1
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0answers
16 views

A method of calculation coordinates in order to implement it to a code language!

lets say that we have three points A(xa,ya,za), B(xb,yb,zv), C(xc,yc,zc) with known coordinates in 3d space. Is there a method to calculate the coordinates (x,y,z) of another point D for which the ...
1
vote
1answer
82 views

Find fourth coordinates given other three points

Find coordinates of $D$, given coordinates of $A,B,C$, torsion angle and angle between $BCD$. Is there any other way other than the torsion angle equation, $$n_1=⟨b_1\times b_2⟩ \;\text{ and }\; ...
0
votes
0answers
71 views

Gradient definition of the unit vector

Given some coordinate system ($q_1,q_2,q_3$), it seems that the unit vectors $\hat{q}_i$ can be defined by $$\hat{q}_i = \frac{\nabla q_i}{||\nabla q_i||},$$ that is, the normalized gradient of $q_i$. ...
4
votes
2answers
348 views

How to calculate x,y position of 3D points?

I have points in 3D system like this $$p1=(2,3,4)$$ $$p2=(3,5,5)$$ Here I would like draw point $p1$ and $p2$ in $2D$ view. Project type = orthographic. Coordinate system = Cartesian X- axis, ...
1
vote
0answers
111 views

Circle-Circle intersection coordinate system

Consider two points in the 2D Euclidean plane, the origin $0$ and $x$. One can define a co-ordinate system such that for any point $y$ in the plane, $y$ is parametrized by its distance from $0$, call ...
1
vote
1answer
45 views

Defining a set of axes.

I was reading up a little on reference frames and am confused about a certain detail. Is it correct to say that the positive $x$-axis, for example, can be defined as follows? $$ X^+ = \lim_{C ...
0
votes
1answer
334 views

Finding the sign of $\phi$ in spherical coordinates

I know its a little silly, but I got the wrong sign several times. Just to be clear, $z=r\cos(\phi), -\frac{\pi}{2}\leq\phi\leq\frac{\pi}{2}$ when converting from cartesian to spherical. So, how do I ...
1
vote
1answer
319 views

Index/Einstein notation to derive Gibbs/Tensor relations

In a few continuum classes I have seen indicial notation used to derive relations in Gibbs notation. However, Gibbs notation is valid for all coordinates while indicial notation is valid only for ...