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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1answer
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How to efficiently determine whether or not there is a collision between two 3D triangles?

What formula can efficiently tell if two 3D triangles collide or not?
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0answers
27 views

Find 3D axis parallel to given vector passing through given point

Doing some university study and I'm stumped on the proper way to find a 3D axis (which will be used later for a rotation transformation). For example: How do I find an axis that is parallel to n = 2i ...
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0answers
12 views

How To Find a Set of Points Farthest Apart Within 3D Solid

I am trying to find out a method to solve the following problem: There are two parameters: 1) There is a solid 3D region plotted in a cartesian coordinate system. 2) There is a number of points that ...
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0answers
11 views

Turning a point in 3d space to a point on the surface of an object

guys. I'm feeling really stupid, but I'm unsure how to do this. Basically, imagine you have a box in a 10x10x10 grid. You can look at it from any angle in the room, and calculate exactly where in the ...
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0answers
8 views

Move a distance $d$ from $x_i, y_i, z_i$ using yaw, pitch, roll angles as 'headings'

I'm trying to write some code for 3D turtle graphics for a Lindenmayer System, which is similar to how a plane moves. I have a current position in Cartesian coordinates. I know a set of current ...
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0answers
12 views

Finding plane from corners of a rectangle

I have a structure with 2 3D coordinates, each a corner of a rectangle. While they're co-linear, I also know that they will never be the adjacent corners, e.g. they always lie on the diagonal of the ...
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0answers
31 views

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

I know how to generate random points uniformly distributed on the surface of a sphere: ...
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1answer
43 views

Volume of water [on hold]

Please Calculate volume of water in a sphere container with radius r that is filled with water up to the height h.
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1answer
217 views

How to recover three successive rotations of a vector

I have a vector, which I rotated with respect to $x$, $y$ and $z$ axes, respectively. Now I want to recover this operation, that means I want to bring it to the previous position by rotating it with ...
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1answer
17 views

Assuming a ray defined by a starting point and a direction. How can I tell if a plane is behind it or in front of it?

If I have a ray defined by a starting point and a direction, and a plane defined by its normal and its distance from the origin, how can I tell if the plane is in front versus behind the ray? By ...
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0answers
22 views

To minimize surface area of integer cuboid of ​​the known volume

There is a cuboid (a * b * c), (a, b, c ∈ N). S (Surface area of a cuboid) = 2 * (ab + bc + ca). V (Volume of a cuboid) = a * b * c = n. I need to minimize S, provided that I specified the volume ...
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0answers
11 views

Translating Quaternion rotation from one frame of reference to another.

I have been having issues getting around this for quite a few days. I will appreciate any input or advice. I have a sphere (A) with an applied axis rotation of lets say -45 degrees around the Z-axis. ...
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2answers
26 views

What formula will tell if three vertices in 3d space are ordered clockwise or counter-clockwise from the point of view of a camera?

Assuming 3 ordered vertices in 3d space and a camera looking toward those points. What formula will tell me if they are seen clockwise or counter-clockwise in relation to their order?
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1answer
38 views

Implicit 3d plot with depending bounds

I would like to plot this plane ($k1,k2,k3$ are constants): $x-k1=0$ such as $x=k1..n$ ; $y=(z-k3+k2)..n $; $z=k3..n$ The difficulty is that second variable y depend on z. I was trying to use Maple ...
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1answer
18 views

What is the spherical parametrization of an ellipsoid NOT centered in the origin?

I would like to know how to parametrize an ellipsoid not centered in the origin, but with its axes parallel to the main axes of the reference system. The result I am looking for would be an ...
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0answers
19 views

Volume of a tetrahedron given length of edges.

I found this method to find the volume of a tetrahedron given the length of edges on Wikipedia I found this Interesting, and was looking for a formal proof, but didn't find it anywhere. Could ...
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2answers
89 views

3D Geometry Problem

If we have 4 equal sized spheres with radius $R$ arranged surrounding another smaller sphere such as to make a triangular pyramid from the centers of the $4$ spheres with radius $R$. The radius of ...
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1answer
18 views

When are two 3D Lines parallel in Plücker matrix form?

