Calculate Ellipse based on 4 points

In summary, To move an object based on 100 images rotating, the object must follow a path forming an ellipse. To calculate the X/Y values of the next/previous points, the four points on the ellipse must be used to solve a system of equations with four unknowns, including a and b, the semi-major and semi-minor axes of the ellipse, and x_0 and y_0, the coordinates of the center of the ellipse. This can be done using the equation of an ellipse.
  • #1
HellScream_
1
0
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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  • #2
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.
 

1. What is an ellipse?

An ellipse is a geometric shape that is defined as a curved line forming a closed loop. It is similar to a circle, but with two different radii instead of just one. It can also be described as a flattened circle.

2. How do you calculate an ellipse based on 4 points?

To calculate an ellipse based on 4 points, you will need to use the equation: (x-x0)^2/a^2 + (y-y0)^2/b^2 = 1, where (x0, y0) is the center of the ellipse, a is the semi-major axis, and b is the semi-minor axis. You will need to plug in the coordinates of the 4 points into this equation and solve for the center and axis values.

3. What are the 4 points needed to calculate an ellipse?

The 4 points needed to calculate an ellipse are any 4 points on the perimeter or inside the ellipse. These points will be used to determine the center and axis values of the ellipse.

4. Can an ellipse be calculated with more than 4 points?

Yes, an ellipse can be calculated with more than 4 points. However, using 4 points is the minimum requirement to determine the center and axis values of the ellipse. Using more points can help to increase the accuracy of the calculation.

5. What are some real-world applications of calculating an ellipse based on 4 points?

One real-world application of calculating an ellipse based on 4 points is in satellite orbit prediction. By using 4 points on the orbit path, scientists can accurately calculate the ellipse of the satellite's orbit and predict its future path. It can also be used in astronomy to calculate the shape of planetary orbits and in engineering for designing curved structures such as bridges and arches.

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