Computing cone equation using data points

In summary, the problem being discussed is related to the propagation of waves in a 2D space with respect to time. The problem involves finding the number of right circular, infinite cones with a specific predetermined angle between the conical surface and axis that pass through three given points in 3D space and determining the coordinates of the apex point. The points are all on one side of the cone and another representation of the problem involves finding the number of points that belong to the surface of three right circular cones with apex points at the given points. The question also asks for a possible solution or method for dealing with noise or inaccuracy in the data points.
  • #1
Saeid
2
0
Dear All
I have a problem that can be represented in two different forms.
Problem is related to propagation of waves in 2D space with respect of time.
I have three random points in the 3D Space.
How many right circular, infinite cones with specific predetermined angle between conical surface and axis we can find that passes these three points.
I need the 3D coordinates of the apex point.
Three points are in one side of cone. I.e., if we draw a plane perpendicular to axis of cone that meets the axis in apex point, all three points will fall in one side of the plane.
Another representation of the problem is, if I draw three right circular, infinite cones with specific predetermined angle between conical surface and axis which their apex points are these three points in the 3D space, how many points I can find that belongs to surface of these three cones. Or, in how many points these three cones coincide with each other.
What will be the result if I use four different points in the space?
If my points (data points) have noise (inaccuracy) what solutions or method exists or you suggest for solving it?


Thank you
 
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  • #2
Welcome to PF!

Hi Saeid! Welcome to PF! :smile:

Hint: if the points are A B and C, and the axis of the cone is the line L, and the apex is at the point X on L, and the half-angle of the cone is θ, then the equation relating the lines XA XB XC and L is … ? :smile:
If my points (data points) have noise (inaccuracy) what solutions or method exists or you suggest for solving it?

No idea! It might be better to ask that question in the computing part of the forum. :smile:
 
  • #3
tiny-tim said:
Hi Saeid! Welcome to PF! :smile:

Hint: if the points are A B and C, and the axis of the cone is the line L, and the apex is at the point X on L, and the half-angle of the cone is θ, then the equation relating the lines XA XB XC and L is … ? :smile:


No idea! It might be better to ask that question in the computing part of the forum. :smile:
Thanks tiny-tim
Another hint, required cone is vertical.
 
  • #4
right circular cones

Saeid said:
Thanks tiny-tim
Another hint, required cone is vertical.

Hi Saeid! :smile:

What do you mean by "vertical"? :confused:

The question only says "right circular" … in other words, an "ordinary" cone.

See http://en.wikipedia.org/wiki/Cone_(geometry) :
In common usage in elementary geometry, however, cones are assumed to be right circular, where right means that the axis passes through the centre of the base (suitably defined) at right angles to its plane, and circular means that the base is a circle. Contrasted with right cones are oblique cones, in which the axis does not pass perpendicularly through the centre of the base.
 

What is the computing cone equation using data points?

The computing cone equation using data points is a mathematical formula that represents a cone-shaped surface that can be used to model data points in a three-dimensional space. It is often used in computer graphics and data visualization to represent data in a visually appealing way.

How is the computing cone equation derived?

The computing cone equation is typically derived using a process called regression, which involves finding the best-fit cone that passes through the given data points. This is usually done using a mathematical method called the least squares method, which minimizes the sum of the squares of the errors between the data points and the cone surface.

What are the applications of the computing cone equation?

The computing cone equation has a wide range of applications, including data analysis, computer graphics, and data visualization. It can be used to model and predict trends in data, create 3D visualizations of data points, and even generate 3D surfaces for use in computer-aided design (CAD) software.

What are the limitations of the computing cone equation?

While the computing cone equation is a useful tool for representing data points in three-dimensional space, it does have some limitations. For example, it may not accurately model data points that do not conform to a cone shape, and it may not be suitable for highly complex data sets with a large number of data points.

How can the accuracy of the computing cone equation be improved?

The accuracy of the computing cone equation can be improved by using different regression techniques, such as higher-order regression or non-linear regression, which can better fit data points that do not conform to a cone shape. Additionally, using a larger number of data points can also improve the accuracy of the equation.

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