When are two lines in 3 dimensional space parallel, when the lines are both represented by Plücker matrices $L$ and $L'$. I'm trying to prove the solution to this question: ...
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5answers
14k views

Parametric Equation of a Circle in 3D Space?

So, my dilemma here is... I have an axis. This axis is given to me in the format of the slope of the axis in the x,y and z axes. I need to come up with a parametric equation of a circle. This circle ...
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1answer
27 views

Test if a point is inside a 3D cuboid

I have a cuboid in 3D space, it is not regular at all. I do have the coordinates of its 8 vertices and my problem is how to determine a given point coordinate is inside or outside this cuboid. I ...
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0answers
23 views

Isometries of S^3 and some Lie algebras

By considering $S^3$ as the group of unit quaternions, and letting it act on itself from both the left and right, one can get an isomorphism $SO(4)\cong (S^3\times S^3)/C_2$, where the $C_2$ subgroup ...
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1answer
270 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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1answer
26 views

Torus helix radius change equation

If we draw a closed helix trajectory on the surface of a torus (with helix center axis corresponding to that of torus), the radius will cyclically change between inner and outer radius (r and R). Can ...
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0answers
19 views

Signed angle bewtween two normals

I have two abitrary planes in 3D space which share two vertices. Each plane has a unit normal and boh planes follow the same 'handedness' which describes the 'up' side of the plane. The line between ...
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1answer
16 views

Number of variables and dimension of a function

Why is a function $f(x)$ called a single-variable function if it has coordinates represented by $x$ and $y$? Can it be called a 1D function if its plot is 2D? Subsequently, can two-variable functions ...
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2answers
51 views

The easiest way to find distance between point and a line defined by two points in 3D

Let's assume I have two points with coordinates $(x,y,z)$ and $(x_1,y_1,z_1)$ and there is line between them. I am given a point with coordinates $(x_2,y_2,z_2)$. What's the easiest way to calculate ...
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1answer
350 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
13 views

Intersection of a Plane with the Riemann Sphere

While reading Fundamentals of Complex Analysis by Saff and Snider, I came across an example (see page 47, edition 3) where it is shown that "all lines and circles in the $z$-plane correspond under ...
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1answer
21 views

Why 2 equations of the form F(x,y,z) = 0 for one 3D curve

It says in my analysis 2 book that a curve is given by $F_1(x,y,z) = 0$ and $F_2(x,y,z) = 0$. Why do we need two equations of $x,y,z$ To define a curve in 3D, shouldn't one be enough?
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1answer
23 views

Rotating a plane defined by a normal and a distance from the origin around an arbitrary point in 3D space

I have a plane defined by its normal and its distance from the origin. I have a rotation matrix and a point in 3D space around which to do the rotation. What formula will allow me to do the rotation? ...
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2answers
25 views

Considering a convex polygon lying on a plane in 3D space, how can I know if a point on that plane lies inside or outside that polygon?

I have a plane in space and a polygon in it. I know the position of each vertices making the polygon. I also know the position of the point on the plane. How can I know whether the point is inside or ...
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3answers
260 views

Center of Mass in 3D object?

How would I find the center of mass in a 3D object (a "spinning top" or "dreidel") that consists of a cylinder welded on top of a box welded on top of an upside down cone? Assume building material is ...
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1answer
232 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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2answers
16 views

Make a multivariable function continuous

What can we do with this function, so the function will be continuous in $(0,0)$? $f:\mathbb{R}^2\rightarrow\mathbb{R}:(x,y) \mapsto \frac{x^2+y^2-x^3y^3}{x^2+y^2}$ What I think we should do, is: ...
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3answers
63 views

Showing that a Unit Speed Curve is a Circle.

