# Tagged Questions

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### Counting points in/on cuboid

Given a cuboid that extend in x,y,z axis such that |x|≤N, |y|≤N, |z|≤N where N is given and can have value up to 10^9.Now a shooter is standing at origin (0,0,0).He need to shoot on any of the ...
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### Collision detection between two accelerating spheres with no initial velocity?

We have two non-touching spheres of radii r1 & r2 are lying in space at rest. Both of them are then given accelerations a1 & a2 respectively at time t=0. Find whether they will ever come in ...
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### Mapping between two unknown 3D coordinate systems from common motion

Coordinate systems A and B are rigidly linked in an unknown way. The platform then moves and the motion vectors [RA|TA] and [RB|TB] are calculated in each coordinate system. They are parallel but not ...
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### How to find the $x,y$ coordinates of a point in between $2$ points in $3$ dimension

Point $1 = (0,0,0)$ Point $2 = (5,6,7)$ Given that point $3$ have a $z$-coordinate of $3$, how can I find the $x,y$ coordinates of point $3$?
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### Calculating 3D points corrds from 2D image

The current scenario I have is that I have an image of a retangular board from an angle and I need to calculate the 4 corrdinates of the 4 corners of the rectangle. Currently I have gone through the ...
719 views

### How do I calculate roll, pitch, yaw from a unit vector?

I am provided a unit vector giving a direction in x, y, z coordinates, and that the roll is defined as about the x axis, pitch around y, yaw around z. I'm trying to determine how to calculate roll, ...
173 views

### sketching regions of three variables

If i had a solid region, V, such that $x^2+y^2+z^2\le9$, $x^2+y^2\le4$, $x\le0$ and $z\ge1$ what would be the easiest method to sketch this region? Can someone run me through steps as how to tackle ...
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### Change of coordinates in 3D

It's been a while since my last geometry class and I need some help in solving a very simple problem I have. I need to implement a zoom function in 3D in a piece of software I am writing. My system ...
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### Coordinate Transformation on Local coordinate system

I am having a point $P(x,y,z)$ in $3D$ with respect to global coordinate system. I want to create an another Local Coordinate System by picking three points $N1, N2, N3$ in 3D. Now I want to know the ...
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### How to solve a distance problem inside of a picture?

sorry for my bad english. I have the following problem: In the picture you can see 4 different positions. Every position is known to me (longitude, latitude with screen-x and screen-y). Now i want ...
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### Tetrahedron problem (proving)

Prove that if $P$ is the intersection of the altitudes of a tetrahedron $ABCD$ and $r$ is the circumradius then $PA^2+PB^2+PC^2+PD^2=4\cdot r^2$.
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### Rotating co-ordinates in 3D

Suppose I have 3 axes, $x$, $y$, and $z$ such that $x$ is horizontal, $y$ is vertical, and $z$ goes in/out of the computer screen where $+$ve values stick out and $-$ve values are sunken in. Suppose ...
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### move a point up and down along a sphere

I have a problem where i have a sphere and 1 point that can be anywhere on that sphere's surface. The Sphere is at the center point (0,0,0). I now need to get 2 new points, 1 just a little below the ...
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### 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, ...
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### Gram-Schmidt Orthogonalization - does it distort?

I am writing a 3D solar panel positioning programme and have a section of code where I use the Gram-Schmidt Orthogonalization process to go from 3D to 2D for easier calculations. (For reference, here ...
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### how to get rotation component of quaternion form using 3d coordinates

I have a series of 3d coordinates distributed in a 3d space according to a root point. I can determine the x, y , z component using reducing the vectors. but I am not clear how to get rotation ...
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### Z-index of an arbitrary point on a flattened 3-dimensional triangle

I have a triangle in a 3-dimensional coordinate system that I want to draw to a screen. I'm able to flatten the triangle to 2 dimensions and determine whether an arbitrary point on the screen falls ...
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### Finding an equation of a sphere for a specific plane

I am not sure how to proceed with this question from Stewart's SV Calculus text: Find equations of the sphere's with center $(2, -3, 6)$ that touch (a) the $xy$-plane, (b) the $yz$-plane, (c) ...