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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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Prove dataset is linearly separable in 3 dimensions

I'm trying to figure out if my dataset is linearly separable. My instinct was that in a 3-D space, if I could come up with a plane that separate the data points correctly, it is. My points and ...
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2answers
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Determining whether a large series of 3D points all line on a plane

TL;DR: For a large series of precise 3D coordinates that describe a real-world orbit, how can we determine if they all lie exactly on a plane? The Problem I've used NASA's highly precise SPICE ...
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1answer
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Why is the surface area of a sphere equal to $4\pi r^2$ [duplicate]

I have absolutely no idea where that formula comes from, considering the fact that I am a fifteen year old. According to me, one way to think of it is to arrange $4$ circles having radius equal to ...
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1answer
53 views

What will a sphere look like if it's unwrapped?

I actually google alot, but all results are related to 3D design apps like blender bla bla bla, No direct answers or even something to help. I tried to imagine it like some triangles arranged and all ...
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0answers
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3D geometry converting equation of line from symmetric form to general form(as intersection of 2 planes)

I wanted to find out an easy way to convert the equation of line in 3d from symmetric to general form. I find it difficult to express a line (3-d) as an intersection of 2 planes given the equation of ...
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2answers
29 views

Find the exact coordinates of all possible points D on the line through A and B so that D is four times as far from A as it (D) is from B

A(4, 7, -3) B(-3, 1, 2) AB <-7, -6, 5> parametric equation for AB: x = 4 - 7t ; y = 7 - 6t ; z = -3 + 5t I tried to use the distance formula where I set 4d (d being the distance of D to B) as ...
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2answers
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How to make an object face another object in 3D space?

I have a question that maybe it is an easy calculation but I am a motion graphic designer not a Math guy so... here it goes. I have a 3D scene with a perspective camera in it. I want to make a 2D ...
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0answers
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Boundaries of integration - 3 dimensional

Question Let D be the region in the first octant that is bounded below by the cone $z = \sqrt{x^2+y^2}$ and above by the sphere $x^2+y^2+(z-1)^2 = 1$. Set up an iterated triple integral to ...
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1answer
37 views

How to Find A Shear Matrix in 3D?

In particular, I'm struggling with this question: Give me a rotational matrix, a scaling matrix, or a reflection matrix and I can provide it quite easily. No online resources I've found give me much ...
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2answers
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Prove following points lie on a circle.

I found this in a textbook without a solution and I wasnt able to solve it myself. Let ABCD be a tetrahedron with all faces acute. Let E be the mid point of the longer arc AB on a circle ABD. Let F ...
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0answers
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how to compute the intersecting area for n number of spheres, given their radii and center point?

The title says it all...I have already looked at this and found it was only helpful if the spheres were on the same plane, which seems rather useless.
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2answers
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Parametric form of plane in Cartesian form

Consider three vectors $a$, $b$ and $c$ which are position vectors of three non-collinear points. Then the equation of plane contains these points is: $$r=a+kb+lc$$ where $k$ and $l$ are scalars. This ...
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1answer
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How many points are there in the following set? [closed]

Let us consider the following set: $A=\{(x, y, z) \in \Bbb{R}\times\Bbb{R}\times\Bbb{R} : ax+by+c=0,z=0 \},c\neq 0$ and $B=\{(x, y, z) \in \Bbb{R}\times\Bbb{R} \times\Bbb{R} : ax+by=0,z=0\}$. Then ...
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0answers
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Projecting multiple 2d frames onto a 3d plane [closed]

I have multiple 2d stick figure images and want to create a 3-dimensional model from them. Is this possible and are their tools to do so that interact with python? There are 25 joints that make up the ...
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1answer
29 views

Coordinates of the centroid in a 3D rectangle

I have a 3D rectangle and I have to find the 3D coordinates of its centroid. I tried to take 4 vertices, one let's say the origin $o$ and the three adjacent vertices $a, b, c$. I computed the ...
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1answer
14 views

Equation of line in 3d space passing in two points in a form of ax+by+cz+d=0

I'm sorry for asking probably such easy question, but need help with this.. I need to get the parameters with the equation of a straight line passing through two points in 3d space. ex: ...
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2answers
42 views

How to create rotation matrix in 3D space?

