The (3d) tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For geometry that is not on a plane, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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1answer
40 views

Intersection of Three Planes proof

I'm supposed to be making a study guide answer for this question, but I'm struggling with proof. Show that the three planes intersect at the point provided that Note that the ...
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2answers
29 views

Width of rotated plane

I'm trying to get the width of a rotated plane, but my knowledge of trig functions didn't really help me get what I want. I have a plane, that is $310$ units wide, and is $200$ units away from the ...
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2answers
32 views

Final transformation matrix

I have a 3d object, to which I sequentially apply 3 4x4 transformation matrices, $A$, $B$, and $C$. To generalize, each transformation matrix is determined by the multiplication of a rotation matrix ...
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1answer
27 views

3 Points in 3D Space to Develop an Arc or Circle

Background: I'm a Robotics Engineer and I am trying to develop a more flexible, modular, and robust program for our welding robots, which will minimize teaching time for new robots and also minimize ...
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4answers
47 views

Points on 3d line

Say we have $2$ points on a 3d line, point $A(x,y,z)$ and point $B(x,y,z)$. If we want to get the coordinates of a third point, beyond point $B$ but a certain distance from point $A$, how would we do ...
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4answers
40 views

How to find perpendicular vectors in 3D

Find all values of a such that the vector $q = \langle 2, a, –2\rangle$ is perpendicular to the vector $p = \langle –3, a, 5 \rangle$.
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1answer
55 views

8 cubes ($2$x$2$x$2$) crossed by a straight line

There are 8 cubes forming a bigger cube whose dimension is $2$ x $2$ x $2$. Let a straight line (or a laser) try to pierce through as many small cubes as possible. At most how many small cubes can be ...
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0answers
19 views

Intersection of two moving objects in 3D

There are two objects, where the known data is the position and velocity in 3D vector format. I`m interested in the time and position of the intersection between the two, and possibly without ...
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2answers
376 views

puzzle 3-d visualization

729 small cube are painted pink on each face and then arranged to form 27 identical middle-size cubes.Each middle size cube is painted black and then arranged together to form one large cube. And ...
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0answers
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3D Geometry-If alpha /2 ,beta /2 and gamma /2 are the angles with 3 axes.Then, cos alpha + cos beta + cos gamma [on hold]

If alpha /2 ,beta /2 and gamma /2 are the angles which a line makes with the x,y,z axes respectively.Then, cos alpha + cos beta + cos gamma = ? a-> 1 b-> (-1) c-> 2 d-> 3
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1answer
41 views

Perpendicular vectors in $\Bbb R^3$

Hi I am struggling with this simple question. Let $\vec{v}$ be a unit vector in $\Bbb R^3$. How can I construct two periodic functions $\vec{x}(\theta)$ $\vec{y}(\theta)$ such that $\vec{v}$, ...
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3answers
65 views

Sphere packing question

I'm a secondary school maths teacher, currently on my holidays working through some maths problems for fun. Here is one I have done, but it felt too easy, so if you could check if there's any ...
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3answers
46 views

Do these points make a straight line?

I'm trying to prepare for my calculus 3 class coming up this fall and doing some practice problems. I'm having a hard time visualizing some of these 3D coordinates. $D(0,-5,5)$ $E(1,-2,4)$ ...
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2answers
35 views

Find closest point on a plane to a given point. Discrepancy with normal vector.

I have a point $(9,5,0)$ and a triangle with points $(1,1,0), (3,3,1), (6,1,0)$, let's label them as $A,B,C$ respectively. In order to get the normal vector, I do the cross product of two vectors. If ...
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0answers
24 views

Given a single point in 3d space, and 3 points that make up a triangle, find the closest point in/on the triangle to the point.

Given point $(p,q,r)$ and 3 points which make up a triangle, find the closest point in the triangle to the point in space. From the triangle, we can find the equation of the plane $Ax+By+Cz+d=0.$ ...
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1answer
65 views

Find the shortest distance from the triangle with with vertices in $(1,1,0),(3,3,1),(6,1,0)$ to the point $(9,5,0)$.

