# 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.

2,355 questions
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### If a right circular cone has three mutually perpendicular generators then find its semi-vertical angle.

If a right circular cone has three mutually perpendicular generators then find its semi-vertical angle. We see that if $ax^2+by^2+cz^2+2fyx+2gzx+2hxy=0$ has three mutually perpendicular generators, ...
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### How can I plot an animated Klein Bottle in Graphing Calculator 3D? [on hold]

How can I plot an animated Klein Bottle in Graphing Calculator 3D? I mean, is it possible to change the shape to cut it and see Moebious bands?
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### 3D plot difference Matlab and Wolfram

I'm trying to plot the function $z = 6x^2 - 4x^2y^2$ in Matlab. The code I'm using for this in matlab is the one below, also the plot is shown: ...
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### Volume of cylinder cut by two planes

I try to find volume of cylinder $x^2 + y^2=9$ cut by inclined plane $z = x + y - 4$ and plane $z=1$ I should solve it in Cartesian, so my idea is to rotate the plane $z=x + y - 4$, and to split the ...
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### rotate plane according to pitch,yaw and roll

Lets say, i have ground-plane equation = $ax + by + cz + d$ . Then, i rotate camera and i know new yaw ( $\theta$ ), pitch ( $\alpha$) and roll( $\gamma$) angle of camera. How can i calculate new ...
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### How can I graph the same 3D graph in 2D with z as y, and using a constant with a slider for y in Graphing Calculator 3D? [on hold]

I found a really cool graph in Graphing Calculator 3D, and would like to transfer it onto a 2D graph. I used the exact same equation, except I exchanged z with x and y to a constant that can be ...
2answers
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### Parameterize union of two shapes in 3space

I am supposed to parameterize the union of the two shapes $x^2 + y^2 = 1, z = y$. I do not even know how to get the union of the two shapes. When I graph the two shapes the intersection does not ...
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### Plane rotated about line of intersection to another plane?

The plane ax+by=0 is rotated about its line of intersection with the plane z=0 through an angle n. What is the equation of the plane in its new position? I saw a question in stack exchange relating to ...
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### Miscellaneous Solids. How do I solve this problem? [closed]

Can anybody help me with this Find the volume in the first octant inside the cylinder $x^2/a^2 +y^2/b^2 =1$ under the plane $z=3x$. Use the given slice in the figure to compute the volume.
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### What does shape does $\bigl\{x\in{\mathbb R}^3\bigm| A\times x=B\bigr\}$ define?

If vectors $A$ and $B$ are fixed, then by definition of the cross product, I know that if $B$ is not perpendicular to $A$ then there will be no solutions. So assume $B$ is perpendicular to $A$, then ...
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### Rotation matrix from axis-angle representation

I came across the following representation of a rotation matrix given an axis of rotation $\begin{bmatrix}n_1 & n_2 & n_3\end{bmatrix}$ and an angle $\theta$. I'm trying to figure out where ...
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### Area of the base of the prism formed by three planes

The three planes $P_1: kx + y+ z=2$,$P_2:x+y-z=3$,$P_3: x+2z=2$ form a triangular prism and area of the normal section (where the normal section of the triangular prism is the plane parallel to the ...
1answer
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### Light Reflection in a 3D Plane [Raytracing]

This is a problem that I need to figure out to complete a Java Raytracer Render Engine. Let's say a Light is positioned at (x, y, z) position in a 3D Environment. There's also a metallic object, let'...
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### How to find the distances between P0 to P1 in this 3 dimensional ellipsoid? How to find distance b/w two foci? [closed]

(Kindly think your idea before looking at details file ) 1. How to find the distances between P0 to P1 in this 3 dimensional ellipsoid? Can give example please ? 2. How to find the distance D between ...
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### Checking if lines intersect or skew from directions ratios and a point on each line

