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Questions tagged [3d]

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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Would parallel lines in 2 parallel planes have the same slope?

If I am given 2 points in Plane A and 2 points in Plane B and I connected those points, would the lines have the same slopes? How can I show that algebraically?
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Aligning point cloud using camera local coordinates only [on hold]

I have the stanford bunny point clouds taken from different views and the config file containing all the local camera poses for each of these clouds. ...
2
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1answer
27 views

Gaming AI, courage and retaliation

This is a bit oblique but maybe some of you will find it fun and it's been wrecking my brain for a while. Here's the background of what I'm trying to achieve, but if you want to skip to the actual ...
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0answers
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Finding an equation in 3D [on hold]

How do we find the equation for the set of all points at distance square root (130) from the z-axis (this is an infinite hollow cylindrical surface)?
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2answers
53 views

Real World 3D Geometry Question: Finding the Intersection Point of a Line and a Plane

My team and I are developing a product which includes LASER systems and 3D geometry. We are stuck with a problem and I have tried my best to frame it into mathematical question. Here it goes, $P_1=(...
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2answers
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Translating a 3D point from one frame to another

Me and my friend have ran into trubbels with translating a point in a 3D-space from one cartesian coordinate system to another. In this case we have 3 coordinate systems called the Base-frame, h-...
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3answers
85 views

Plane described by three vectors?

Suppose the vectors $a = [1, 0, 1]^T$ , $b = [2, 7, -2]^T$ and $c = [3, 1, 5]^T$ are lying on a plane in $\mathbb{R}^3$. Prove that $d = [4, 8, 2]^T$ also lies on that plane. (Hint: A plane can be ...
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how to get the center of moved equilateral triangle according to endpoints displacement?

sorry if I did not use the proper jargon because I can't recall any specific words. $\mathbf Conditions:$ There is an equilateral $\Delta ABC$ in $\Bbb{R^3}$ with given side-length which lies on $...
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Order Face up-down parallel projection

I'm currently working on a parallel projection program and I have a math problem that I can't solve. My 3D objects are defined by faces defined by an undefined number of vertices: Object: Face 1: ...
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2answers
22 views

To find the equation of a plane [duplicate]

How to find an equation of a plane when 2 lines lying on the plane are given ? Q)Find the equation of plane which contains the lines $$(x-4)/1 = (y-3)/-4 = (z-2)/5$$ and $$(x-3)/-2 = (y+3)/8 = (z+...
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2answers
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How to transform points from a plane to a different plane?

I have a plane $\Pi_1$ expressed as $ax+by+cy+d=0$ and a different plane $\Pi_2$ expressed as $ex+fy+gz+h=0$. I am looking for a transformation which rigidly brings points lying on $\Pi_1$ to points ...
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1answer
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How to get 3d point of 2d triangle?

I am writing a 3d graphics engine for a small project. Heres my problem. I currently have a 3d triangle. I then map each vertex to 2d with the formulas $ x = 1000*X/Z$ and $y=1000*Y/Z$ Where x ...
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2answers
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3D vector question

I am not very good at math. I have a problem where I have two arbitrary 3D points. I also have a disc facing in the Y (up) direction with it's center on one of the points. How do I calculate the ...
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1answer
53 views

The Torus is compact $T= -1\leq z\leq 1,x^{2}+y^{2}=\left ( 2-\lambda \right )^{2}$ where $\lambda ^{2}= 1-z^{2}$

Sorry guys, but i'm stuck on this problem since a week ago, trying to figure out how to proof this Torus is compact by Heine-Borel Theorem, i guess the hardest part of it, is to proof is closed, i ...
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1answer
35 views

Angle difference between 2 directions in 3d

I have a view direction in 3d space described with 2 values: Horizontal and Vertical (x and y) ranging the full 360 degrees (from -180 to +180), thus describing every possible view direction. It ...
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3answers
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Representation of coordinate frames in 3 dimensions

I am dealing with transformation of vectors from one 3D Cartesian reference frame to another one. My question is, what formalism specifies a 3D Cartesian reference frame: perhaps the origin, the ...
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1answer
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all vectors making $ \text{negative dot product} $ with the vector $(1,1,1)$.

