What is the best approach for finding the equation of a pursuit curve?

In summary, to find the equation for a curve, you can use a mathematical fitting algorithm to find the best fit for your data points.
  • #1
deepthishan
38
0
I am trying to find out the equation for a curve:
http://shandeepthi.blogspot.co.uk/2012/05/target-curve.html

I have tried some equations e.g.
http://shandeepthi.blogspot.co.uk/2012/05/trials.html

However, I cannot get it sufficiently accurate.

Can you please help? At least a pointer in the right direction?

Many Thanks!

(PS: Please note that this is not a HW assignment of any sort. Also, you may need to refresh the links at least twice sometimes to get it to work - apologies!)
 
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  • #2
One approach you can take is to use a mathematical fitting algorithm. This type of algorithm finds the equation that best fits the data points you have to form the curve. There are many different fitting algorithms available, so you will have to do some research to find one that best suits your data and the accuracy you are looking for. Many mathematical software packages include fitting algorithms, so if you have access to one, then you may be able to use it to generate the equation you are looking for.
 

Related to What is the best approach for finding the equation of a pursuit curve?

What is a Pursuit Curve?

A pursuit curve is a mathematical concept that describes the path taken by a moving object as it pursues or chases another moving object. It is commonly used in the field of physics and engineering to study the motion of objects in pursuit situations.

What is the function for a Pursuit Curve?

The function for a pursuit curve is a mathematical equation that describes the relationship between the positions of the two objects involved in the pursuit. It is typically written as a parametric equation, where the x and y coordinates of the pursuer are determined by the position of the target at any given time.

What are some real-world applications of Pursuit Curves?

Pursuit curves have many practical applications, such as in robotics, navigation, and sports. For example, they can be used to program robots to track and follow a moving target, to optimize the flight paths of missiles, or to calculate the trajectory of a soccer ball being kicked towards a moving goal.

How do you calculate the parameters of a Pursuit Curve?

The parameters of a pursuit curve, such as the speed and direction of the pursuer, can be calculated using various mathematical methods, such as differential equations or vector calculus. These calculations take into account factors such as the speed and direction of both objects, as well as any external forces acting on them.

What are the limitations of Pursuit Curves?

While pursuit curves can be useful in many situations, they have some limitations. For example, they assume that the pursuer and the target are moving in a straight line, and they do not take into account factors such as obstacles or changes in direction. Additionally, they may not accurately predict the behavior of objects with complex or unpredictable movements.

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