I have two polyhedral cones represented by their rays. I am looking to find their intersection, which would also be a polyhedral cone, hopefully efficiently. Does anybody know a way to do that?
Thanks
Deepanshu
Related
What is the fastest way to compute the two vertices of the line-segment of intersection between two triangles (given by their vertex positions) in 3D space ?
I would have thought the solution to this problem should be rather easy to find somewhere, but unfortunately I could not find ANY (even minimally elegant) solution. :/
This paper answers precisely this question: https://cis.temple.edu/~lakaemper/courses/cis350_2004/etc/moeller_triangle.pdf
I have a bunch of data points that depict the frequency (no unit) at different times (seconds). I have several of these for different parts of a cell. I need to be able to compute the derivatives of each point in each column for all the data using R. Is this possible? Can someone point me in the right direction?
Please let me know if I am not being specific enough.
Thanks
I have a point p and multiple circles C1,C2,C3.... Cn.
How can i find if the point is at the intersection area of this Circles ?
I just know the center(x,y) and the radius of the circles C1...Cn and the coordinates of the point p(x,y).
I have to write a cpp code for implementing this problem.
But at first i need to know the logic. Please help.
Just check if the distances of the point from the three centers are less of all the three radius.
EDIT: homework? I should not have answered :/
I'd like to draw the 3-simplex which encloses some random points in 3D. So for example:
pts <- rnorm(30)
pts <- matrix(pts, ncol = 3)
With these points, I'd like to compute the vertices of the 3-simplex (irregular tetrahedron) that just encloses these points. Can someone suggest a package/function that will do this? All manner of searching for simplex-related material is dominated by answers that relate to using simplices for other purposes, of which there are many. I just want to compute one and draw it. Seems simple, but I don't seem to know the relevant keywords for what I need.
If nobody can find a suitable package for this, you'll have to settle for doing it yourself, which isn't so difficult if you don't require it to be the absolute tightest fit. See this question over at mathexchange.
The simplest approach presented in this question seems to me to be translating the origin so that all points lie in the positive orthant (i.e, all point dimensions are positive) and then projecting the points to lie within the simplex denoted by each unit vector. To get this simplex in your original coordinate system you can take the inverse projection and inverse translation of the points in this simplex.
Another approach suggested there is to find the enveloping sphere (which you can for instance use Ritter's algorithm for), and then find an enveloping simplex of the sphere, which might be an easier task depending what you are most comfortable with.
I think you're looking for convhulln in the geometry package, but I'm no expert, so maybe that isn't quite what you are looking for.
sorry for posting this in programing site, but there might be many programming people who are professional in geometry, 3d geometry... so allow this.
I have been given best fitted planes with the original point data. I want to model a pyramid for this data as the data represent a pyramid. My approach of this modeling is
Finding the intersection lines (e.g. AB, CD,..etc) for each pair of adjacent plane
Then, finding the pyramid top (T) by intersecting the previously found lines as these lines don’t pass through a single point
Intersecting the available side planes with a desired horizontal plane to get the basement
In figure – black triangles are original best fitted triangles; red
and blue triangles are model triangles
I want to show that the points are well fitted for the pyramid model
than that it fitted for the given best fitted planes. (Assume original
planes are updated as shown)
Actually step 2 is done using weighted least square process. Each intersection line is assigned with a weight. Weight is proportional to the angle between normal vectors of corresponding planes. in this step, I tried to find the point which is closest to all the intersection lines i.e. point T. according to the weights, line positions might change with respect to the influence of high weight line. That mean, original planes could change little bit. So I want to show that these new positions of planes are well fitted for the original point data than original planes.
Any idea to show this? I am thinking to use RMSE and show before and after RMSE. But again I think I should use weighted RMSE as all the planes refereeing to the point T are influenced so that I should cope this as a global case rather than looking individual planes….. But I can’t figure out a way to show this. Or maybe I should use some other measure…
So, I am confused and no idea to show this.. Please help me…
If you are given the best-fit planes, why not intersect the three of them to get a single unambiguous T, then determine the lines AT, BT, and CT?
This is not a rhetorical question, by the way. Your actual question seems to be for reassurance that your procedure yields "well-fitted" results, but you have not explained or described what kind of fit you're looking for!
Unfortunately, without this information, your question cannot be answered as asked. If you describe your goals, we may be able to help you achieve them -- or, if you have not yet articulated them for yourself, that exercise may be enough to let you answer your own question...
That said, I will mention that the only difference between the planes you started with and the planes your procedure ends up with should be due to floating point error. This is because, geometrically speaking, all three lines should intersect at the same point as the planes that generated them.