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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Estimating the missing points of a 3D point cloud

Consider a cloud of N points (forming a smooth 3D object), in which n points are missing. Also, consider that there is no prior knowledge about the original shape of the point cloud. The only ...
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0answers
13 views

Best fitting circle to points in 3D

I have a set of n ≥ 3 points in 3D that are measurements of a possible circle. The measured points are "noisy" so best-fitting algorithms are involved. I'm programming in C# and have put together some ...
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1answer
31 views

Using several curves in 3D to create a surface

I have a set of several closed curves in 3d (like image below is showing my set of curves from 3 views). To clarify my idea, i ask my questions in two different ways showed by diction 1 and diction ...
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0answers
23 views

Incorrect angle detected between two planes

I want to calculate the angle between 2 planes, Reference plane and Plane1. When I feed the X,Y,Z co-ordinates of pointCloud to the function plane_fit.m (by Kevin Mattheus Moerman), I get the output ...
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Every three of $n$ points is the vertices of an isosceles triangle. What is the max of $n$?

Suppose that we have $n\ (\ge 3)$ points in the three dimensional space and that every three of the $n$ points is the vertices of an isosceles triangle. Here, suppose that the vertices of an isosceles ...
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2answers
40 views

Reflections on a sphere

There is a sphere located in a point s with radius r. The Sphere is a perfect mirror. If i'm sitting in the point c, I want to cast a ray to the sphere such that I hit the point p after bouncing in ...
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1answer
25 views

Shortest distance between two given lines (Hint)

There seems to be this question that I can't seem to be able to solve. I'm hoping someone could help me figure out how to solve it. Question: Find the shortest distance between the lines ...
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2answers
24 views

Midpoint of the shortest distance between 2 rays in 3D

I would like to come with an algorithm to find the midpoint of the shortest between 2 rays a+tb and c+sd, where t and s are scalars. I have a scenario which I try to depict like this. One of the ...
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3answers
131 views

Is the rhombic dodecahedron the only isohedral polyhedron that tiles 3-space (other than the cube)?

Is the rhombic dodecahedron the only face-transitive (or isohedral, i.e. all faces are the same) polyhedron that seamlessly tiles 3-dimensional Euclidean space (other than the cube)? I'm looking ...
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1answer
36 views

How to draw or plot illustrative figures?

stackexchange users I would like to plot or draw some illustrative figures for my research paper. I've tried GeoGebra already. But couldn't draw them as I wanted. So my question is How can I draw ...
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2answers
22 views

Parabolic equations [closed]

It has been a long time since since I've performed any 3D math equations, and I'm trying to figure out how best to calculate a square parabolic mirror from some mylar I have. I've looked at the focal ...
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0answers
20 views

Triple integral, finding the volume between two planes and a surface in 3D

So I have tried to solve this problem, but I'm running into a problem, because the top circle (intersection of the function with z=1) when you project it onto the xy plane is smaller than the circle ...
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0answers
14 views

How to do the calculation of the error in positioning in 3D Space?

I'm mathematically calculating a position on given data in a program. But I need to validate that the calculated values against the original position value. If the Original position is Xi,Yi and Zi ...
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0answers
10 views

parametric representations 3d object

I'm trying to model a 3 dimensional body that is sort of ellipsoidal and am looking for parametric representation of 3D objects similar to the quadratic surface representation of a sphere or ...
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1answer
255 views

How do you get 3D gradient direction and magnitude?

I know that we can get the magnitude and direction from 2D gradient ? 1) mag(Gx,Gy) = sqrt ( Gx^2 + Gy^2 ) 2) angle(Gx, Gy) = tan^-1 (Gy/Gx) What about in ...
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0answers
31 views

From Icosahedron to Pentagonal hexecontahedron (Floret Tessellation)

Inspired by this post: Floret Tessellation of a Sphere I tried to transform myself an icosahedron into its simplest Floret tessellation. But I am having trouble when applying the 'method' given in the ...
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1answer
405 views

Shortest distance between a 3D parametric surface and a point

Right now I'm working on a library for finding the distances between objects in Lua. I've had some trouble finding the distance between a point and a bounded plane. I'm using these parametric ...
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0answers
20 views

Unique representation of each point in 3d space by Linear combination of 3 mutually perpendicular vectors.

