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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Progressively embed ( = superscribe?) and immerse …

$\mathbb R^1$ is superscribed/embedded on $\mathbb R^2$ and $\mathbb R^2$ in turn immersed in $\mathbb R 3$. Graph of a line $ x(u,v), y(u,v), z(u,v),f(u,v)=0 $ is superscribed or embedded on ...
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79 views

Euler angle to direction vector which is right?

I tried to implement a first person shooter camera using Euler angles with the order pitch-->yaw rotation.(pitch is rotate round X axis, yaw is rotate round Y axis) Many tutorial gave the formula ...
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1answer
38 views

Geometric Optimization

In 1990 W. Kuperberg conjectured that it is impossible to have seven infinite mutually disjoint unit cylinders all touching a unit sphere. As a first step towards a solution I would like to answer the ...
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25 views

Does 3D euclidean space allows vector sum in 2 dimensions?

Is this right to add two orthogonal vectors to to get one vector, using this vector in calculations and after getting results, decomposing result vector to get orthogonal components? I am a programmer,...
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1answer
33 views

Angle between planes challenging Question

The plane $r.(a,3,5)=10$ is inclined at an angle of $45^\circ$ to the plane $r.(-5,1,4)$ Find the value(s) of $a$ up to $2$ decimal places. I attempted this problem by forming an equation where I ...
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1answer
31 views

How to programmatically find dodecahedron's edges as couple of vertices

I'm a newbie here, and I'm not a mathematician, so I hope you could help me. Online I found that the 20 vertex of a dodecahedron can be easily expressed as: ...
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1answer
25 views

Finding the radius of a sphere inscribed in a right prism

We have right prism $ABCA_{1}B_{1}C_{1}$ and points $E$, $D$ such that: $A_{1}E:EB_{1}=B_{1}D:DC_{1}=1:2$ The distance between lines $AE$ and $BD$ is $\sqrt{13}$. Find the radius ...
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1answer
75 views

Trigonometric Word Problem in 3D

The question I am having trouble on is as follows: "As an Expert Mathematics Witness, you have been presented with a Ballistics Report, and a Police Report as your evidence. Use the information ...
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2answers
35 views

Calculating cosine of dihedral angle

Let $O,A,B,C$ be points in space such that $\angle AOB=60^{\circ},\angle BOC=90^{\circ},\angle COA=120^{\circ}$ Let $\theta$ be the acute angle between the planes $AOB$ and $AOC$. Find $\cos\theta.$ ...
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1answer
20 views

How to calculate rotation quaternion between two orientation quaternions?

I have some device (3D pointer) connected to my computer which returns it's position (in cartesian XYZ system) and orientation (in quaternions). I receive this values about 30 times/sec. Now I need ...
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10 views

What is the formula for a cone built from two arbitrary vectors?

Suppose there is an arbitrary vector in 3D space : $\vec v = (a,b,c)$ , starting from point $(x_0,y_0,z_0)$ which is the center or 'spine' of the cone. There is also the vector $\vec u = (h,i,j)$ , ...
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27 views

Calculate a normal to vector lying on a plane formed by $2$ vectors

Let's presume I have two vectors $V_1$ and $V_2$. As far as I understand normal to a vector is all vectors lying on a plane perpendicular to it. What I need is a normal to $V_1$ that lies on a plane ...
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1answer
34 views

Converting a 3D line's equation into vector form.

How exactly can I convert the below equation into the vector form? (i.e. V(i,j,k) form or $a*i+b*j+c*k$ form): $$\frac{x-5}{-10}=\frac{y-3}{-6}=\frac{z-2}{-4}$$ I'm actually trying to find the angle ...
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1answer
25 views

Find cone-plane intersection points in a construction

I have two points on the X axis, A and B, which are connected to the two points, C and D on the sketch plane parallel to XY plane. I have a point E which lies at distance h from D point in Y direction ...
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10 views

Transformation of 3D vectors to other planes in 3D

Suppose I have a set of points A, B, C, D, E, F... defined by the 3D vectors AB, AC, AD, AE, AF, AG etc. I can describe the geometry of these by defining them in an arbitrary plane e.g. z = 0 ...
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1answer
15 views

Determine plane rotation in 3D when only knowing the length of it sides?

