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
1k views

How can I determine the radius of a dodecahedron?

I am making a dodecahedron that needs to fit inside of a sphere. The sphere has a diameter of 56mm. What is largest possible measurement of one segment of a pentagon side of a dodecahedron that would ...
3
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2answers
8k views

Line and plane intersection in 3D

How would one calculate the intersection of a line and a plane in 3D ? Given for example are 4 points which form a plane (x1,y1,z1)...(x4,y4,z4) and 2 different ...
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1answer
480 views

Equation to a Perpendicular Line Along A Plane

I have the following problem, which Google has not yet been able to answer. I have the equations to two lines in 3D space. I also have the co-ordinates of a single point on each line. I can therefore ...
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1answer
494 views

3D correlation visualization?

Incomer per person (x axis) correlates with life expectancy (y axis). These two indicators change over time (z axis). x correlates with y. Moreover, x and y both correlate with z. The question is: ...
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3answers
5k views

Vector Rotation in 3D

Given: Two points: ($x_1$, $y_1$, $z_1$), ($x_2$, $y_2$, $z_2$) A vector that is parallel to the $x$-axis and points to ascending numbers (intuitively stated, the vector points 'East'). I am ...
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1answer
73 views

Geometry: problem with defining the vertices of a tunnel around a given path

I'm trying to create some kind of demo that rushes through a tunnel. I have made a random path generator that creates smooth looking paths in 3D space (just some 3D points) Now I would like to ...
2
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1answer
220 views

How to determine the intersection of 6 planes?

ABCD is a tetrahedron (not necessarly a regular one). A Monge's plane is a plane which is perpendicular to an edge and goes through the middle of the opposite edge. I want to prove that the 6 ...
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1answer
816 views

Explicit function of a cylinder

Can I transform an implicit function of a cylinder to explicit form? Lets say we have a cylinder $$x^2 + y^2 - 1 = 0$$ and we want to have it expressed as function $f(x,y,z)$.
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4answers
4k views

Can the Surface Area of a Sphere be found without using Integration?

When we were in school they told us that the Surface Area of a sphere = $4\pi r^2$ Now, when I try to derive it using only high school level mathematics, I am unable to do so. Please help.
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5answers
18k 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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3answers
1k views

How to show two points in $\mathbb{R}^3$ form a plane and determine equation?

Given two arbitrary equidistant points in $\mathbb{R}^3$, ($p$ and $q$), how would one show that they form a plane and what would the equation of that plane be? Defining two vectors in ...
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0answers
741 views

Is there a formula for the solid angle at each vertex of tetrahedron?

A tetrahedron has four vertices as much as a triangle has three vertices. A tetrahedron therefore can have four solid angles as much as a triangle can have three angles. I am wondering: Is there a ...
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2answers
1k views

Overlap volume of three spheres

Given three spheres and their coordinates with equal radii that are known to have a triple overlap (a volume contained within all three spheres), is there a known closed form for the calculation of ...
8
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2answers
565 views

Coloring a sphere with minimum colors (with constraints)

This is a problem we've been considering in our undergraduate math club, and I thought it would be nice to get further thoughts on the subject. I will start with a two dimensional case and then ...
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2answers
237 views

If a rectangular grid, where left<->right and top<->bottom wrap, can be mapped onto the surface of a torus, what does a cube map to?

If you roll a sheet of paper so left and right touch, then bend the cylinder so its ends also touch, you can see the surface of a 2D rectangle maps onto the surface of a 3D torus, a doughnut. I was ...
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2answers
1k views

Calculate surface normal of each equilateral triangle in a tetrahedron

How can I calculate the surface normal of each equilateral triangle that makes up a tetrahedron? These are the xyz coordinates of the tetrahedron (+1, +1, +1) (−1, −1, +1) (−1, +1, −1) (+1, −1, −1)
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2answers
966 views

3 Rotations to unit vector (3D)

I've been trying to solve this problem for some time now, but I could really need some help: I have 3 rotations (one per axis) for an object, and want to create a unit vector telling me in which ...
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1answer
150 views

Decomposing a quarternion into unit axes rotations

I'm using unit quaternions to represent rotations. Given rotation angles X, Y and Z, I can construct 3 quaternions that rotate around each unit axis. Qx = ( sin(X/2), cos(X/2), 0, 0 ) Qy = ( ...
10
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1answer
262 views

What is $f(x, y) = |x| - |y|$ called?

