this on a computer, and you're only interested in the distance, how about just minimising (pa + qb + rc)2 for p+q+r = 1, and p q and r all non-negative? :wink:
 

Related to Distance between a point and a triangular plane segment

1. What is the formula for calculating the distance between a point and a triangular plane segment?

The formula for calculating the distance between a point and a triangular plane segment is based on the Pythagorean theorem, where the distance is equal to the perpendicular distance from the point to the plane, divided by the cosine of the angle between the point and the plane.

2. How do you find the perpendicular distance from a point to a triangular plane segment?

To find the perpendicular distance from a point to a triangular plane segment, you can use the cross product of two vectors representing the plane and the point to calculate the area of the triangle formed. Then, divide this area by the length of the base of the triangle to get the perpendicular distance.

3. Can the distance between a point and a triangular plane segment be negative?

No, the distance between a point and a triangular plane segment cannot be negative. It is always a positive value as it represents the length of the perpendicular line segment from the point to the plane.

4. How is the distance between a point and a triangular plane segment affected by the position of the point relative to the plane?

The distance between a point and a triangular plane segment is affected by the position of the point relative to the plane. If the point is outside of the plane, the distance will be greater than if the point is inside the plane. Additionally, the orientation of the plane and the angle between the point and the plane can also affect the distance.

5. Are there any practical applications for calculating the distance between a point and a triangular plane segment?

Yes, there are many practical applications for calculating the distance between a point and a triangular plane segment. This concept is commonly used in fields such as computer graphics, engineering, and architecture to determine the shortest distance between a point and a surface or object, as well as for collision detection and spatial analysis.

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