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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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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0answers
27 views

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
67 views

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
46 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
59 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
16 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
25 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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0answers
21 views

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?
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0answers
37 views

3D extension of Euclidean algorithm jigsaw method - help!

Recently I've been learning about how the Euclidean algorithm = jigsaw method (filling a rectangle with squares) = forming continued fractions. And today I'm wondering how a 3D version of the jigsaw ...
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1answer
87 views

Assuming an assembly robot arm with various rotation axes, how to find the angles it needs to take to get at (or closest to) a given point?

For each rotation axis, I know its current angle and its angle range (its minimum angle and its maximum angle). Assuming I want a point on its "hand" to be at a given coordinate or as close as ...
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0answers
37 views

$3D$ surfaces multivariable Calculus

A surface is constructed as follows: First a curve $(0, y, −((y − 1)^2)((y + 1)^2))$ is drawn in the yz–plane. Then a parabola $(u, u^2)$ is drawn in the uv–plane. Finally, in each plane y = b, a copy ...
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0answers
27 views

Help me understand chained rotations

Ok, so for my thesis I am trying to do some stuff with ellipsoids in 3-dimensional space. I am trying to rotate an ellipsoid to face a certain direction using Tait-Bryan chained rotations. That is, ...
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0answers
105 views

Helix around helix parametric equation?

I know the parametric equation for a 3d helix is: x = R cos t y = R sin t z = h t can somebody explain to me this parametric equation (image and equation from Wolfram) for a "Helix around helix" / ...
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1answer
61 views

3D plane rotation about a line

In three dimensional space we have a plane and a line. These can be oriented in any way. The plane is rotated about the line by n degrees, meaning that originally the position of the plane is fixed to ...
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2answers
31 views

Collinear points in Space

I need help understanding how to do this question. Are (1,4,2) (4,-3,-5) (-5,-10,-8) points on the same line? Show why and how you know.
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1answer
36 views

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
47 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
18 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
40 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
26 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
202 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
22 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
57 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
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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
35 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
62 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
45 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
30 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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1answer
45 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
26 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
38 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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1answer
57 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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1answer
21 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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0answers
23 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
22 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
32 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
42 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
942 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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2answers
21 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
85 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 ...
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0answers
99 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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2answers
95 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
42 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
16 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
79 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
77 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 ...
0
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1answer
37 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
58 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 ...
2
votes
1answer
32 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
48 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 ...