For an assignment in computer graphics, i need to be able to determine a plane's rotation by just holding it in front of my webcam. So basically I only got 2D coords of the plane's points. I searched ...
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2answers
39 views

Confusion in Total faces in Cone: 3D

I have checked in many places about how many faces does a Cone have.. As per this link. There is 1 face in Cone As per this link, there are 2 faces in cone As per this Video, A Cone has one face ...
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20 views

Finding extremas of a function

$f(x,y) = xe^{-{x^3}+{y^3}}$ and I am to find extrema values of that 2-variable function. I come up with the point $P(3^{1/3},0,f(3^{1/3},0))$ is its only critical point. I tried to apply second ...
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2answers
49 views

Quaternion angle - Opengl rendering

I have been using a 6dof LSM6DS0 IMU unit (with accelerometer and gyroscope). I am trying to calculate the angle of rotation around all the three axes and Render a 3D cube using opengl to immitate the ...
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0answers
12 views

Calculate 2D into 3D coordinates by given edge-points of Polygon

im drawing an image with a orthogonal projection matrix and need to calculate a 2D Point back into its 3D Point. I have a Polygon and i know its 3D-World and 2D-Screen edge coordinates. Now i want to ...
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1answer
32 views

How to understand rotation around a point VS rotation of axes?

I am puzzled about linear transformation and coordinate transformation, any help will be appreciated. From wiki rotation matrix, we know rotates points in the xy-Cartesian plane counter-clockwise ...
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51 views

Convert direction vector to euler angles

How do I convert a direction vector to euler angles? I need to change the position of a character's head in a Java program that I'm writing. The pose of the head uses euler angles. I know the ...
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1answer
28 views

Sketching the surface $z=\frac{x^2y}{3}$

I am trying to sketch the part of $x^2+y^2=9$ which lies in the first octant between the surfaces $z=0$ and $z=\frac{x^2y}{3}$. I understand that $x^2+y^2=9$ is a cylinder with radius three, ...
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33 views

Change of Basis between linear Transformations

I am trying to get a better understanding in change of basis with matrices and linear transformations, therefore I am using several linear Transformations $^{i-1}A_i=\begin{bmatrix} \cos\theta_n ...
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51 views

Prove that 3d rotation is linear

In a 2d space, a transformation is linear if $f(v+w) = f(v) + f(w)$ and $f(kv) = k*f(v)$, and rotation preserves addition so it is linear. In a 3d space, similar rules apply: $(x, y, z) + (l, j, k) = (...
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36 views

3D bend equation derivation.

This is how the bend work: (The number is the angle) I was searching for an equation to bend an object in a specific axis and I found one,It worked pretty well,but unfortunately I don't know why it ...
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17 views

How to determine what kind of curve in 3d geometry

I am having difficulty in determining type of given curve in 3d geometry.Is there any test in which I can differentiate between 1) Circle 2) Cone 3) Cylinder 4) Circle When equation of 3d curve ...
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97 views

Rotating one 3d-vector to another only by using rotations about the coordinate axes.

If I have a vector v=(x,y,z) and would like to transform another vector u by using only rotations about the coordinate axes to be in the direction of v, how can I find required angles and the order of ...
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3answers
44 views

Shortest Distance between planes

This is a question which puzzled our entire math class including our teacher, I'm referring to part (b), we're fine with part (a). We don't understand the reason for taking the dot product and the ...
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19 views

find the length of the path traversed by a particle

Let the position of a particle in three dimensional space at time t be (t, cos t, sin t). Then the length of the path traversed by the particle between the times t = 0 and t = 2π by my approach i'm ...
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1answer
35 views

$O$ is a point inside cube such that $\vec{OA}+\vec{OB}+\vec{OC}+\vec{OD}=\vec{OM_1}$

Given a cube $ABCDA_1B_1C_1D_1$ with lower base $ABCD$ and upper base $A_1B_1C_1D_1$ and the lateral edges $AA_1,BB_1,CC_1,DD_1$ respectively. $M$ and $M_1$ are centres of the faces $ABCD$ and $...
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1answer
33 views

How to calculate top base area with bottom base area and height of frustum?

I have the following frustum The bottom base area $A_1$ is known, the top base area $A_2$ is unknown. We know this about the frustum We know the height $h$ and the angle $a$ of the frustum. Can ...
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2answers
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How would the volume of a frustum with irregular polygon area be calculated?

I want to calculate the volume of this shape, it's basically a frustum with an irregular polygon base. The bottom area $A_1$, the height of the frustum shape $h$,the sideways distance between $A_1$ ...
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2answers
44 views

What would moving in the 4th dimension look like in 3d?

I've been reading "Shape of Space" and watching videos from the videogame Miegakure. Both talk about >3 dimensional space. I'm not sure if Miegakure's interpretation is accurate and it's limited to ...
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1answer
38 views

How to derive 2D equation representing minimums of constrained 3d equation?