Well , this is what's in my book $DR_1(m1,m2,m3)$ with $A(a1,a2,a3)$ $DR_2(n1,n2,n3)$ with $B(b1,b2,b3)$ \begin{vmatrix} m1 & m2 & m3 \\ n1 & n2 & n3 \\ a_1-b_1& a_2-b_2 & ...
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### How to find the distances between P0 to P1 in this 3 dimensional ellipsoid? [closed]

(Kindly think your idea before looking at details file ) How to find the distances between P0 to P1 in this 3 dimensional ellipsoid? Can give example please ? How to find the distance D between two ...
0answers
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### minimum distance between 2d and 3 d curves [duplicate]

Let $P(x,y,1)$ and $Q(x,y,z)$ lies on the curve $\displaystyle \frac{x^2}{9}+\frac{y^2}{4}=4$ and $\displaystyle \frac{x+2}{1}=\frac{\sqrt{3}-y}{\sqrt{3}}=\frac{z-1}{2}$ respectively. Then the square ...
0answers
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### Graphing Polar on Graphing Calculator 3D

I would like to be able to restrict the angles (theta) that are graphed when I choose to do polar on the Graphing Calculator 3D. I know how to change my window, but not these restrictions.
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### Hexahedron made with similar polygons

The isohedra are made with congruent polygons. I wondered what could be built with similar polygons that are not congruent. Here is one where edgelengths are powers of $\sqrt{\psi}$, where $\psi$=...
1answer
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### Intersection points of a line with xy plane

A line passing through (0,0,1) and intersecting lines x+2y+z=1 , -x+y-2z =2 and x+y =2 ,x+z=2 What is the intersecting points of the line with xy plane My attempt I computed the line of ...
2answers
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### Plane Equation from two parallel Lines in OpenGL - need help

I am attempting to determine a plane for slicing 3D objects in OpenGL. For this I have traced two parallel rays into the 3D world (from a 2D window). It is possible to determine a plane by two ...
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### How to get the endpoint of a vector by quaternion?

If I have the start point of a vector(not zero), and I also have the magnitude and the quaternion of the vector, how can I get the end point?
1answer
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### How to intersect arbitrary 3d plane (with form ax+by+cz + d = 0) with the XY plane?

So I know there have been other stack exchange questions around intersecting two arbitrary 3d planes like here (Plane-plane intersection in python) however I have a special case where I want to ...
3answers
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### To find minimum distance between two curves

Let $P(x, y, 1)$ and $Q(x, y, z)$ lie on the curves $$\frac{x^2}{9}+\frac{y^2}{4}=4$$ and $$\frac{x+2}{1}=\frac{y-\sqrt{3}}{\sqrt{3}}=\frac{z-1}{2}$$ respectively. Then find the square of the minimum ...
0answers
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### Move a point in 3D space a given distance and angle

so I'm fairly new to maths and need to know how to move a given 3D point in space, a certian distance and a certian angle and get the new position, that angle being in radians and being an x angle and ...
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### Given in 3D Ellipsoid semi major axis, how can we find the distance between two focal points?

Given in $3D$ ellipsoid semi-major axis $a=5$, $b =4$ and $c=3$ . How can we find the distance $D$ between two focal points: $F_1$ and $F_2$? Also how can I find the distance from focal point $F_1$ or ...
1answer
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### Equation of cylinder from given parameters

I have the following data returned from a least square fitting function: ...
1answer
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### How can I plot $X, Y, Z$ in 3D chart in Graphing Calculator 3D [closed]

I couldn't do it in Excel. Can I draw a $X, Y, Z$ plot using Graphing Calculator 3D?
1answer
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### 3D Trigonometry

So this is the question. There is a cuboid $ABCDEFGH$; $ABCD$ is the horizontal rectangular base and $EFGH$ is the horizontal rectangular top. $AB = 4x$, $AE = 3x$, and $BC = y$. If the angle between ...
1answer
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### Rotating a triangle in 3d specified by the normals

In my surface reconstruction algorithm I need to calculate the right direction of the triangles. The coordinates of the original triangle are known. The original (initial) normal, the new desired ...
0answers
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### Pattern fromation from distributed 3-D points in space.