I have to find the shortest distance from the triangle with with vertices in $(1,1,0),(3,3,1),(6,1,0)$ to the point $(9,5,0)$. I cannot figure out how to do this. There are three possible cases: ...
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1answer
21 views

Can I break up the 3D line integral $\int_{K,p} (2xydx + (x^3 + 3z)dy + 3ydz)$ in three single integrals?

$$\int_{γ,p} (2x \ y \ dx + (x^3 + 3z) \ dy + 3y \ dz)$$ where $$γ = [(0, 0, 0),(0, 1, 3)] ∪ \{ (x, y, z) ∈ \mathbb{R^3}|y = 0, \ x^2 + (z − 3)^2 = 9, \ x ≤ 0\} ∪ [(0, 0, 6),(1, 1, 6)]$$ and p is the ...
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1answer
32 views

Small Stellated Dodecahedron, generating triangle vertices

I have been trying to draw a small stellated dodecahedron (would post an image if I had enough rep) using OpenGL, and would like to generate the vertices programmatically. I'm looking for a way to map ...
2
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2answers
44 views

How to rotate cuboid to plane

I have a cuboid with 8 points that is axis aligned with its center at the origin 0,0,0. Now I have a plane and want my cuboid to rotate so that instead of being axis aligned, it is now aligned to this ...
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0answers
63 views

Math behind No Man's Sky, or Math of Minecraft in Space [closed]

I recently received a question from one of my students which is a bit outside my life experience. However, I expect this may be of interest to many: I was reading up on a new video game that's ...
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1answer
33 views

How to find the points of intersection of the perpendicular vector two skew lines

Correct me if im wrong, but this is what i know so far The cross product of two skew lines is the perpendicular vector between both those lines. The perpendicular vector intersecting two skew lines ...
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0answers
28 views

Calculus | Parametrization of boundary in $\mathbb{R^3}$

The Problem Given the volume $$ K = \left\{ (x,y,z)\in \mathbb{R^3} \big| \frac{x^2}{9} +y^2 \le z^2 +1, -\frac{1}{3}\sqrt{\frac{x^2}{9} +y^2} \le z \le 3 \right\} $$ What are $a$, $b$, and $K(z)$ ...
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1answer
20 views

In an icosahedron subdivided n times, how can I find the coordinates of adjacent centroids?

I think it would be helpful to refer to this image when trying to follow my description: http://i.imgur.com/nRXQo3W.jpg (taken from http://experilous.com/1/blog/post/procedural-planet-generation). ...
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0answers
53 views

3D Shape with only coplanar faces?

I just thought of this problem, and it's bugging me that I can't find any sort of shape that fits it. Are there any 3D shapes with only faces that have coplanar matches with other faces in the shape? ...
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0answers
21 views

can't figure out multilateration with xyz positions of each post and difference in time

I'm having some real issues figuring out multilateration. I'll start by saying I'm not a math whiz, but I am usually able to figure most things out, but this one has been throwing me through a loop ...
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0answers
11 views

How can i reflect position and direction vectors from a plane

I'm now working on a project that has mirrors. I'd like to reflect a virtual camera and the way which i can do this is to reflect two vectors - position and normalized direction vectors of the camera. ...
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1answer
20 views

Fracturing of a 3D Object

Although this is a computer science applied subject, all the underlying logic is mathematical and geometric. I am trying to write code that will enable me to split an object into random fragments, ...
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2answers
18 views

How to find the 3d direction of a particle sliding down an inclined plane?

So, I'm working in 3D space. I have a frictionless particle sitting on an inclined plane. There's gravity (pushing down on the Y axis), so the particle will slide down the slope. If I know the ...
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1answer
31 views

How you could you change the surface area formula for a cylinder to calculate the curved surface area of the half pipe?

Skateboarders use half pipes for doing tricks. A half-pipe is a half cylinder. Explain how you could manipulate the surface area formula for a cylinder to calculate the curved surface area of the ...
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0answers
21 views

What is the total volume of wood used for the model?

A person makes a model of a house in construction class. The block of wood for the base measures 6 inches by 4 inches, and is 4 inches tall. He used a triangular prism for the roof, whose ...
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2answers
58 views

How to derive the 3D equation of a torus?

I'm doing a presentation on 3D surfaces for college and one of the equations I am using is a Torus. I know that the equation is $$z^2 = 25 - \left(10 - \sqrt{x^2 + y^2}\right)^2$$ For a torus with ...
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1answer
20 views

Change from one cartesian co-ordinate system to another by translation and rotation.

There are two reasons for me to ask this question: I want to know if my understanding on this issue is correct. To clarify a doubt I have. I want to change the co-ordinate system of a set of ...
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0answers
15 views

How shall I find the angle between two vectors inside a sphere using spherical coordinates.