I have a 3D (multivariate) function f(x,y) which can be represented as a surface with constraints. When the surface is viewed from the side (as below), such that the Y axis is not visible, there is ...
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Projecting a 3D point to a fisheye plane

I am trying to calculate if a point in 3D space is in front of my fisheye camera, so looking at the OpenCV documentation (I'm not actually using OpenCV, however), we have: $a = x/z$, $b = y/z$, $r^2 =...
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27 views

Difference between a Möbius Strip and a Simple Surface

I am trying to distinguish between a Möbius strip and a surface that has no separations, holes and a connected boundary (homeomorphic to a disk or a half-sphere). Since a Möbius strip also has all the ...
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2answers
35 views

Transforming integral in cylindrical coordinates into cartesian.

I am trying to transform the following integral to an integral in cartesian coordinates. $$\int^{2\pi}_0\int^1_0\int^{\sqrt{1-r^2}}_0r \ dzdrd\theta$$ I cannot really visualise how the region enclosed ...
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1answer
34 views

how to generate Bezier curves from 3D mesh?

after generating 3D mesh (car chassis) By : RGB-D camera (Like : Kinect - Intel Real Sense etc ... ) and extracting feature lines on the surface of the 3D mesh. I need to generate the Bezier curves ...
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23 views

How to find out position of a point, given a vector, projection on the vector, and angle.

I need to find the position of a point q given a vector $\vec{se}$, projection of q on $\vec{se}$, and angle $\theta$ between $\...
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0answers
28 views

Perpendicular Vectors in 3D space

I was wondering whether given two Vector's v0 and v1 whether I could find the two perpendicular vectors at a given distance, d, from v1, perpendicular to the v0/v1 line. I know that v0 and v1 will ...
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2answers
60 views

Dynamics of a three dimensional system

I have a dynamical system in three dimensions given by: $\dot x = (1-x^2-y^2-z^2)x+xz-y$ $\dot y = (1-x^2-y^2-z^2)y+yz+x$ $\dot z = (1-x^2-y^2-z^2)z-x^2-y^2$ I analyzed the system by first finding ...
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1answer
34 views

Bounding inequalities in three dimensions

I want to write $z^2 \ge x^2 + y^2$, $x^2 +y^2 +z^2 \le 1$ and $z \ge 0$ in the form $$a \le z \le b, \quad c(z) \le y \le d(z), \quad f(y,z) \le x \le g(y,z)$$ or $$a \le z \le b, \quad c(z) \le ...
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1answer
43 views

Calculating a quaternion that represents a given rotation

This is the first time I'm attempting to do a quaternion and I am not quite getting the concept. This is part of a 3 calculation homework question The initial question is Given a 3-D point at ...
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1answer
14 views

Component of vector perpendicular to a given plane

I have two vectors $a\hat j$ and $b\hat i$ and the plane $x+y+z=1$. I want to find the components of the vectors perpendicular to the plane. Now as far as I know, the unit normal vector to the plane ...
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1answer
30 views

Understanding Hempel's proof of uniqueness of cube with handles

In Hempel's 3-Manifolds book, Theorem 2.2 says that if $P$ and $Q$ are two cubes, both with $n$ handles, and both are orientable, then they are homeomorphic. He defines a cube with handles as a 3-...
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Part of 3D annulus (cylinder)

Is there a special name of an object that is basically a 3D annulus? I mean a case of a simple 2D annulus that is "elevated" straight from the ground up. A short tube/pipe could be an example of such ...
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Show that the co-ordinates of the point on the join of $(-3, 7, -13)$ and $(-6, 1, -10)$ which is nearest to the intersection of the planes

Show that the co-ordinates of the point on the join of $(-3, 7, -13)$ and $(-6, 1, -10)$ which is nearest to the intersection of the planes $3x-y- 3z + 32 =0$ and $3x+2y-15z= 8$ is $(-7,-1,-9)$. ...
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Find the equivalent iterated integral.

Given : $$\int_0^1 \int_0^{1-x^2}\int_0^{1-x} f(x,y,z) \,dy dz dx $$ I need help with this integral, since there is nothing in yz plane so I solved both equations for y and z. My attempt:(Is it ...
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1answer
33 views

Find the co-ordinates of the point on the join of two points which is nearest to the intersection of two planes

Find the co-ordinates of the point on the join of $(-3, 7, -13)$ and $(-6, 1, -10)$ which is nearest to the intersection of the planes $3x-y- 3z + 32 =0$ and $3x+2y-15z= 8$. Please give me an ...