$f(x,y)=x^2-y^2$ is your friendly neighbourhood hyperbolic paraboloid. $f(x, y) = |x| - |y|$ naturally has similar appearance. Do shapes of the latter form have a name?
3
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1answer
179 views

Supposedly “trivial” implication that injective surfaces are incompressible

My question is about a passage in Algorithmic Topology and Classification of 3-Manifolds by Sergei Matveev. Let $F$ be a surface in some $3$-manifold $M$. $F$ is called incompressible if for every ...
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2answers
953 views

Tranforming 2D outline into 3D plane

I am writing a program where I would like to allow the user to draw 4 connecting lines, such as: And convert this shape into a 3D plane. Is this possible? Is there an existing algorithm to do so? ...
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2answers
1k views

Averaging quaternions

Given multiple quaternions representing orientations, and I want to average them. Each one has a different weight, and they all sum up to one. How can I get the average of them? Simple multiplication ...
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2answers
1k views

How to calculate volume of 3d convex hull?

Convex hull is defined by a set of planes (point on plane, plane normal). I also know the plane intersections points which form polygons on each face. How to calculate volume of convex hull?
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4answers
2k views

Find whether two triangles intersect or not in 3D

Given 2 set of points ((x1,y1,z1),(x2,y2,z2),(x3,y3,z3)) and ((p1,q1,r1),(p2,q2,r2),(p3,q3,r3)) each forming a triangle in 3D space. How will you find out whether these triangles intersect or not? ...
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2answers
417 views

How to divide a $3$ D-sphere in “equivalent” parts?

My goal is to put $n$ points on a sphere in $\mathbb{R}^3$ to divide it in $n$ parts, so that their disposition would be as "equivalent" as possible. I don't exactly know what "equivalent" ...
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1answer
636 views

Find point in 3D space based on start point, three angles and a distance

I have a start point, {x,y,z} a distance, d and three angles, rotation about the x axis, rotation about the y axis and rotation about the z axis. Each angle is clockwise. How do I calculate the point ...
2
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1answer
273 views

general (asymmetric) real rank-2 tensor visualization in 3d

I have general rank-2 real tensor in 3d space represented as a 3x3 real matrix $M$ (it is gradient of a vector field). I am writing some code to visualize it in several isolated points, this is what I ...
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0answers
462 views

What is an isosurface?

I am trying to understand the marching cubes algorithm. I would like very much an easier definition of an isosurface than what is available online. Could anyone please explain it? Thanks.
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1answer
270 views

Are these sufficient conditions to define an elliptical cone?

I was successful in deriving the equation for an elliptical double-napped cone in rectangular coordinates. All I did was define a line with slope $a$ on the xy-plane, and another line of slope $b$ on ...
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1answer
530 views

3 line / 3 plane intersection

I am confused on a very simple thing, so I need your clarifications. Here is my doubt: I want to find the intersection point of three straight lines. Alternatively, I can find it by using three ...
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1answer
301 views

Identifying 3D shape from matrices analytically

I have a set of matrices (a 3D matrix, that represents a quantized body), for instance: (the size 5x5 here is just an example, the real size is a lot higher) $ M_1 = \left[ {\begin{array}{cc} 0 ...
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1answer
52 views

Linear transformations and primitive search in 3D

This question is about differentiation in $\mathbb{R}^3$. Let $V : \mathbb{R}^3 \to \mathbb{R}$ be a smooth enough function, $f:\mathbb{R}^3\to\mathbb{R}^3$ its gradient, and $M$ a $3\times 3$ real ...
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1answer
193 views

Projection of 5 skew lines

Given five skew lines, is it possible to find a point $P$ and a plane $\pi$ such that the projections of the five lines from $P$ onto $\pi$ intersect in the same point $Q$? [editet: rewritten clearly, ...
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3answers
1k views

How do I map a 3D triangle into 2D?

