0
votes
1answer
27 views

transform line and point in 3d and 2d space [closed]

I have a line which is described with two point and I know (x0,y0,z0) and (x1,y1,z1). After that I transform it to 2d space dividing with -z0 and -z1 values. Problem is that if I know (a,b) how can ...
2
votes
1answer
21 views

proof for euler-rodrigues formula - matrix form

I need for a matrix representation. Exactly I want to know how to get the Euler-Rodrigues formula in a matrix form like here. Thanks!
1
vote
1answer
254 views

How to find out if four points are on the same plane, only by using distances?

There is a method called Cayley-Menger determinant in order to find if 3 points are collinear, 4 points are coplanar etc. provided that all the pairwise distances are given. However, in 2-D, there is ...
1
vote
1answer
38 views

How to Create a Plane Inside A Cube

I have a $e \times e \times e$ cube and I want to create random planes with equation $ax + by + cz + d = 0$ inside this cube. I will put random points on those randomly created planes as well. Here ...
-1
votes
1answer
64 views

Rotate the Points on a Plane $P = ax+by+cz + d = 0$ parallel to $z = 0$ plane

I have a plane $P = ax+by+cz + d = 0$ and many points on that plane. I want to rotate $P$ so that it becomes parallel to $z = 0$ plane. Which method should I use? I know that the normal vector of my ...
2
votes
1answer
170 views

How To Generate Random Points on the Positive Side of a Plane in 3-D

Edit: The question can also be interpreted as: How to generate random coplanar points in a cube? Here is what I am struggling with: I have a cube, whose origin is $(0,0,0)$ and one edge length ...
1
vote
0answers
87 views

How to calculate center coordinates of two reverse arcs in 3D space

Given 3D points P1(200,60,140), P2(300,120,110), P3(3,0,-1), P4(-100,0,-1) and the radius of arc C1MP3 is equal to radius of arc C2MP1. How do I calculate coordinates x, y, z of points C1 and C2? ...
0
votes
1answer
363 views

Find Equation of a Perpendicular Line Going Through a Point

I have the following parametric equation for line g: $$ x=3t\land y=-7+5t\land z=2+2t $$ I have to find the equation of a line perpendicular to $g$ and going through point $Q(3,-2,4)$ which lies on ...
1
vote
2answers
590 views

Rotation in 3D (coordinate system transformation)

How do I rotate a point around point [0,0,0] in 3D. In picture I draw specific situation for illustration. At first I know point G[x,y,z] and I will tranfer it on axiz Z, where distance to center is ...
1
vote
1answer
616 views

Angle between line and a plane

I want to calculate the angle between the plane with a normal $N = [N_x,N_y,N_z]$ and the vector $V = [V_x,V_y,V_z]$ and I used this formula for angle $$\alpha = \arccos \frac{V \circ N} {|V|\; ...
0
votes
2answers
321 views

Angle between planes

If the angle between two planes is $\alpha$ , why is the angle between normal of the two planes is $\pi - \alpha$ ? Also Why angle between a line and normal to a plane is $\pi/2 -\alpha$ if angle ...
0
votes
1answer
174 views

3D Road - Rotate around 3d curve

First of all, I'm not sure whether to post this on stackoverflow or here, but since there's some mathematics needed here (especially at the end of this question) I posted it here. I'm given a ...
2
votes
1answer
88 views

3D Geometry Question

In $3$-dimensional Geometry, if angle made of line segment $OP$ with $X,Y,Z$-axis are in $1:2:3$, then what is the angle made by line segment with $Y$-axis? My Solution: Let $\alpha,\beta$ and ...
3
votes
1answer
306 views

Draw an arc in 3d coordinate system

I have some legacy code which is supposed to draw an arc with constant radius in 3d space however it is drawing the arc in the wrong position. I would like to know and understand the mathematical ...
0
votes
1answer
93 views

How to get Euler angles where an initial value of Euler angle is set as baseline

I have a sensor which gives me Euler angles (roll,pitch,yaw). There is a baseline value of Euler angle (assume it is 5,10,15) at the beginning.I want to calibrate this baseline values from all ...
-1
votes
2answers
84 views

Is it possible to find the coordinates of a point in 3D space, given its distance from a known point?

Is it possible to find the coordinates $(x,y,z)$ of a point in $3d$ space when given: A) the unknown point is $(x,y,z)$. B) the known point is $(a,b,c)$. C) the distance between the two points is ...
1
vote
2answers
82 views

How to find angle of plane $7x+13y+4z = 9$ with $xy$ coordinate plane?

How can I calculate inclination of $7x+13y+4z = 9$ with $X-Y$ plane As for as I understand from question is that the angle of plane $7x+13y+4z=9$ with $ax+by+0z=d$ for $(XY)$ plane.
2
votes
2answers
292 views

How to define a perspective circle in xy?

You can see a perspective view of a square(FCED) and a circle in 2D screen. O is center of the circle. How can I define the perspective circle equation that shown as red in the picture? Thanks a ...
0
votes
1answer
836 views

How do I “describe the region” of $\Bbb R^3$ represented by an inequality?

I don't really understand what these two questions are asking. Nor do I know how to start it. 1) Describe in words the region of $\mathbb {R}^3$ represented by: $x^2 + z^2 \le 9$. 2) Write ...
2
votes
2answers
920 views

How to calculate distance between point and object in 3d space

I have object in 3d space created from points $P_i(x, y, z)$ from which I can create triangles, and I need to calulate distance from point X to this object. I try to take 3 points from smallest ...
3
votes
3answers
489 views

What is the tangent plane equation on the 3 spheres?

3 spheres are on $z=0$ plane and touch each other as shown in the picture. Coordinates of their centers are $O_1=(0,0,5),O_2=(0,y_2,3),O_3=(x_3,y_3,2)$. What is the tangent plane equation on 3 ...
1
vote
1answer
239 views

Are these sufficient conditions to define an elliptical cone?

I was successful in deriving the equation for an elliptical double-napped cone in rectangular coordinates. All I did was define a line with slope $a$ on the xy-plane, and another line of slope $b$ on ...
2
votes
1answer
328 views

Finding the radius of the largest sphere possible between a corner and another sphere

In a 3 dimensional Cartesian plane there is a sphere A that is in the first octant and is tangent to all coordinate planes. Now, imagine we want to find the another sphere B also tangent to all ...
0
votes
2answers
7k views

How to find shortest distance between two skew lines in 3D?

If given 2 lines $\alpha$ and $\beta$, that are created by 2 points: A and B 2 plane intersection I want to find shortest distance between them. $$\left\{\begin{array}{c} P_1=x_1X+y_1Y+z_1Z+C=0 ...