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
15 views

Paramaterization of paraboloid and plane.

Consider the paraboloid $z=x^2+y^2$. The plane $2x-4y+z-6=0$ cuts the paraboloid, its intersection being a curve. Find "the natural" parameterization of this curve. I have set each equation equal ...
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2answers
20 views

Find the point at which the line intersects the plane. Is the intersection perpendicular?

Find the point at which the line $$x = 1 - t \\ y = 3 + t \\ z = 7 + 2t \\$$ intersects the plane $$x + 2y + z = 20$$ Is the intersection perpendicular? I have found the point of intersection to be ...
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0answers
22 views

**Location** of shortest distance between two skew lines in 3D?

I can find the shortest distance $d$ between two skew lines $\vec{V_1}$ and $\vec{V_2}$ in 3D space with ...
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0answers
13 views

Stellating the Octahedron

I am trying to create a very primitive animation/demonstration that shows the stellation of an octahedron to yield the stella octangula. Unfortunately, it seems that the mental image I have for ...
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0answers
9 views

What is the perspective projection of a 3d point relative to a quarternion encoded camera?

I'm representing a camera on the cartesian space as a tuple of a 3d point (position) and a quarternion (rotation). I get the front, right and up vectors of the camera by applying the quaternion to the ...
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1answer
31 views

How do I represent a Mobius Band Triangle Parametrically

I am trying to describe a Mobius band in the shape of a triangle like this: parametrically in terms of its $x$, $y$, and $z$ functions. Is this even possible? I know a basic mobius strip can be ...
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2answers
50 views

What are the Eigenvectors in the following matrix?

I have the matrix A: \begin{bmatrix} 4 & 2 & 2\\ 2 & 4 & 2\\ 2 & 2 & 4\\ \end{bmatrix} I found $\lambda I_n - A$ to be: \begin{bmatrix} (\lambda -4) & -2 & -2\\ -2 ...
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1answer
44 views

Determining the angle of a photograph containing known parallel objects/lines.

I have a photograph of a house and a window taken at an angle. I'm trying to determine the angle at which the photograph was taken. The house has wooden siding that can be safely assumed to be ...
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0answers
15 views

Direction of polyline curvature [closed]

Is it possible to estimate the direction of curvature of a curve or polyline in the 3D case? In the 2D case the description clockwise and counterclockwise makes sense. Is there any notation for these ...
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1answer
34 views

Finding extreme point of a set determined by two planes in $\mathbb R^3$

Problem asks to find a extreme point the set $\{(x,y,z) \mid x-2y \leq 3 , 2y+3z \geq 4 \}$. But I don't think it has a extreme point, because it is intersection of two hyper planes in 3D, which ...
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1answer
36 views

Calculating the volume of a surfboard

I'm building a website for a client in which customers can customise the shape of their board (curvature, length, width, thickness, and so forth) and the client has asked if we can calculate the ...
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1answer
24 views

How to get circle points in 3d given a radius and a vector orthogonal to the circle area?

I already know how to get a point on a circle (here), but I need a circle in 3d which should be the orthogonal to a given vector. I got: Angle in degree/radians Circle radius Orthogonal vector I ...
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1answer
14 views

Fit a plane in data set which passes through maximum number of points in this data set and disregards noise

I have a set of 3D points (cartesian coordinates). I want to find the best fit plane. As I understand, there are many algorithms to get a best fit plane. One of them is this by Dan Couture. This fits ...
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2answers
38 views

Showing that the image of a curve lies on a surface?

I am looking for an intuitive explanation to a problem in one of my practice tests. I'm given a parameterized curve from $\Bbb R$ to $\Bbb R^3$, called ${\bf r}(t) = (\sin t \cos t, \cos^2 t, \cos ...
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0answers
28 views

. Find the projection of the triangle on the coordinate planes.

Given the following, three vectors: a⃗ =3i−2j+5k b⃗ =i−6j+6k c⃗ =2i+3j−k Relative to cartesian coordinate systems with origin O. I calculated the sides to be 4.58,11.45 and 7.87. I also calculated ...
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1answer
23 views

Move point onto circle-outline in R3

I need to do all this in $\mathbb{R}^3$ a plane by $n \cdot p = -k$ a circle within this plane by radius = $r$ and center = $c$ a point $a$ on the inside on the circle (on the plane) a direction ...
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1answer
15 views

Scaling 3D-Points in Plane

I have some points (3D) all on the same (known) plane. Now I want to scale these points within the plane as opposed to the whole 3D space (as in scalar-multiplication of points in 2D space) Is there ...
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1answer
29 views

Calculate 3D Vector out of two angles and vector length

What is the easiest way to calculate vector coordinates in 3D given 2 angles vector length? Input: Angle between X and Y axis: $$\alpha \in [0, 360).$$ Angle between Y and Z axis: $$\beta\in [0, ...
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0answers
10 views

3D Linear-geometry with coordinates

Truncated pyramid has a smaller opening with sides ABCD, and a bigger opening with sides FGHE ( where F is o top of A, G on top of B, H on top of C and E on top of D). This figure has 3D coordinate ...
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1answer
67 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
31 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
38 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
44 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
51 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
57 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
22 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
394 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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1answer
42 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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2answers
77 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
49 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
44 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
25 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 $Ax+By+Cz+d=0.$ ...
3
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1answer
71 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
24 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
49 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
46 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
83 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 ...
1
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1answer
37 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
29 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
22 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
71 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
12 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
21 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
47 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
26 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
68 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
32 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 ...