In a 3d space $(x,y,z)$ where $y$ is the height, I have a plane which I constructed from 2 angles (creating a normal vector). For example: $$\alpha = -\pi, \beta = \frac{-\pi}{2}$$ To calculate ...
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1answer
56 views

Connect Two Points in 3D Space with Three Lines

I have two points in 3D space, $P_1$ and $P_4$. From either point, I have a line extended ($L_1$ intersecting $P_1$ and $L_3$ intersecting $P_4$). I want to join these two lines together with another ...
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0answers
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Calculate 3d Rotation Maintaining Orientation

My Current Setup: Let's assume we have these 3 axes in 3d space. Let's also assume that x = blue; y = red; green = z; To calculate a rotation on the x axis, i.e.,...
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3answers
100 views

Line intersecting 2 lines and parallel to another

The problem is : Find parametric equations of the line L intersecting the given lines L1 and L2 and parallel to the given line L3. L1: x = 1 + (t1), y = 2 + 2(t1), z = -2 + (t1) L2: x = 2 + (t2), y ...
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1answer
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If $v\times w = 4i + 7j + 5k$ then what is $v\times w + w\times v$?

If $v\times w = 4i + 7j + 5k$ then what is $v\times w + w\times v$? $v$ and $w$ are vectors, they aren't given. I have no idea how to do this and apparently it's asked on a quiz as a "surprise" ...
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1answer
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Planes, lines, and perpendiculars!

I'm having trouble with this problem - Let $Q = (-2, 3, 4)$, and let $P$ be the foot of the perpendicular from $Q$ to the plane through points $A = (0,1,1), B = (1,1,0)$ and $C = (1,0,3)$. Then $\...
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0answers
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Finding the absolute maximum of a 3 variable function

How do I approach finding the maximum for an $f(x,y,z)$? $f(x,y,z)$= $6.365+7335000y-24450xy-0.5* \sqrt {10614564y^4+2391210000x^2y^2-1434726000000xy^2+31858027.2zy^2+215208923890984y^2+23904276.64z^...
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4answers
32 views

How to determine if a point is above or below a plane defined by a triangle

I'm doing some 3D graphics stuff and in order to add some simple lighting, the program needs to determine whether or not a point is below a triangle. (For now just the plane defined by the triangle. I'...
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1answer
23 views

Create Wall 3D math oriented away from camera

I have 2 Points which has x,y,z let's say from and to I am drawing wall between them using ARkit ios To draw wall I use static ...
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1answer
29 views

Intersection of $2$ planes.

Find the intersection of a line formed by the intersection of two planes $\vec r . \vec n_1 = p_1 $ and $\vec r . \vec n_2=p_2$. I know that the line would be along $(\vec n_1 \times \vec n_2)$. So i ...
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1answer
25 views

How to figure to the angle between a plane defined by three 3-dimentional points and a line defined by two

I'm writing a simple 3D render engine. In 3D graphics, everything is made of triangles. To figure how bright to make each triangle, it needs to know what angle it is relative to the direction of the ...
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1answer
23 views

integral of 3d gaussian with hollow integral space

I am trying compute the triple integral of a 3D Gaussian within a sphere hollow space. My questions are at the end. You can think the problem in this manner. There is a very large ball whose center ...
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1answer
47 views

what is the similar triangles argument?

I’m reading a textbook on 3D graphics math. It’s describing how to model a pinhole camera, using a film plane at z = 1. However, the book then says this: Given a point p in the scene with eye ...
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2answers
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Tri(cubic?)-interpolation on finite sets

I have two sets of data of same size, representing binded triplets, we can represent these two sets like this: $\mathbb{N}_A=\{i \in\mathbb{N}\mid i\in [0;256[\; \mid i \equiv 0\, [8]\}$ $\mathbb{N}...
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1answer
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triple integral over region defined by the pyramid$ (0,0,0), (1,0,0), (0,2,0), (2,2,0), (1,0,2)$

$∭ z dV(x,y,z)$ over the region defined by the pyramid with base $(0,0,0), (1,0,0), (0,2,0), (2,2,0)$ and vertex $(1,0,2)$. I tried finding the planes connecting $(0,0,0), (0,2,0), (1,0,2)$ and $(0,2,...
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2answers
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Equation of sphere circumscribing the tetrahedron bounded by planes $x+y=0$, $y+z=0$, $z+x=0$, $x+y+z=1$

I found a following question in 1st year undergrad course: Find the equation of sphere circumscribing the tetrahedron bounded by the planes $$x+y=0 \qquad y+z=0 \qquad z+x=0 \qquad x+y+z=1$$ ...
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1answer
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Envelopes of the family planes

Im trying to compute the envelope of the family of planes $2a_1x+2a_2y-z+a_1^2+a_2^2$. So far, I got $\frac{dF}{da_1}=2x+2a_1=0$, $\frac{dF}{da_2}=2y+2a_2=0$, therefore $a_1=-x$, $a_2=-y$. Thus, the ...
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4answers
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Cartesian equation of plane through $3$ points

Let there are three points $(2,5,-3),(5,3,-3),(-2,-3,5)$ through which a plane passes. What is the equation of the plane in Cartesian form? I know how to find it in using vector form by computing the ...
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1answer
15 views

Determine the slope of a plane whose rise in z is zero, but whose change in x and y are not.

