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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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
37 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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2answers
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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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1answer
35 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
21 views

Parabolic equations [on hold]

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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0answers
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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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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
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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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28 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
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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
74 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
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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
12 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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0answers
30 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
24 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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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
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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
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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
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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
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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
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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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1answer
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$5$ 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
13 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 ...
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1answer
21 views

Calculate projection of a line in a square

Said that we have two points (P1, P2) that form a line, and 3 points (S1,S2,S3) that form a square, how would we calculate the position X and Y of the point resulting from the intersection of the line ...
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2answers
27 views

Find 3rd point in 3D space based on position of 2 points

Assuming i have 2 points $P_1$ and $P_2$ having coordinates of $P_1 = (x_1, y_1, z_1)$ $P_2 = (x_2, y_2, z_2)$ I want to find the coordinates of a 3rd point ($P_3$) where it creates a straight line ...
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3answers
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Definite method for finding the intersection of two cartesian lines in 3D.

I have the following problem: Determine if these lines intersect. If so, find their point of intersection. $L1 = (4,5,-1)+t(1,1,2)$ $L2 = (6,11,-3)+s(2,4,1)$ I managed to solve this ...
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1answer
26 views

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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2answers
34 views

How to check if a 3D line segment intersects a cylinder?

I have developed a check for a 2D case of a circle intersecting a 2D line segment, however there is a particular case that I can't figure out how to extend to 3D: If one endpoint on the 3D line ...
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6answers
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Finding the length from a point to a line in 3D??

Here is the question: What is the distance from the point $(4,1,-2)$ to the line given by : $$x=2+t$$ $$y=3+3t$$ $$z=4-t$$ Help would be greatly appreciate, as i do not even understand where to ...
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1answer
26 views

How to find line parallel to direction vector and passing through a specific point?

I am give the point $(1,0,-3)$ and the vector $2i-4j+5k$ Find the equation of the line parallel to vector and passing through point $(1,0,-3)$ Could one use the fact that the dot product between the ...
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2answers
25 views

Configuration of five or more mutually equidistant points in space.

How is it proved that there is no configuration of five or more mutually equidistant points in $R^3$? Is it done by induction? I'm stuck. Help would be appreciated. Well, surely equilateral ...
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How is the Uniqueness of Equilateral Tetrahedra Proved? [duplicate]

Equilateral tetrahedrons all have this property: For any two of its vertices exists a third vertex, which forms an equilateral triangle with these 2 vertices. (It doesn't necessarily have to be a ...
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0answers
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Beautiful problem about polyhedrons [duplicate]

A regular tetrahedron has this property: For any two of its vertices exists a third vertex, which forms a regular triangle with these 2 vertices. (But it doesn't mean any 3 vertices form a regular ...
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0answers
34 views

Determine position and orientation of a rigid object, given certain limited informations

I have a rigid 3d object with an unknown position and orientation. I want to determine this pose of the object. On the surface of the rigid object are 4 reference points. I know the spatial ...
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1answer
40 views

Convert coordinates to a different coordinate axis

Sorry for any forum rules I have broken, I needed a quick answer. I want to create a plane including 3 nonlinear points on a 3d coordinate system, one being the origin. I also need to create a ...
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1answer
14 views

Find a plane defined by a point, a ray, and a vector starting from the point and parallel to another plane

I am trying to figure this out for implementation into a Graphics manipulator I've been trying to work out. I need to find a plane (a normal vector to the plane will suffice) and I know some of its ...
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1answer
22 views

Is there a way to depict using matrix operations or equivalent, the practice of z-culling in a 3D-to-2D render algorithm

To clarify, the purpose of the question is to try and identify (if possible) a way to accomplish the entire 3D-to-2D projection/render process, including the z-buffering and depth-culling steps, using ...
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Folding a Given Net into a Polyhedron Automatically!

There are some applications to fold predefined nets into the polyhedra, e.g. "Poly" or this applet. Is there any application which automatically folds any net generated by the user, if possible?