The problem I'm having is mapping a 3D triangle into 2 dimensions. I have three points in x,y,z form, and want to map them onto the plane described by the normal of the triangle, such that I end up ...
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1answer
759 views

Find out the border of a planar figure for given a set of points – 2D case

Original post is edited after getting some suggestions; I am looking for a fast algorithm which is able to detect outer most boundary of a plane for given set of points. Suppose, I have 3D point ...
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1answer
151 views

Reconstructing a ring from a stack of 2D images (radially aligned)

I have a stack of images (about 180 of them) and there are 2 black dots on every single image. Hence, the position(x,y) of the two stars are provided initially. The dimensions of all these images are ...
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1answer
65 views

Find the form of $f(x,y)$ knowing the form of contour lines in the $XZ$ and $YZ$ planes

I am trying to find the form of $z=f(x,y)$. I know that: Contour lines in the $XZ$ plane are of the form: $$z=A*ln(x)+B$$ (the $A$ and $B$ parameters vary with $y$) Contour lines in the $YZ$ plane ...
3
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1answer
693 views

Plane intersecting line segment

I have a plane which is represented as a 3d point $\vec{p}$ with a normal $\hat{n}$. I also have a line segment specified by two points $\vec{v_1},\vec{v_2}$ . I want to get the intersection point (if ...
0
votes
1answer
145 views

Creating random triangles with points on the radius of a sphere and passing through center

I'm trying to create a pointy "ball" in 3d space using triangles. I want each triangle to pass through a sphere's center, with each point lying on the surface. I can easily make points on the ...
0
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3answers
668 views

Formula for gallons in a trough

I have a trough which is a circular container. How do I determine how many gallons of water it takes to fill up the trough? I was thinking that we measure the height and the width but I think it's a ...
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4answers
339 views

Term for Tetrahedron with Three Right Angles at a Point

Is there a name for the tetrahedron/pyramid (four vertices, four triangular faces, six edges) where three edges meet orthogonally at a point? Three of the faces are right triangles. Another ...
2
votes
1answer
371 views

Finding the radius of the largest sphere possible between a corner and another sphere

In a 3 dimensional Cartesian plane there is a sphere A that is in the first octant and is tangent to all coordinate planes. Now, imagine we want to find the another sphere B also tangent to all ...
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1answer
572 views

Coordinates of point on a line defined by two other points with a known distance from one of them

I have two points in 3D space; let's call them $A=(a_x, a_y, a_z)$ and $B=(b_x, b_y, b_z).$ Now, I need to place a third point, let's call it $C=(c_x, c_y, c_z)$, which lies on the line between $A$ ...
2
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1answer
265 views

Projecting a 3D vector to a screen, with the size $X\times Y$?

I am currently programming something, and I'm stuck on how to take a 3D vector, then project it on a screen. Say $X_s$ = the screen width and $Y_s$ = the screen height, Pa = pitch and $Y_a$ = yaw, ...
2
votes
1answer
500 views

quaternion representation of the rotation of a sphere into plane displacement

I do have a sphere of known radius which does have a coordinate frame rigidly attached to it. Let's call the coordinate frame attached to the sphere XYZs. The sphere can be rotated and displaced ...
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vote
1answer
224 views

Keeping camera and focal point relative after translation

I'm creating a program that has a 3D view. The 3D world uses three vectors (X,Y,Z). Now, the way the camera works is by having two points, the focal point and the camera. The camera is set to look ...
5
votes
3answers
842 views

Largest Triangle with Vertices in the Unit Cube

How would one find a triangle, with vertices in or on the unit cube, such that the length of the smallest side is maximized? And what is that length? A lower bound for the length is $\sqrt{2}$, by ...
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4answers
7k views

Calculate distance in 3D space

Imagine I want to determine the distance between points 0,0,0 and 1,2,3. How is this calculated?
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1answer
1k views

Subtract gravity from 3D object in different orientations

I'm currently working on a project that involves calculating a sensor module's distance and orientation. The problem I'm running into is the fact that once the sensor is, for example, rotated around ...
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8answers
33k views

Recommended (free) software to plot points in 3d

I am looking for (preferably free) software to: 1) plot 3d points read from a file. A scatter plot would be fine. 2) Optionally color the points by a property - also read from the file It would be ...