I intuitively accepted that there is an unique representation of any point in a 3d space by linear combination of 3 mutually perp. vectors. But now I'm wondering is this an axiom or a theorem? If ...
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1answer
26 views

Flatten 3D VectorA so it's perpendicular to VectorB

Basically I have 2 3D vectors: Vector A (green) and vector B(red). I need to calculate a third vector that is perpendicular to VectorA (green) but points in the same direction than VectorB (red). ...
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0answers
5 views

Inertia tensor of a triangle in 3d

I am computing inertia tensor of a triangle given by its 3 vertices. The tensor should be computed at some local origin. I used covariance as explained in this Wikipedia article, but I am not sure ...
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1answer
312 views

Intersection of a line segment and a paraboloid in 3D

Suppose I have a line segment $L$ in 3D: $$x=a_1(1-t)+b_1t$$ $$y=a_2(1-t)+b_2t$$ $$z=(a_1^2+a_2^2-k_1^2)(1-t)+(b_1^2+b_2^2-k_2^2)t$$ Because $L$ is line segment then $0\leq t\leq 1$. And defining ...
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0answers
30 views

3D equation of a cone-like shape

Imagine there are two parallel planes (base plane and plane1) in the following image: There is one point on the base plane and there are several points on the plane1. The positions of these points ...
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2answers
35 views

How to find closest point on the 3D line from a point [closed]

we suppose to have 3 point. Two of them represent a line $A_1(x_1,y_1,z_1)$ and $A_2(x_2,y_2,z_2)$ and the other point is $B(x,y,z)$. So, how can be found the closest point $C(a,b,c)$ on the line ...
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1answer
76 views

Is it true that a arbitrary 3D rotation can be composed with two rotations constrained to have their axes in the same plane?

I am interested in decomposing an arbitrary rotation in 3D space into the product of two rotations which are constrained to have their axes in the same plane (for instance x-y plane). Statement of ...
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0answers
12 views

What the Surface function will it be if a circle tilted with an angle and then rotating around z axis

My first idea is this will result in a elliptic torus. The horizontal semi-axis a=R and the vertical semi-axis b=R*cos(beta). assuming the titled or inclined angle is beta. The distance away from ...
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0answers
14 views

how to find opposite corner of 3d rectangle with another opposite corner points

I'm having two points say point1 and point3(one diagonal) as 3D points . Diagonal is sloped diagonal , like opposite corner of front mirror of a car. How can I find another two points(p2 and p3) of ...
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0answers
14 views

How to create cube in 3d with given center , height vector , width vector and depht vector?

I want to create cube in 3d. I have center point of cube, height vector , width vector and depth vector. using this information i want to create vector. e.g. Center point = (1, 5, 7) Height Vector = ...
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0answers
17 views

How to calculate translation matrix?

I have a point cloud, which consists of three points. First point cloud has points A(xa, ya, za), B(xb, yb, zb) and ...
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0answers
27 views

unique cube arrangments

i have received this math riddle which i cannot solve, the riddle: given a set of cubes, a unique shape is any shape that was created joining cubes sides together and does not match any previously ...
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0answers
25 views

An example of a space curve with given normal and osculating planes

I am student currently taking calculus 3 and I recently was given a quiz with a very difficult question. The question relates to the chapters in my book which talk about "Arc Length and Curvature" and ...
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1answer
13 views

Intersection between two surfaces

Find Find parametric equations for the tangent line to the curve of intersection of $z=x^2+y^2$ and $6x^2+5y^2+3z^2 =23$ at $(−1, 1, 2).$ I tried plugging in $z=x^2+y^2$ in the second equation to ...
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1answer
312 views

Equation of plane through intersection of planes and parallel to line

Find the equation of the plane through the intersection of the planes of $x-2y+z=1$ and $2x+y+z=8$ and parallel to the line: $\frac{x-3}{1} = \frac{y-1}{2} = \frac{z-2}{1} $ I'm facing difficulties ...
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1answer
235 views

Rotating a system of points to obtain a point in a given place

Given an arbitrary number of points which lie on the surface of a unit sphere, one of which is arbitrarily <0, 0, 1> (which I will call K) in a rotated system ...
3
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1answer
256 views

3D Rotation Decomposition?