How to a $3D$-figure that describes all vectors making $ \text{negative dot product} $ with the vector $(1,1,1)$. The vector $(-1,-1,-2)$ has negative do product with $(1,1,1)$ because $(1,1,1) \...
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2answers
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What is the maximum number of regions in 3D space a plane can intersect?

Since there are 8 regions or"quadrants" I thought it would be 6 regions as the max. I do not know if I am right.
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0answers
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Calculate area of random polygon with specified 3D coordinates of boundaries

Introduction I am a Belgian software engineer working in a company that is producing press brakes. I now have an interesting problem, where I would like to know the best solution, performance is ...
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2answers
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Equation of Plane involving Intersection of planes

Find a plane through $A$ $(2, 1, -1)$ and perpendicular to the line of intersection of the planes $2x + y - z = 3$ and $x + 2y + z = 2$. Not too sure of what to do here, I know I need to find the ...
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0answers
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Best way to divide Kernel smoothed density estimates

I am currently working with multivariate probability distributions (Matlab function mvksdensity to be exact) but I have two main problems holding me up: 1) I have a 3D distribution (X) which ...
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1answer
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Do these lines in 3D space intersect?

Th lines formed by $(0,0,0)+ \lambda(1,1,1)$ and $(0,6,0)+ \lambda(0,-3,2)$ ever intersect? It seems like the do but they don't. How do I show this algebraically?
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2answers
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What are the intercepts of the planes $x = 0$ and $2y + 3z = 12$?

What are the intercepts of the planes $x = 0$ and $2y + 3z = 12$? The word intercept is confusing me because I don't understand if I should say they intersect at point $(0,6,0)$ or the intercept is at ...
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2answers
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What does $x= (0,0,0)$+$\lambda(-1,-1,-1)$ mean?

What does $x= (0,0,0)+\lambda(-1,-1,-1)$ mean? does it mean that the planes cross at the origin? Then what does $(-1,-1,-1)$ stand for?
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Constant offset, constant climb rate spirals [on hold]

Show that any two of the following three conditions leads to the third. Constant offset / constant width spirals on a surface of revolution Constant arc rate of climb $ z^{'}= \dfrac{dz}{ds}$ on it. ...
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2answers
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Given coordinates of vertices a convex quadrilateral, find which pairs of vertices determine the diagonals

I'm writing a program that will take in four $(x, y, z)$ points that form a quadrilateral, and produce two sets of $(x, y, z)$ points that form the two largest triangles that comprise the ...
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0answers
26 views

Equations in Three Dimensions

Graph the planes x – y = 0 and y – z = 0. Then graph the line "a", if it exists, defined by the intersection of x – y = 0 and y – z = 0. Describe line "a" including all its intercepts, if it exists. ...
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1answer
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Simplest Unhalvable Shape

Consider a connected 3D-printable shape such as the below. It appears that any plane passing through the centroid will divide the shape into more than two pieces. Define a shape with this property ...
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1answer
28 views

Number of regions in space from planes through origin

I've seen that the cake numbers give the largest number of regions that can be created by cutting 3-D space by N planes. I have a variation on that question. How many regions can be created by N ...
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1answer
50 views

Why is the plane x=2/5 crossing the y-axis instead of the x-axis?

Why is the plane x=2/5 crossing the y-axis instead of the x-axis? I thought it would be opposite like when you graph a line. Would the vector be (.4,0,0)
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1answer
24 views

Finding the equation of a line that is the intersection of two planes?

