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Questions tagged [3d]

For things related to 3 dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For non-planar geometry, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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Heesch numbers in 3D

At the Tiling Database there are 3, 20, 198, 1390 (A054361) non-tiling polyominoes of order 7 to 10. In 3D, solids with a particular Heesch number don't seem to be well known. Glenn Rhoads found ...
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0answers
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Separation of variables to solve Laplace's equation for the V in a cube 3D rectangular coordinates

Watch this videoLaplacian in 3D and tell me whether $C_{n,m}$ missing y in the argument of $\cosh{\sqrt{(\frac{n\pi}{a})^2+(\frac{m\pi}{a})^2}}$ in the denominator. So the final answer is $V_{(x,y,z)}=...
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1answer
19 views

Sum of all values along a line

This picture is a representation of a problem I've been trying to tackle for a while now. Basically, I've got a grid with dimensions Latitude, Longitude, and Altitude. Time is also a dimension, but I'...
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2answers
20 views

Check if 3D point is inside sphere

I know there is a pretty simply way to check if a 2D point is inside a circle, I wanted to know how to do there same but in the 3rd dimension. The variables are the point's X, Y, Z and the sphere's 3D ...
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2answers
15 views

3D Vector Rotation Matrix with Radians

I have been working on a simple C++ vector library and needed 3D rotation so I found these 3D rotation matrices on Stack Overflow: ...
11
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2answers
107 views

Probability that $\vert x\vert +\vert y\vert +\vert z\vert +\vert x+y+z\vert=\vert x+y\vert +\vert x+z\vert +\vert y+z\vert$

Real numbers $x, y$, and $z$ are chosen from the interval $[−1, 1]$ independently and uniformly at random. What is the probability that $$\vert x\vert +\vert y\vert +\vert z\vert +\vert x+y+z\vert=\...
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1answer
34 views

Two identical cubes are stacked inside a cone of height $34$ and radius $3$. What is the volume not taken up by the cubes?

Two identical cubes are stacked and they are placed inside a cone. The height of the cone is $34$ and the radius is $3$. The cubes have the same height. What is the volume of the space not taken up by ...
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3answers
33 views

The plane $\frac{x}{2}+\frac{y}{4}+\frac{z}{3}=1$ intersects the $x$, $y$, and $z$ axes at points $P$, $Q$, and $R$. Find the area of $\triangle PQR$.

The plane $\frac{x}{2}+ \frac{y}{4} +\frac{z}{3}=1$ intersects the $x$, $y$, and $z$ axes at points $P$, $Q$, and $R$. Find the area of $\triangle PQR$.
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0answers
41 views

General form of quadric surfaces

The general form of quadric surfaces is $$Ax^2 + By^2 + Cz^2 + Dxy + Eyz + Fxz + Gx + Hy + Iz + J = 0$$ I want to classify all of the possibilities including degenerate cases with the help of ...
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0answers
24 views

Rotation between two ellipsoids?

Suppose I have two ellipsoid. One ellipsoid is inside of another ellipsoid. I know all 3 principal axis of both ellipsoid. Now, I can think of 3 possibilities that smaller ellipsoid can be placed ...
5
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1answer
80 views

Show that $AB=CD $.

Let $ABCD $ a tetrahedron s.t. $ \angle ABD=\angle BDC $ and $ \angle BAC=\angle ACD$. Show that $AB=CD $. I construct $DD_1, CC_1 \perp AB $, $C_1, D1\in AB $ and $AA_1, BB_1\perp CD $ , $B_1, A_1\...
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2answers
40 views

Linear isometry and its trace

(We're in $\mathbb{R}^3$) What can we say about type of linear isometry $F : \mathbb{R}^3 \to \mathbb{R}^3$ if trace of $\mathrm{m} (F)$ is $-2$ or $\frac{1}{\sqrt{2}}$ or $\sqrt{2}$? Which one of ...
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0answers
31 views

angle made by vector with the plane

Let the angle between the vector a and vector b is $\pi/6$, between vector b and vector c is $\pi / 4$ and between vector a and vector c is $\pi /3$. Then what is the angle made by vector with the ...
2
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1answer
34 views

Triple integral : volume

I need to calculate the volume between $x^2+y^2\le z^2-1$ and $2x^2+y^2+z^2\le 2$. So It's a hyperboloid of two-sheets intersected with an ellipsoid. their intersection leads to: $3x^2+2y^2=1$ which ...
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0answers
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What are the properties of an 3d ellipsoid? [closed]

I have 3d images of biological cells. I am assuming each cell is analogue of an 3d ellipsoid. So, now I can get length of major axis, minor axis, medium axis, volume, surface area and orientation. ...
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1answer
22 views

How to map point from one csys (coordinate systems) to another csys

I have two $3$-dimensional coordinate system csys1, csys2. I have a known point in csys1 called $p_1(x,y,z)$. I want to define the same point with respect to csys2.(i.e. find a $p_1(x,y,z)$ with ...
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1answer
20 views

Finding a quantity between two points in three dimensional space

I'm obligated to let you know I've cross posted this on stack overflow earlier today but decided after some comments that I this question is probably less one of code and more one of the mathematics ...
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0answers
16 views

Cutting 3D Point cloud and interpolate between points

I have the following data https://www.mediafire.com/file/f8tz1zbpxvyvko7/Waltersdorf_F3.csv/file Which is a 3D point cloud. I can visualize it correctly, but I want to do Cuts like the ones in the ...
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1answer
37 views

Prove the condition $a+b+c=0$ for three mutually perpendicular generators of a cone.