What are the ways you can classify or analyse a set of three dimensional points in space? An extension to this: there are two different sets of three dimensional points. what are the ways you can ...
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### Three Dimensional Trigonometry

From an observation point at sea level, an aircraft is observed on a bearing of N30E, elevation 20 degrees and at height 600 m. The aircraft then flies due east for 1000 m, without altering its height....
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### Algorithm to sort 3d segments from back to front depending on z-Order

I have a set of $n$ segments in 3D space with start and end points $A_i$ and $B_i$ $(i \in \{1, ... n\})$ in $\mathbb{R}^3$. Those segments are projected on screen and their $x$ and $y$ coordinates ...
1answer
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### Interesting Property of Tri-Rectangular Tetrahedron [duplicate]

For starters, we know that a trirectangular tetrahedron is a tetrahedron where all three face angles at one vertex are right angles. Here's an interesting property I stumbled upon, of which I look ...
1answer
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### Calculating the efficiency of glass [closed]

Is the integral in the meme picture correct when it comes to calculating the efficiency of the glass? Assuming the cup is a perfect frustum of a cone.
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### Help in vector and cross product relation

Let A(1/3;-2/3;1/3) B(1/2;-1/2;1/4) be 2 points of midpoint I, let M(x;y;z) be a variable point in space distinct from I How can I prove that if the cross product of these vectors equal to the ...
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### How to find an incidence point on a sphere for a point and its reflection.

Given two points P, S and a sphere with center C and a radius R, how can I find an incidence point I through which a ray cast from P reflects on the circle and intersects S? Directly using the ...
1answer
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### Find area under inequality

The volume of the region defined by the inequality : $S :$ { $(x,y,z)$ : $|x|+|y|+|z|$  $$$\leq$$$  $1$ } is to be solved using integration . Please help . For computer simulation , ...
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### Projecting a point in 3D unto a 2D image with a camera that can move.

Having a camera that can only move on the shell of a sphere, is it possible to calculate where on the 2D image a dot in the 3D space would be? The camera's position is known as the two spherical ...
4answers
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### How do I check if a 3D point is between 2 other 3D points? [closed]

How do I check if a 3D point is between 2 other 3D points? For example, if I had an imaginary line between two 3D points, how would I check if a point is on that line?
2answers
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### Geometric Interpretation of System of Equations

Perhaps I am overlooking something but this is puzzling me. I have a system of equations which can be represented by three planes: \begin{align} \Pi_1&: \ x-7y+5z=3\\ \Pi_2&: \ x-y+3z=-1\\ \...
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### Rotating a 3D vector by a quaternion?

I am looking into performing a rotation of a 3D vector by a quaternion. I understand this entails pre-multiplying the vector $v$ (made into a "pure" quaternion) with $q$ and then post-multiplying the ...
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### How to translate from one plane to another?

Good afternoon all, I hope I posted in the right area which i felt closest to linear algebra more than chemistry. I do apologize if its not! With that being said: I am trying to get Molecule X (from a ...
1answer
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### Caculate area of polygon in 3D [closed]

I have a list vertex with 3D coordinate of a polygon. How to canculate its area. Should I convert it into 2D?
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### Tessellations of 3-sphere

How many are there regular geodesic tessellations of the 3-sphere? What kind polyhedrons are used in those?
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### How can I shade an area enclosed by points in Graphing Calculator 3D?

I want to plot some specific points, but fill in the area between those points with a solid color in order to represent a three dimensional object.
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### Intersection between line segment and a polygon in 3D space [duplicate]

I have a line segment defined by two $(x,y,z)$ coordinates, and a polygon (triangle) defined by three coordinates and a normal vector. I have to find out if the line segment intersects the polygon. ...