Can someone please explain this part of the problem attached herewith? I have no idea what's going on in the highlighted region. Thanks.
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1answer
23 views

Seeking 3d rotation

I have a 3d rigid body rotation under which the unit vector $(0, 0, 1)$ becomes the unit vector $(n_x, n_y, n_z)$. I need to find what the vector $(w_x, w_y, 0)$ transforms to under that same rotation....
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2answers
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Polyhedrons exclusively made out of even sided polygons

I know that the cube is the only 3 d shape which falls in polyhedrons but still is composed of squares, exclusively although its a even sided shape. I have noticed that after square there is no single ...
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1answer
19 views

Angle between two planes from maximum dip and azimuth in 3D

I have 2 planes, of which I know the maximum dip and azimuth. Here I am defining the azimuth as the direction of the maximum dip. How would one calculate the intersection angle between these 2 planes? ...
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2answers
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Number of Regular tetrahedron from Unit cube

Can we count number of Regular tetrahedrons formed out of Unit cube? If vertices of Unit cube are taken as $(0,0,0,)$, $(0,0,1)$, $(0,1,1)$, $(0,1,0)$, $(1,0,0)$, $(1,0,1)$, $(1,1,1)$ and $(1,1,0)$ ...
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0answers
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$P\in \beta $ s.t. $PA+PB+PC+PD $ is minim

Let $\alpha, \beta $ two planes s.t. $\alpha || \beta$ and $A, B, C, D\in \alpha $ four distinct points. Find $P\in \beta $ s.t. $PA+PB+PC+PD $ is minim.
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noncoplanar points define 3-space

It takes four noncoplanar points to define a 3-space. Explain whether each of the following is true or not and explain why: a) Two skew lines define a 3-space. True because skew lines are Two or ...
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0answers
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Get the transform matrix between identical 3D objects

The problem: I have two instances of the same object in a space coordinate system. I want to know the transform Matrix between those objects (translation and rotation). I have access to all the ...
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1answer
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how many line segments can be drawn that connect the point to the line so that the segment and the line are perpendicular in 3-space?

Given a line and a point not on the line, how many line segments can be drawn that connect the point to the line so that the segment and the line are perpendicular in 2-space? In 3-space? In 2-space, ...
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2answers
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two lines that are perpendicular to a third line do not have to be parallel.

In 3-space, two lines that are perpendicular to the same plane must be parallel. However, two lines that are perpendicular to a third line do not have to be parallel. Explain why. I am having a very ...
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1answer
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How many line segments can be drawn that connect the point to the line in 2- space? In 3-space?

Given a line and a point not on the line, determine the following. How many line segments can be drawn that connect the point to the line in 2- space? In 3-space? In 2-space I think it would be ...
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0answers
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Determining Positions, Sizes, and Rotations Of Two Right Triangles To Fill Between Three Points In 3D Space

(P.s.: I have depicted as much of this question as I can in images. The bare minimal reading needed (not saying it is a good idea) is the "Question" blockquote and bold/italic sentences). In Roblox, ...
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1answer
55 views

Points inside a 3D rectangle [duplicate]

my task is to find, and mark, all the points from a point cloud that are inside a 3D rectangle. I have the coordinates of all the 8 vertices. Is there a mathematical formula which I can use? To be ...
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2answers
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Volume of Revolution - 3d object

Recently we were given an assignment in which we have to model the cross-section of a 3d, symmetrical object utilising functions. Then we must find the volume of revolution of the object. I need ideas ...
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1answer
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matrix to transform set of point to another set of points

I would like to start by saying that I'm not an expert mathematician, neither an expert in English and that's why I have so much problems at present. What I'm trying to do is to generate 2 matrix R ...
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1answer
21 views

Would a single point and a fixed distance determine a unique segment in 2-space or 3-space?

Would a single point and a fixed distance determine a unique segment in 2-space or 3-space like it does in 1-space when given the length of the segment and location of its midpoint? Explain your ...
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0answers
9 views

relationship between surface variance and curvature

I have an explicit surface in 3d, given as map $z=h(x,y)$ ("2.5D") in discrete points on regular grid over $x$-$y$. My goal is to evaluate radius of curvature in each point on the grid. I currently ...
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3answers
52 views

How to calculate angle between two vectors in 3D with clockwise or counter clockwise notation?

If I have vectors a and b sharing a common point of intersection then I know how to calculate angle between them by using the formula for dot product. But whether b lies to the right or left of a if I ...
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0answers
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A cube with round “lenses” attached

A lot of geometry problems with weird combinations of shapes can be solved by breaking it down, so I suspect it is the same with this problem (which I thought of): There is a cube with side length $...