Question: Prove that for the cone $$ax^2+by^2+cz^2+2fyz+2gzx+2hxy=0$$ having three mutually perpendicular generators, $a+b+c=0$. Proceed: If the cone has three mutually perpendicular generators, then ...
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0answers
9 views

Calculating magnitude of 3D vector in specific circumstance.

I’m writing a program where there exists points in space and each point is at the exact center of a cube. For each point, I have two angles (vertical and horizontal rotation, or pitch and yaw) as well ...
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2answers
38 views

Can i find a 3D function given some points?

is it possible to find a 3D function given a set of data points? i tried plane-fitting it did not work, too chaotic for a plane. I am trying to find a 3D equation that cover most of points, how can ...
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3answers
94 views

Show that planes $x+2y+3z=8$ and $2x+3y+4z=11$ intersect in a line coplanar with $\frac{x+1}{1}=\frac{y+1}{2}=\frac{z+1}{3}$

Question is Show that the line of intersection of the planes $$ x + 2y + 3z = 8 \quad\text{and}\quad 2x + 3y + 4z = 11 $$ is coplanar with the line $$\frac{x+1}{1}=\frac{y+1}{2}=\frac{z+1}{3}$...
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1answer
27 views

Connecting points of triangles in 3D space (help needed)

First time caller here and let me say first, I am not a mathematician, but a science / management writer instead. Today I am very interested in this article, here on the stack: Spreading points over ...
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2answers
87 views

Viewing a circle from different angles - is the result always an ellipse?

Take a piece of rigid cardboard. Draw a perfect circle on it. Hold it up, and take a picture, with the cardboard held perpendicular to the direction we're looking. You get a photo that looks like ...
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2answers
15 views

How to turn a function r(t) into a quadratic surface equation?

I encountered a question where I have to match some given quadratic surfaces with some given functions r(t). I have the solution below but what I don't get is how they got the equations using the ...
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1answer
60 views

Volume and surface area of sphere, cone, cylinder etc

Why isn't the volume of a sphere: $\pi$$^\text{2}$$r^\text{3}$, instead it is $\frac{4}{3}$$\pi$$r^\text{3}$? Like wise the surface area is 4$\pi$$r^\text{2}$and not 2$\pi$$^\text{2}$$r^\text{2}$. ...
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1answer
22 views

Finding weight in Megagrams (Mg) given circumference and density

Glaciers often deposit large rocks called erratics. The granite rock has a circumference of 9.5 m. Assuming it conforms to the shape of a sphere, what would be its weight in Megagrams (Mg), where 1 Mg ...
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0answers
24 views

Finding the whole triangle information by one point.

I wonder if there's any way to blend two (or more) RGB colors in a reversible way? I mean, imagine we have an RGB pixel (R: 55, G:35, B:255), and we need to extract the two other RGB pixels that ...
0
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2answers
55 views

The square on the diagonal of a cube has area 1875. Find a side of the cube and its total surface area.

The square on the diagonal of a cube has an area of 1875 cm$^\text{2}$. Find One side of cube The total surface area of the cube Moreover, what does ‘square on the diagonal of a cube’ ...
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1answer
22 views

Why the intercept form and normal form is not applicable in 3d space?

Today one of my folks told me during studying 3d geometry that the intercept form and normal form are not applicable in the 3d space where in 2d they both hold good 1.intercept form: x/a + y/b =1 2. ...
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2answers
24 views

Finding the position vector of a point on a line

Question goes: Find the position vector of the point P on the line AB such that OP is perpendicular to AB. A has a position vector 7i-8j+7k, B has 4i+7j+4k and O is the origin. I started ...
2
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2answers
51 views

Components of a 3d vector given specific angles

I'm looking for 3 formulae for the x, y, and z components of a 3d vector given 2 angles (and a magnitude). I essentially need to convert from spherical to cartesian coordinates in 3 dimensions. The ...
2
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2answers
41 views

A Suitable Function for Terrain, Mountain Modeling

On Google Maps and various other mapping programs, one can see contour lines that correspond to elevation. Sometimes these contour lines are concentric corresponding to a mountain. My question is ...
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0answers
25 views

