Recent content by Asuralm

I mean what's they expression of plane and line in the spherical coordinates. For example, the line is defined as something like {\bf v} = {\bf v}_0 + t\cdot {\bf n}. But here {\bf v} = (v_x, v_y, v_z), i.e. cartesian coordinate. How can a plane and line be expressed in the spherical coordinate...

Hi all: I am wondering if there is any book or course note about the geometry in spherical coordinate. Not just the superficial definition and the convertion with Euclidean coordinate. But something like how a line is defined in spherical coordinate in 3D space, how a plane is defined, how to...

Hi all: Assume in 3D space there is a point [itex]v=[v_x, v_y, v_z][/tex], and a normal vector associate with it as n=[n_x, n_y, n_z]. A line function is defined as u=w+t\cdot l where w=[w_x, w_y, w_z] is a point, and l=[l_x, l_y, l_z] is the normalized direction of the line. l and n are...

Dear all: If I have a white light source which is at the positive infinite, and there is a plane receiving the light. Assuming that the plane is facing to the light source at the beginning. If I start rotating the plane, and keep recording the intensity of one point of the plane, what...

Hi all: My question is how to calculate the overlapped area of a triangle and rectangle. It sounds a simple question but is there any way to do it efficiently? And is it possible there is a uniformed equation to solve such a problem? As there are many cases the triangle can overlap with...

I don't know if this is a good way to solve it. But if in a triangle, the easiest way to check if a point is inside is to check the sum of the area. i.e. for ABC, there is a point P, if P is inside ABC, then, area(ABP)+area(ACP)+area(BCP) = area(ABC). You can check the volume in the tetrahedral...

Have you got the information about any points? What about the voronoi diagram or delaunay triangulation?

Hi all: I need to solve a sparse linear system, I found the iterative methods library which probably fit my requirement. But I couldn't find any good matrix library to work with IML++. The best choice should be Sparse++ but it requires a very old compiler which is gcc 2.7. something like...

Hi all: I have a covariance matrix which is like: 0.00166713 -0.00060678 4.60534e-05 -0.00060678 0.00178576 -0.000244526 4.60534e-05 -0.000244526 0.000772057 And then I want to eigen decompose the matrix to obtain the eigenvector matrix. I tried several methods, one is to use the...

should this |v0- t*n|2- <v0+ t*n,A+B>+ <A,B> be <v0+t*n, v0+t*n> - <v0+t*n, A+B> + <A, B> ?

Hi all: Given a line L:v= v0+t*n; and two points A, B in 2D plane; A and B are on the two sides of the line L. I want to calculate the point C which makes AC is perpendicular to BC I know it's simply that substitude v to C and <AC, BC>=0. But I don't know how to simplify the equation...

I don't think I am talking about Brownian motion as the energy of noise is fixed. Given a length r, the point should only noised by r. Thanks EnumaElish, It really helps.

Dear all: The question is like this: Given a point in a shape like square or triangle. Let's take square as the simplest one. Say the length of the side of the square is l. If add a noise to the point which will move the point [tex]r[\tex] distance and the direction is arbitrary, what will...

Sorry the first post was failed.

Hi all: I have just met a problem. If say there is a triangle ijk on a manifold, D(i), D(j), D(k) are the geodesic distances from a far point to i,j,k respectively. Then g = [D(i) - D(k); D(j) - D(k)], what does g describe? Does is describe the gradient of the vertex k? If u = Vi-Vk, v =...