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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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
22 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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29 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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2answers
38 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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29 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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16 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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54 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
43 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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15 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
34 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
26 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
39 views

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
42 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
30 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 as illustrated here. When the surface is viewed from the side as shown here, such that the Y axis is ...
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5 views

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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22 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
32 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
30 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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16 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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24 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
55 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
31 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
30 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
10 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
27 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 ...
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12 views

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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60 views

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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19 views

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
30 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 ...
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1answer
31 views

How to calculate the different angles the normal of a plane makes with the different axis in a 3D space?

I am working with point clouds and I need to find all of the angles (actually only that ones that the normal forms with the x axis and the z axis) of the normal in each point in my point cloud. The ...
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3answers
1k views

Why is wolfram alpha plotting this differently?

I have an equation for a cylinder as $x^2+(y-b)^2=a^2$ for some $a$ and $b$. so I just plugged in $b=2$ and $a=1$ and tried to plot it using wolfram alpha, and the 3D plot looked like half a cylinder, ...
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Find the equations of the lines of greatest slope and least slope

Find the equations of the lines of greatest slope and least slope on the plane $3x-4y+5z-5=0$ drawn through the point $(1,2,2)$ given that the plane $4x-5y+6z-6=0$ is horizontal. I do not need ...
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1answer
20 views

3D calculate new location of point after rotation around origin

I've tried to boil down my problem as much as possible. I've got two questions, but really I'd be satisfied enough just knowing how to accomplish the first one. I'm looking to do this programatically, ...
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20 views

Finding a x-y-z equation based on data

I have a large number of x, y, z point values. I am wanting to know the equation that represents these values I have in hand. This equation I am looking for should be a fit that will represent these ...
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50 views

Trajectory on a sphere

I've asked a question before concerning a parallel problem, and I read a wikipedia page on spherical caps (Nominal Animal), which gave me an idea to do the following: I have the Cartesian coordinates ...
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1answer
17 views

Set of transformations to get a point on the X-Axis.

I have a two points in the 3D coordinate space. Now, I want to send one of the points to the origin and make it (the line joining the two points) align with the X-axis and get the transformation ...
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16 views

How to determine the equation of a line in 3D, given a known point and an orientation?

Ultimately, I need to find the intersection of a ray with a plane, given the origin of the ray, and its orientation. It seems I'll need to first define a line in parametric form, but I'm not quite ...
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1answer
14 views

Position of point between 2 points in 3D space

I need to find the position v3 between the given points v1, and v2 and a given distance d in 3D space. I came across this post: Position of point between 2 points which is basically what I need but ...
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1answer
35 views

How to find the closest point to three vector lines?

So this is the question here I know the angles $A$ and $B$ for each individual, and their positions in longitude and latitude (assuming height of person $z =0$), am I correct in thinking that for any ...
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2answers
24 views

Ray intersecting a quad mesh

I am trying to solve the math behind rendering a quad-mesh surface. MatLab for instance can take a regularly spaced (x,y) grid with arbitrary third-dimension (z) values, treat each four neighbouring ...
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1answer
31 views

figure-8 knot complement

The figure-8 knot seen as a 2-bridge knot with two maxima and two minima of the height function, has a complement in $S^3$ with one 0-handle,two 1-handles, two 2-handles and a 3-handle which cancels ...
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1answer
61 views

Cartesian equation cylinder along a line

What is the cartesian equation for a cylinder along a line in a 3d space? Imagine two points in a 3d space, (Xc,Yc,Zc) and (Xp,Yp,Zp). The equation for the line connecting these points is: ...
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1answer
18 views

Why and how two skew vectors' cross product gives normal vector of plane containing one of those vectors

I got a question which says : Given $$\vec{v} = <1,0,-1> $$ and line $$L_1 : (1-2t)\vec{i}+(4+3t)\vec{j}+(9-4t)\vec{k}$$ Find an equation of plane $P$ which is parallel to the vector ...
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13 views

Converting homogeneous projection matrix

I have a 4x4 homogeneous projection matrix which converts 3D world space coordinates into 2D image coordinates + a depth value. It is of the form $\mathbf{H} = \begin{bmatrix} m_{1,1} & ...
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14 views

properties of a Varignon parallelogram from a skew quadrilateral,

I was editing https://en.wikipedia.org/wiki/Varignon's_theorem and that made me wonder. At the moment https://en.wikipedia.org/w/index.php?title=Varignon%27s_theorem&oldid=713877982 the ...
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1answer
15 views

Need help understanding what the curve made by two or three intersecting surfaces looks like

I have trouble visualizing what curves are traced out by the intersection of multiple surfaces in $R^3$. for example take the parametric equations $ <cos(t),sin(t),sin(t)$ > Clearly this would ...
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1answer
54 views

Compute weight of a point on a 3D triangle

Let's say I have a 3D triangle $ABC$ with $x$, a random point on it, I know the coordinates of each one of the points. Each of $A$, $B$ and $C$ have a "weight" which is a decimal value between 0 and 1 ...
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1answer
41 views

Is there a good program to download or online for plotting certain functions in 3d?

I am interested in a program that can plot me, without too much trouble shapes in 3d, when I type in the function. For example a elliptical paraboloid and an ellipse of the same time, so I can analyze ...
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24 views

Triangle verticies given 2 points, all angles and sides (3D)

--Visual Image for the problem-- Alright, I hope that you are able to view the visualization of the problem in the link above. If not, I'll give a quick run-down of the information I have as well as ...
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1answer
31 views

Helix along vector in 3D space

Let's say I have a random vector, for example <1, 3, 5>. What would the function be for a helix that spirals around/along this vector with a given radius?