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.

learn more… | top users | synonyms

0
votes
1answer
33 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 ...
1
vote
1answer
36 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 ...
0
votes
1answer
12 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 ...
3
votes
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 ...
0
votes
0answers
15 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 ...
1
vote
0answers
67 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 $(-7,-1,-9)$. ...
0
votes
0answers
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 ...
2
votes
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 ...
0
votes
1answer
34 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 ...
6
votes
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, ...
1
vote
0answers
42 views

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 ...
2
votes
1answer
25 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, ...
0
votes
0answers
24 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 ...
0
votes
0answers
58 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 ...
0
votes
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 ...
-1
votes
0answers
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 ...
0
votes
1answer
16 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 ...
2
votes
1answer
39 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 ...
1
vote
2answers
35 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 ...
2
votes
1answer
33 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 ...
0
votes
1answer
79 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: ...
0
votes
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 ...
0
votes
0answers
14 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} & ...
0
votes
0answers
15 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 ...
0
votes
1answer
16 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 ...
2
votes
1answer
58 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 ...
1
vote
1answer
42 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 ...
0
votes
0answers
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 ...
1
vote
1answer
32 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?
0
votes
1answer
41 views

How to convert 2D coordinates to 3D coordinates?

I am writing some software for image processing where a user can just draw something (e.g. a cube) in paint and the software will give you the 3d coordinates of the corners on that drawing. What would ...
0
votes
0answers
12 views

Distance between a point and a 3D figure

If I have some basic 3D shapes like rectangular prisms, cylinders and spheres (whose positions, orientations and dimensions are fully known), what is the simplest way of finding the shortest distance ...
0
votes
1answer
21 views

Find third vector with opposite deviation

Say there are two unit vectors a and b. I want to find unit vector c such that the deviation between c and a is the opposite to the deviation between a and b. The angles between c and a, and a and b ...
0
votes
1answer
28 views

Concatenating two Rotation-Matrices

I have two $2\mathrm{D}$-planes in $3\mathrm{D}$-space with orientation parameters expressed as rotation $R_1$ and translation $T_1$ and rotation $R_2$ and translation $T_2$ with respect to some ...
0
votes
1answer
29 views

How to find the amount of degrees to rotate a vector to be 90 degrees another vector?

I have a vector V that rotates around an axis K and a vector N all in 3D space. I need to find how much to rotate the vector V around S so that it lies 90 degrees to N. So far I have been doing it ...
0
votes
1answer
18 views

How can the angle between any two azimuth dip pairs be found?

The order of rotation is azimuth then dip. I've tried pythagoras style answers but testing showed it was the wrong approach. How can I find the angle between any two pairs?
1
vote
1answer
36 views

Write the equation $4x^{2}+4z^{2}=5$ in spherical coordinates.

Write the equation $4x^{2}+4z^{2}=5$ in spherical coordinates. I used the facts that $$ \begin{align} x&=ρ\sin\theta\cos\phi\;,\\ z&=ρ\cos\phi\;, \end{align} $$ And ended up with: $ 4 (ρ^2 ...
1
vote
1answer
45 views

Variance of $3$-dimensional vectors

I am currently optimizing some code and thus, I want to replace an inefficient OpenCV function, which calculates a covariance matrix. The thing is, that I only need the trace of this covariance ...
-2
votes
1answer
36 views

Give a geometrical interpretation of the intersection of the planes with equations [closed]

Give a geometrical interpretation of the intersection of the planes with equations \begin{align} &x + y − 3 = 0\\ &y + z + 5 = 0\\ &x + z + 2 = 0 \end{align} what is a geometrical ...
0
votes
0answers
33 views

Finding angle between y axis in two rotated coordinate systems

I basically have two coordinate systems that have the same origin, and can measure the coordinates of a vector (but only one) in respect to both of them. I need to calculate the angle between the y ...
1
vote
2answers
35 views

Given a band of $m$ opaque squares arranged in a circle, can we find a viewpoint from which we see exactly $m/2-1$ squares?

Given a band of $m\ge 3$ opaque squares arranged in a circle, can we find a viewpoint (i.e. a point on a sphere centered at the midpoint of the circle with a radius large enough to see the whole ...
10
votes
1answer
241 views

How many spheres can fit in this box?

HASELBAUER - DICKHEISER TEST #15: What is the maximum number of one inch-diameter spheres that can be packed into a box ten inches square and five inches deep? My attempt to solve this: If i ...
0
votes
2answers
69 views

Geometrical interpretation of solving a $3 \times 3$ system of equations

Solve the following system of equations and give a geometrical interpretation of the result. \begin{align*} x + y + z &= 6\\ 2x + y − 3z &= -5\\ 4x − 5y + z &= −3 \end{align*} I know that ...
2
votes
1answer
42 views

find 3 angles to rotate vector to align with second vector

First I would like to say that I have seen posts such as that found here: Calculate Rotation Matrix to align Vector A to Vector B in 3d? As well as formulas such as: ...
0
votes
0answers
18 views

Visible faces of a polyhedron $P$ on a path of viewpoints on the unit sphere looking at the center of $P$

Let $P$ be an opaque polyhedron. Assuming parallel projection, let's define a viewpoint to be a point on the unit sphere around the center of $P$. Let's say that two viewpoints $v_1$ and $v_2$ are ...
0
votes
1answer
19 views

3D Denjoy–Riesz theorem

The Denjoy–Riesz theorem states that every totally disconnected subset of $\Bbb R^2$ is the subset of a Jordan arc. Is this true in $\Bbb R^3$? Originally I thought Antoine's necklace would be a ...
8
votes
4answers
184 views

Show that every rotation in $\mathbb{R^3}$ can be written as the product of two rotations of order 2.

Show that every rotation in $\mathbb{R^3}$ can be written as the product of two rotations of order 2. Here's my attempt at a solution: We know that any rotation in $\mathbb{R^3}$ can be ...
0
votes
0answers
25 views

Relation between focus and camera intrinsic parameters

Does a focus tuning affect the camera intrinsic parameters? More precisely, if the focus of a camera is changed, does the camera intrinsic parameters matrix remain unchanged? Apparently, since this ...
1
vote
3answers
41 views

Conclusion that can be drawn from 4 points in space whose angles are $90^{\circ}$

Four points A, B, C and D are in space such that angles $A\hat BC, B\hat CD, C\hat DA$ and $D\hat AB$ are all right angles, then A, B, C, D cannot be coplanar A, B, C, D are necessarily coplanar. A, ...
0
votes
1answer
22 views

Rotating prism in 3 dimensional space

Say you have a rectangular prism, whose sides can be expressed as specific domains and ranges of 3 dimensional planes. I'm trying to calculate the new position of the prism after a series of ...
1
vote
0answers
12 views

triangulation of a surface, adapted to curvature

This is about my printed models of mathematical objects. All of the designs that I've published so far consist of grids of bent ‘rods’, and in most of them the spacing of vertices depends on the ...