Book reference for Analytical 3D geometry

I'm looking for a book which covers the following topics: Generating lines, Cone, Cylinder, Paraboloid, Ellipsoid, Hyperboloid of one and two sheets. Their tangent planes, normal lines, director ...
5
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3answers
61 views

Comparing Regular-Faced Toroidal Polyhedra

Many apologies ahead of time, I have no idea how to phrase this question, and I'm certainly way out of my element. I'll do my best but please go easy on me. I wanted to make a polyhedra that was in ...
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0answers
20 views

Finding and Comparing 2 Sensors Rotations, with same reference frame but different initial Orientation

Let's say we want to Compare two different Arm (Humerus) Rotations (series of quaternions) and we do not care about space translation but only for rotation. To measure each rotation we use the same ...
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2answers
29 views

Absolute value of rotation of a point around a line in 3D

am struggling for hours with turning something that already works perfectly in 2D, into 3D space. Really hope someone can help… The task is to determine the absolute rotation of a point around the ...
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1answer
22 views

Shortest distance between two objects

Two objects $O_1$ and $O_2$ move in parallel according to the vectors $\vec{v_1}$, and $\vec{v_2}$. Determine the shortest distance in which objects will be and the time $t$ after which it will occur. ...
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0answers
18 views

3D box measurements from 2D

I'm wondering if there's a mathematical way to work out the 3D measurements on a 2D plane if given the 2D dimensions of an object like a box. If the object is rotated and this translates to 13º on a ...
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vote
1answer
32 views

Is there an analog of the Law of Cosines that applies to polyhedra?

Is there a relationship between the side areas of a polyhedron $A_1, A_2, \ldots, A_n$ similar to the law of cosines for triangles?
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3answers
55 views

Finding the Quaternion that rotates a coordinate system to match another.

Let's say I want to figure out the orientation of my cell phone. Assume that the phone has two internal sensors that report orientation (a quaternion), but both are a bit unreliable, so I'd like to ...
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0answers
24 views

Need help to solve a question of Mensuration

The base radius and slant height of a conical vessel is 3 cm and 6 cm respectively. Find the volume of sufficient water in the vessel such that when a sphere of radius 1 cm is placed into it, water ...
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1answer
35 views

Analytic solution for a 3d dynmaic system with global perodic solution.

The set of equation \begin{cases} (X^2+Y^2+Z^2)^{5/2}X''+(X^2+Y^2-2Z^2)Y'+3YZZ'&=0\\ (X^2+Y^2+Z^2)^{5/2}Y''-(X^2+Y^2-2Z^2)X'-3XZZ'&=0\\ (X^2+Y^2+Z^2)^{5/2}Z''+3Z(XY'-YX')&=0 \end{cases} ...
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1answer
27 views

Function $ f(x,y)=x+\frac{y^3}{3} $ cut the xy-plane in a cutting-curve $h$. Find the tangent fuction of h in point$ P(9,-3)$.

$$ f(x,y)=x+\frac{y^3}{3} , D(f)=\text{(x,y)}\in R |(x^2 +y^2\le2) $$ So what i thinking here is find the function h, then find the tangent. But i dont know how to do or is there another way? Thank ...
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0answers
12 views

Rotation an object (or line) by x and z resulting in an ending x and z

I knew this equation in High School but that was 30 years ago. Let's say I have a cube (or line). I want to rotate it's x, y and z axis' such that the result has a specific x and z rotation. for ...
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1answer
42 views

Width of layer formed from sphere $r = n$ fitted inside sphere $r = 4n$ [closed]

If a volume equivalent to a solid sphere of radius $n$ is pushed onto the surface of a sphere with radius $4n$, how wide is the layer that forms, expressed relative to the radius $n$?
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1answer
25 views

How can we find the volume by integration for $x>0, y>0, z>0$ and $z^2<x+y<2z$?

Intersection of formulas I am trying to find the volume but I can't use the methods in most videos where I should let every 2 variables be zero and solve for the third since there are no values to ...
0
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1answer
34 views

tilting a disc in 3d space - need help

Lets imagine you have a disc like a CD. Then you take that CD and rest it flat on a desk. Now you tilt the disc left to right and forward to back while touching the desk with 1 point on the edge of ...
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votes
2answers
64 views

A cone with guiding curve $x^2+y^2+2ax+2by=0$ contains $(0,0,c)$. Its section by $y=0$ is a rectangular hyperbola. Prove its vertex lies on a circle.

A cone has its guiding curve to the circle $x^2+y^2+2ax+2by=0$ and passes through a fixed point $(0,0,c)$. If the section of the cone by plane $y=0$ is a rectangular hyperbola. Prove that the vertex ...
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votes
0answers
17 views

Distance a from point in R3 to a surface defined by a parametric curve and a radius function?

I'm interested in studying the class surfaces defined by: Take an arbitrary parametric curve f : {0..1} -> ℝ3. Pick an arbitrary radius function ...