Calculate Ellipse based on 4 points

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SUMMARY

The discussion centers on calculating the points of an ellipse based on four specified points, specifically two pairs of opposite points on the X and Y axes. The user seeks to transition from a circular motion to an elliptical path for an object rotating based on gestures. The mathematical foundation provided includes the standard ellipse equation, \(\left(\dfrac{(x-x_0)}{a}\right)^2+\left(\dfrac{(y-y_0)}{b}\right)^2=1\), which leads to a system of four equations with four unknowns: \(a\), \(b\), \(x_0\), and \(y_0\). The solution requires solving this system to derive the necessary parameters for the ellipse.

PREREQUISITES
  • Understanding of the ellipse equation and its parameters
  • Basic knowledge of solving systems of equations
  • Familiarity with coordinate geometry
  • Programming skills for implementing mathematical calculations
NEXT STEPS
  • Research methods for solving systems of equations in programming languages
  • Learn about parametric equations of ellipses for smoother motion
  • Explore libraries for geometric calculations in your programming environment
  • Investigate gesture recognition techniques for object movement
USEFUL FOR

Programmers, mathematicians, and game developers interested in implementing elliptical motion based on user gestures and mathematical calculations.

HellScream_
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I need to move an object based on 100 images rotating. The object needs to move in a path that is forming an ellipse when I'm rotating the image based on my gestures.

I have 4 points, 2 pairs of opposite points on X/Y axis, on the ellipse but how do I calculate the rest of the points so that I can calculate the new X/Y Value of my next/previous point?

Currently I'm just rotating my object in a circle what is a start but not what I want at all...

Is it possible to calculate an ellipse based on 4 opposite points?

Btw - I'm a programmer but I'm not an expert in mathematics, sorry.

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The equation of an ellipse is ##\left(\dfrac{(x-x_0)}{a}\right)^2+\left(\dfrac{(y-y_0)}{b}\right)^2=1## which means you get four equations - for each of your points one - and have four unknowns ##a,b,x_0,y_0\,.## You have to solve this system of equations.
 

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