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
6 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 ...
0
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1answer
21 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 ...
0
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1answer
19 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
26 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
23 views

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 ...
0
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1answer
23 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
27 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
34 views

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 ...
0
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1answer
17 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
22 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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0answers
24 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 ...
2
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0answers
56 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 ...
0
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0answers
26 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 ...
0
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1answer
37 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 ...
0
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1answer
11 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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1answer
31 views

Can anyone please explain how they simplified with intermediate steps? [closed]

Please, explain how they arrived to that equation with intermediate steps
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0answers
17 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
25 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 ...
1
vote
1answer
42 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
35 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
22 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
53 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
39 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
21 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
32 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
33 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
15 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
16 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 ...
0
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0answers
22 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
16 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
90 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 within a window that is the intersection of the sphere with a cone whose base is an ellipse? Following are more ...
1
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1answer
21 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 ...
0
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0answers
31 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
16 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. ...
3
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2answers
31 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?
0
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1answer
47 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 ...
2
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1answer
25 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 ...
0
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0answers
25 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 ...
0
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1answer
34 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
25 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
25 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: ...
0
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1answer
37 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 ...
0
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1answer
17 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
17 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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2answers
69 views

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

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 ...
0
votes
1answer
25 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
32 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
299 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 ...