How shall I find the angle between two vectors inside a sphere using spherical coordinates. I want to compute the angle between two vectors by spherical coordinates only and not by any ...
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2answers
32 views

Get the Equation of a Plane from a Vertex and 2 Angles? [closed]

What is the simplest way to algebraically get the equation of a Plane (ax + by + cz = d), if you only have 1 point on the plane, and 2 angles (horizontal and vertical) which define the direction the ...
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2answers
52 views

Get the camera transformation matrix (Camera pose, not view matrix)

Let's say that I have an object and a camera (its representation) in a 3D world coordinate system. I have the camera pose to see the object (rotation matrix and translation (eye position)). If I apply ...
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1answer
20 views

Curvature of a 3D trajectory for which I know data points

In order to simulate an airplane model, I need to change its orientation knowing the curvature of its trajectory. The simulator gives me the plane position, so in order to perform my orientation ...
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0answers
15 views

Get range of 3D object given lowest and highest point

How do you get 3D range of object (highlighted in red below) given its lowest (PL) and highest (PH) (x,y,z) coordinates and the dimensions and orientation of object?
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2answers
37 views

Find 3D distance between two parallel lines in simple way

Is there a simple way to get 3D distance between two parallel lines given end points of each line?
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0answers
10 views

Calculate camera view and projection matricies from projected points

I’m stuck on a project for a client.. I need to find the answer to this to proceed: Given (n) coordinates in 3D space and (n) corresponding coordinates in 2D space as projected onto a camera’s image ...
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1answer
14 views

Point within a Cube in 3D environment

I have a cube in 3D space with 8 corner points with their X,Y,Z Coordinates. I know how to test if any given point lies inside a cube by Comparing their coordinates to be greater or smaller than the ...
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0answers
24 views

transofrmations (a,b,c) to (x,y,z)

I'm not 100% sure linear algebra will crunch this problem, but hopefully so. This may just be a case of matrices, which would be good cause I like those. Imagine we have a robot with a camera ...
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0answers
18 views

finding the intersection points of three semispheres

I'm currently playing with a project where the math is far over my head. I know enough to visualize it, but not enough to solve it from the numbers. I'm setting up three listening posts on the tips ...
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0answers
23 views

Cartesian/Parametric 3d equation of a cheese twist?

Hi I'm looking for the equation of a cheese twist in 3d (either parametric or cartesian)... Can be multiple planes but was wondering if anyone had any idea to execute something like this? Thanks e.g. ...
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1answer
41 views

Find angles between sides of triangle and coordinate planes ($xy,yz,zx$ planes) using three 3d vectors .

Given the following, three vectors: \begin{align*} \vec{a}& = 3i−2j+5k, \\ \vec{b}& =i−6j+6k, \\ \vec{c}& =2i+3j−k, \\ \end{align*} find the angles between sides of triangle and ...
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1answer
11 views

Finding the best direction for a bird escape from a radiation (function of 3 parametres)

I have this question. My bird is is in this point: (1,1,3) in 3D, and the source of the radiation is in that point too. What is the direction for her to fly from that point, if it wants to minimize ...
2
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1answer
22 views

Number of components needed for 3D rotation

Using Euler angles, a 3D rotation can be expressed using 3 real numbers. Using quaternions, 4 are needed and using rotation matrices 9. Is it possible to express a 3D rotation using less than 3 real ...
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0answers
34 views

Camera calibration: how does checkerboard size/numbers/placement affect accuracy

I am trying to calibrate a camera using a checkerboard by the well known Zhang's method followed by bundle adjustment, which is available in both Matlab and OpenCV. There are a lot of empirical ...
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1answer
26 views

Points on two skew lines closest to one another

Given two skew lines defined by 2 points lying on them as $(\vec{x}_1,\vec{x}_2)$ and $(\vec{x}_3,\vec{x}_4)$. What are the vectors for the two points on the corrwsponding lines, distance between ...
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2answers
69 views

Find perimeter and angle of triangle using three 3d vectors .

Given the following, three vectors: $$\vec{a} = 3\mathrm{i} - 2\mathrm{j} + 5\mathrm{k}\\\vec{b} = \mathrm{i} - 6\mathrm{j} + 6\mathrm{k}\\\vec{c} = 2\mathrm{i} + 3\mathrm{j} - \mathrm{k},\\$$ find ...
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2answers
67 views

Rotate a unit sphere such as to align it two orthogonal unit vectors

I have two orthogonal vectors $a$, $b$, which lie on a unit sphere (i.e. unit vectors). I want to apply one or more rotations to the sphere such that $a$ is transformed to $c$, and $b$ is transformed ...