I have a 3D local xyz coordinate system placed in a world ENU (East-North-Up) coordinate system. The current relationship ...
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0answers
31 views

How to determine 3d measurements

I am trying to reproduce an artwork that is both a 2D drawing and 3D paper sculpture by Romanian artist Liviu Stoicoviu done in the 80s, The Triangle: I have tried to trace the 2D artwork which ...
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0answers
26 views

Is there a way to describe any regular 3D solid polygon?

I'm interested in creating simple geometry at runtime (in 3D programming). I see there's a set called platonic solids that is a good basis for succession. Is there a way to describe these ...
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4answers
3k views

Rotating one 3-vector to another

I have written an algorithm for solving the following problem: Given two 3-vectors, say: $a,b$, find rotation of $a$ so that its orientation matches $b$. However, I am not sure if the following ...
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1answer
29 views

finding two most distant 3d points

I'm trying to write an algorithm. There are 9 points 3 of x ,3 of y,3 of z. How can I find the two most distant? Mathematically, I need explanation. Thank you for all appreciated answers. coordinates ...
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0answers
20 views

What function has a 3D graph that will look like a spiral into a singularity?

I am trying to draw text spiraling into a black hole, from a more interesting slightly off-orthogonal viewpoint. I think a function that defines a black hole/singularity surface might look something ...
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2answers
13 views

Equation of line gives equation of plane

Given a 3D line in parametric form $$x = 5 + t$$$$y = 1 +3t$$$$z = 4t$$ I did the following calculation: $$x + y + z = (5 + t) + (1 + 3t) + (4t)$$ Therefore $$x + y + z = 6 + 8t = 6 + 2(4t) = 6 ...
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2answers
20 views

How to determine the increase in the Z-Axis. Of a tessellated sphere

I have been tasked with drawing the sphere below for a programming assignment using openGL. I have the assignment mostly completed however I am having issues figuring out the math for the sphere. For ...
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0answers
12 views

Check if an axis aligned bounding box intercepts with a triangle

As the questions says I am trying to check if an AABB intersect with a triangle. I've divided the problem in 3 parts: check if any of the triangle edges intersect any of the AABB faces check if the ...
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1answer
18 views

Given unit quaternions $q_0,q_1$, find $q$ such that $q_1 = q^* q_0 q$

I rotate an object in space and find two orientation (unit) quaternions. $q_0 = {}^{M_2}_{M_1} q$ is the orientation at the 2nd position relative to the 1st position, measured in frame M. $q_1 = ...
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1answer
13 views

3D Vector Equation

Consider the points $A (1, 5, 4)$, $B (3, 1, 2)$ and $D (3, k, 2)$, with $\overline{AD}$ being perpendicular to $\overline{AB}$. (i) Find $AB$ (ii) $AD$ , give the answer terms of $k$. Show that ...
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1answer
575 views

Determine if projection of 3D point onto plane is within a triangle

In 3D, given three points $P_1$, $P_2$, and $P_3$ spanning a non-degenerate triangle $T$. How to determine if the projection of a point $P$ onto the plane of $T$ lies within $T$?
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1answer
21 views

Spherical Sector Volume

I'm trying to find the volume of a spherical sector without knowing the height of the cap. Wikipedia provides this formula: And says: "where φ is half the cone angle, i.e., the angle between the ...
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0answers
141 views

Random 3D points uniformly distributed on an ellipse shaped window of a sphere

How can I generate random points uniformly distributed on the surface of a sphere such that a line that originates at the center of the sphere, and passes through one of the points, will intersect a ...
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1answer
18 views

$5$ General Planes make how many CLOSED SPACES?

Actual problem is How many spaces $5$planes divide a space into? and by some analogy and proof, I found that $5$planes divides a space into $26$spaces. in fact, I considered first "How ...
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1answer
14 views

Distance between two skew lines

I have 2 skew lines $L_A$ and $L_B$ and 2 parallel planes $H_A$ and $H_B$. The line $L_A$ lies in $H_A$ and $L_B$ in $H_B$. If the equations of $H_A$ and $H_B$ are given like this: $x+y+z = 0$ (for ...
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1answer
33 views

Calculate X Y Z from two specific degrees on a sphere

I am a programmer, don't know much about advanced math. I would need the exact formula(s) that could achieve this, so I can translate it to my programming language. I am having a headache trying to ...