Determine the slope of a plane whose rise in z is zero, but whose change in x and y are not. Explain what this plane looks like. Would it be a plane in the xy plane? Not sure how to start this ...
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0answers
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Move Point to corner of 3D Plane

I have one 3D plane which is act like a wall which always rotated Euler y angle. on that plane I have to add another Plane with 2 Position with the same angle wall has. I did this with ...
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2answers
71 views

Why are there 48 symmetries of a cube?

I'm trying to prove that there are a total of 24 rotation and 24 reflection symmetries of a cube. I can show the first part, but I don't have a good proof for why there are also 24 reflections. The ...
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1answer
36 views

Find the planes of symmetry between two intersecting planes

Okay, so I have two planes which intersect at a right angle. I have their normal vectors (which have different lengths). They intersect and form a line. I now need to find the equations of these two ...
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0answers
64 views

Equidecomposability of a Cube into Trirectangular Tetrahedra and a given tetrahedron

My original problem is: 1) Let $XYZT.X'Y'Z'T'$ be a cube. Given $A\in XYY'X',B\in XYZT,C\in Y'Z'$ and $D\in TT'$. Is there a way to dissect the cube into Trirectangular Tetrahedra and $ABCD$? I ...
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1answer
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Finding vector equation of image of line through $A$ and $C$ under a reflection with respect to L.

$A(1,-3,2),B(0,-4,5),C(5,0,-3)$ are points in $\mathbb{R}^3$. I have found the vector equation of the line L through A and B. $L=i-3j+2k+t(-i-j+3k)$ I have also found the foot of perpendicular from ...
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0answers
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Are the two congruent helices that form a double helix parallel?

I know that they are parallel but I do not know how to explain it. The strands are equal lengths so they would be equidistant from one another. Is there another way I can show it or explain it? This ...
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3answers
608 views

Count the number of shapes in a polyhedron.

So this is a question that was asked in the International Kangaroo Math Contest 2017. The question is: The faces of the following polyhedron are either triangles or squares. Each triangle is ...
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0answers
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how to find a rotation angle of given 3 points in 3D?

As per the above picture, I have point p0, p1 and p2 given. how to can I find angle a? Thank you
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0answers
23 views

Is two distinct rhumb lines with the same bearing on a perfect sphere parallel?

Is two distinct rhumb lines with the same bearing on a perfect sphere parallel? I am defining parallel as 2 objects as parallel if they do not intersect, go in the same direction, and a constant ...
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3answers
46 views

Finding a 4th point in 3D space knowing 3 other points and 2 distances to the 4th point from them

I have 3 points in space A, B, and C all with (x,y,z) coordinates, therefore I know the distances between all these points. I wish to find point D(x,y,z) and I know the distances BD and CD, I do NOT ...
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0answers
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Converting basic angles over each axis of a 3d rotation to euler angles or axis angles or quartenion

For a 3d rotation, if I know that I want to rotate e.g. around X axis with 15 degrees, around Y axis with 226 degrees and around Z axis with 0 degrees: how to calculate Euler angles from this ? I need ...
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0answers
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Two different formalisms of rotation matrices: the x and z are opposites

I have two different graphic representation systems that differ in the sign of the x and z vectors of the 3×3 rotation matrix. They appear to have the same handedness (right). I have read the ...
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1answer
31 views

parametric-ish equation of a plane [closed]

I know that there are other questions on this site about this, but I haven't gotten from them what I want. Say we have two points $a_1,a_2\in\Bbb R^2$. thus the line $A$ connecting them is given by $...
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1answer
21 views

Separating disks in 3-manifolds

Let M be a (smooth or PL) connected three manifold with boundary, such that one boundary component is a sphere S. Let D be a properly embedded disk whose boundary lies on S. Must D separate M into ...
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3answers
32 views

Composition of rotations around nonintersecting axes

I know how to compute the composition of two rotations using quaternions (or by multiplying rotation matrices), and this theorem by Hamilton is very helpful in understanding geometrically how it works....