In my recent differential geometry tutorial, we were given the question: Given the unit speed curve, $$\boldsymbol{r}(s)=\left(\frac{4}{5}\cos(s),1-\sin(s),-\frac{3}{5}\cos(s)\right)$$ show that ...
2
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1answer
322 views

points of intersection on a randomly situated plane and ellipsoid (spherical) in 3d space

if i have an ellipsoid and a plane oriented in any way in a 3 dimensional coordinate system, and they intersect; is there a way to find an equation that describes (or at least approximates) all points ...
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1answer
394 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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0answers
24 views

Equation for Circle in 3D Space Given Center, Radius, and Point

I'm looking for how to derive the equation of a circle, in 3D space, given the following information: The Center Point The Radius One point on the circle I understand that this is functionally the ...
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1answer
25 views

Algorithm for solving line line intersection in 3d

I am trying to find an algorithm that a computer can execute that finds the intersection point between two lines each defined by a point on the line and a direction vector. Does anyone know of one? It ...
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0answers
13 views

For an app teaching about polyhedra, what are some core characteristics to include?

For fun: I'm building a 3d app that teaches about polyhedra. What should I include? The obvious didactic elements for each polyhedron would be: Fundamental polygon's Vertices 
Edges
 Faces
 (and ...
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1answer
47 views

Drawing 3D stomach structure in Matlab [closed]

I would like to plot a 3D structure representing the stomach in Matlab. A sketch of what it should look like is here: http://thoracicsurgery.stanford.edu/patient_care/images/normal-stomach.jpg Still, ...
2
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1answer
56 views

Is it possible to accurately calculate an irregularly shaped frustum's volume?

I have the following water basin Now imagine this basin is filled with water to the top, is there anyway to accurately calculate the volume of water stored in it using only top and bottom areas A1 ...
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3answers
949 views

Making a convex polyhedron with two sheets of paper

Suppose that we have two sheets of paper $S,T$ and that each of $S,T$ is in the shape of a convex quadrilateral. Also, suppose that the length of the perimeter of $S$ equals that of $T$. (Note that ...
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2answers
91 views

Is it possible to find the coordinates of a point in 3D space, given its distance from a known point?

Is it possible to find the coordinates $(x,y,z)$ of a point in $3d$ space when given: A) the unknown point is $(x,y,z)$. B) the known point is $(a,b,c)$. C) the distance between the two points is ...
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1answer
35 views

Counting points in/on cuboid

Given a cuboid that extend in x,y,z axis such that |x|≤N, |y|≤N, |z|≤N where N is given and can have value up to 10^9.Now a shooter is standing at origin (0,0,0).He need to shoot on any of the ...
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2answers
25 views

Rotate and translate a line so that it passes through two given points

I have 2 point and a line segment in 2d space. The line only rotates and translates using its mid point. How do I calculate the translation and rotation required for the line to be touching the 2 ...
13
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8answers
19k views

Calculate Rotation Matrix to align Vector A to Vector B in 3d?

I have one triangle in 3d space that I am tracking in a simulation. Between time steps I have the the previous normal of the triangle and the current normal of the triangle along with both the current ...
2
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1answer
27 views

Surface of 3D Triangle

The coordinates $A(-1,0,2), B(2,-1,3)$ and $C(4,0,1)$ are the corners in the triangle $ABC$. a) Find the length of the sides in the triangle. b) Find the area of the triangle. Now I'm able to ...
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0answers
25 views

Get Vector From Angle In $3D$ Space

I have a camera angle in $x,y,z$ with values between $0$ and $360$, I'm trying to compute this into an 'aim vector' which would have values between $0,0,0$ and $1,1,1$ depending on what the angles ...
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0answers
31 views

Is it possible to create a volumetric object which has a circle, a square and an equilateral triangle as orthogonal profiles?

This question was posed to me by a friend (formulated as creating a peg to fit perfectly into holes of these shapes), and after an experiment in OpenSCAD it seems it is not possible - either one ...