# Tagged Questions

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### Get Vector From Angle In $3D$ Space

I have a camera angle in $x,y,z$ with values between $0$ and $360$, I'm trying to compute this into an 'aim vector' which would have values between $0,0,0$ and $1,1,1$ depending on what the angles ...
47 views

### Finding a 3rd coordinate of the rectangle points in 3d

I have a 4 3-D-points, each of them has only 2 of 3 known coordinates, as follow (? is unknown here): P5 (P5x, P5y?, P5z) P6 (P6x, P6y?, P6z) P3 (P3x, P3y, P3z?) P4 (P4x, P4y, P4z?) They build ...
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### Calculate coordinate of any point on triangle in 3D plane

I am really stuck and can't find right way to write a formula(s) that will calculate Z coordinate of point on triangle plane in 3D plane. I know all coordinates of triangle points ( Ax, Ay, Az, Bx, ...
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### Generate rotations about X & Y axes between certain 3D vectors

Given a semi-arbitrary 3D vector (the z will always be positive for my purposes), how could I find rotation about the X and Y axis? Alternatively, how might I simplify an XYZ rotation to the X and Y ...
82 views

### Finding the missing coordinate of a point within a 3D triangle

We have an equilateral triangle $ABC$ in 3-dimensional space. The points are known, such as: $A = (x_1,y_1,z_1)$ $B = (x_2,y_2,z_2)$ $C = (x_3,y_3,z_3)$ Point $P$ is on triangle $ABC$. If I know ...
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### How do I calculate the dimensions of this Frustum?

So, I saw this question in a book, You have been given a cone. The cone's base angles are both equal to 75° and the vertical angle is (of course) 30°.The radius of the cone is 7 metres.Now, ...
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### Rotate $z = 0$ plane in 3D

I have 100 points on $z=0$ plane. I want to rotate those points, such that they lie on any plane $P(a,b,c,d)$, preserving distances. Hence, I need a rotation matrix. For instance, if my points are ...
96 views

### How to draw arrows by rotating lines in 3d space?

I am trying to figure out direction vectors of the arrowheads of an arrow. Basically I'm given a normalized direction vector ...
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### How do I multiple these matrices together?

As a personal brain exercise, I've recently been trying to work out the math involved with rotating vertices around an arbitrary axis in 3D space. To do so, I've been relying very heavily on the ...
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### How do I calculate the inverse of these matrices?

In learning how to rotate vertices about an arbitrary axis in 3D space, I came across the following matrices, which I need to calculate the inverse of to properly "undo" any rotation caused by them: ...
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### Find a 3D vector given the angles of the axes and a magnitude

I would like to know how one would find a point from the angles of three axes and a magnitude. I know how to do this in 2D: $(\cosΘ * m, \sin(Θ) * m)$. However, I would like to know how this would be ...
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### solving 3-d coordinates from x, y and z distance

I working with WiFi positioning and i want to know the exact coordinate where I am. Here is the problem..
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### Taking into account Camera Direction in 3d models using Trig

I have been working on a 3d rendering project as code. I am a bit stumped on the math though. I know how to render points using arctangent on an HTML canvas using JavaScript, like this: ...
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### How to get angle bewteen two vectors in range -1 to 1 without using arc cosine?

Given two normalized vectors in 3d space, how can I get a value from $-1$ to $1$ based on their angle without using arc cosine? With use of arc cosine, I think this would give me the correct result. ...
286 views

### A controlled trapezoid transformation with perspective projecton

I'm trying to implement a controlled trapezoid transformation in Adobe Flash's ActionScript using the built-in perspective projection facility. To give you an idea of how the effect looks like: ...
235 views

### Determining camera orientation (possibly using calibration images).

I need to generate a camera calibration pattern. Cameras are expected to be placed at an average height of 15 to 30 feet above ground pointing downwards at roughly 30 degrees. These cameras are ...
241 views

### What does negative sine mean in this diagram?

I thought cos was x and sin was y. In quadrant two, cos is negative and sin is positive. Why does this diagram have a negative sign as the x-coord and cos as the y coordinate for q prime's vector? ...
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### Determining a point in 3D space

So given a point, a rotation around the y-axis, a rotation around the x-axis, and a distance, how can one calculate the relative point in space? For example, the beginning coordinates are (0,0,0). ...
268 views

### Distance between two objects in a picture

lets say I have a photo that has a picture on a wall and a book upright on the desk. now i know the size of both of these objects. I want to find the distance between two of them on the photo, I was ...
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### Find point in 3D space based on start point, three angles and a distance (need example)

I know this has been asked before but the answer wasn't very helpful, sorry. I need an example and to see each step of the equation being solved. Let's say we have 45 degree angles to each axis and ...
463 views

### Finding the distance between the centre of an arbitrarily rotated cylinder and a point on that cylinder

this is a bit more complicated than the post title suggests because I was running out of words. I suppose the full title would be: "Finding the distance between the centre of an arbitrarily rotated ...
311 views

### Determining angle of tilt from length of axes?

When taking a picture of a cross, if the center of the cross is known, is there any way to determine the angle at which the picture was taken based on the number of points on the y axis above and ...
592 views

### Find 3D rotation vector and angle to transform a rectangle into a given quadrilateral

I have a given rectangle that I need to transform into a given quadrilateral shape that resulted from a rotation and translation in 3D space, and subsequent projection. ...
210 views

### Finding the radius of a particular center voxel in 3D cylinder-like structure

From the image above, assume that it is a 3D image that is of m*n*o size. Each voxel can only be either 0 or 1. White is 1. Black is 0. In this 3D environment, there is one cylinder-like ...
So let's assume I have a point $P$ in $3d$ space $(x_0, y_0, z_0)$. And I have a circle $C$ that is centered at $(x_1, y_1, z_1)$ with a radius $r$. I need to find the distance from $P$ to the nearest ...